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- Oct 12:
- Insurers sharpen criticism of health-care bill
- Colorado already has public option for health care
- Oct 11:
- Wait for benefits is 3 years if health care passes
- Oct 10:
- Heavy infant in Grand Junction denied health insurance
- Medical tort reform could save $41 billion, congressional budget analysts say
- Even if health bill is posted online, most will find it hard to decipher
- Oct 4:
- Proposal to tax "Cadillac" health plans hits political potholes
- Sep 27:
- Obama tells Black Caucus "we cannot wait" longer
- Mayo Clinic as model for reform questioned
- Sep 25:
- Let's be reasonable
- Sep 24:
- The morality of health care
- Sep 23:
- Staying the course on health care reform
- Sep 20:
- Tending to the health care garden
We all remember how it ended. The ship, built to be magnificent and unsinkable, started to sink; the crew and passengers swarmed onto the deck trying to find safety. The band famously saluted each other and began to play their last beautiful serenade, and those remaining, prepared to die.
In James Cameron's film, Titanic, Denver's own Unsinkable Molly Brown, played by Kathy Bates, is hard not to like. Exuberant and sassy, she takes charge in the crisis, helping fill lifeboats; her practical sensibilities crucial amidst the panic and chaos.
Yet, there is the scene when Molly, realizing that the lifeboats are half empty, reaches for the flailing survivors, and is shouted down by those in her boat who fear capsizing. Looking utterly defeated, she sits down and realizes that she is among the selfish, lucky few.
The Titanic had twenty lifeboats when it set out on its maiden and last voyage - enough seats for 52% of the people on the ship. It was a political, financial decision to send the ship out this way; a calculated risk. This boat can't sink, remember?
The total capacity of the lifeboats was 1178. Only 705 people survived the Titanic. There were 473 seats on the lifeboats that were left unfilled. Four hundred and seventy-three lives that could have been saved but weren't because people were scared to share their life rafts, scared to reach into the icy waters and pull survivors to safety, and scared they might have to sacrifice something for others.
Naturally, this reminds me of the current national health care debate. Once again we are witnessing an enormous, unwieldy ship trying not to sink and once again we are throwing each other into the depths; afraid our own safety will be unsettled by the changes. Why?
We have all heard the stories of people dropped from their insurance companies after they file a claim. Too high deductibles making the insurance worthless for anything less than a catastrophic illness and tales of bankruptcy and heartbreaking decisions.
How many times do we have to hear the stories of treatment denied by insurance bureaucrats, of doctors unable to order necessary treatments, and the outrageous and absurd cost for every tiny thing?
You don't need to be a creative genius to imagine the tragedies unfolding around you every day - you just have to pay attention.
I don't have health insurance. I would have to pay several hundred dollars a month to have a basic, high deductible plan with co-pays and percentages for the blood tests I need to have done twice a year for my thyroid. I would end up spending a small fortune annually in insurance costs to "save" myself a pittance in office visits. For me, insurance is only a benefit if something catastrophic happens - like I hit an internal iceberg.
So let's imagine that. I pay $300 a month minimum for health insurance and then I have a heart attack from the stress caused by years without adequate health care - I am unable to work while I am undergoing my treatment. How will I pay for my monthly insurance premium if I am too sick to leave my house? How will I pay my rent, for that matter? How will I pay my 20 percent share of the hospital bills, my $1000 deductible or my co-pays?
Wait, I remember. I will beg for help from the financial services people at the hospital. I will beg for leniency from my creditors. I will beg from my working class friends and family. And I will worry, day and night that I will not be able to find my way through the complicated system of fine print, maximum payouts and pre-existing conditions ripe for disqualification.
The tragedy of the Titanic was one of hubris and greed. Short term financial payoffs trumped compassionate sensibility and everyone came away damaged, not just the poor souls who died that night. I can't imagine how the survivors could live their lives knowing that those empty seats on their life rafts could have been filled. They could have reached out to those treading water; they could have tried.
For the millions of us treading water, which grows continually colder and deeper, I offer a simple warning: We know how this could end. The unsinkable will be sunk and everyone will die knowing more could have - and should have-been done to save it. And for those of you sitting snug in your life raft, remember - the sea is filled with icebergs. Pray you don't hit one.
Tana Lucero is a recent graduate of Emporia State University with a master's degree in library science and an intern at Denver Public Library. She lives in Denver. EDITOR'S NOTE: This is an online-only column and has not been edited.


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Japan Academy Boss Hits Back at Takeshi Kitano's Awards Criticism
Yusuke Okada claims his prize ceremony is the cleanest in Japan.
Yusuke Okada claims his prize ceremony is the cleanest in Japan.
TOKYO — Joshua and Benny Safdie's gritty New York drug scene drama "Heaven Knows What" was awarded the Tokyo Grand Prix on Friday at the closing ceremony of the Tokyo International Film…
Iconic comedian-actor-director receives inaugural 'Samurai Award' at Tokyo Festival.
Celebrity Kiran Rao calls for structural change in Indian film as she lends weight to the release of "Ship of Theseus"
PARIS — Hengameh Panahi's Paris-based Celluloid Dreams, one of Europe's most respected sales companies, and Brussels' uMedia, a burgeoning Euro mini-studio, have tied the knot on an alliance that…
The body count holds steady but the bloodshed is considerably easier to take in "Outrage Beyond," the controlled if excessively labyrinthine sequel to Takeshi Kitano's "Outrage."
What, it's fair to ask, is a Welsh-born director doing in Jakarta making martial arts movies?
From "Heidi" and "Harold and Maude" to Takeshi Kitano's "Kikujiro," there's been no shortage of odd couplings of the very young and very old.
Mapfre Foundation teams with San Sebastian on Contemporary Mexican Film showcase
Takeshi Kitano doesn't try to do much new, but the results are so visually stunning, why quibble?
Hideo Higashikokubaru, governor of Miyazaki Prefecture and a former comedian, told reporters Monday that his recent TV appearances were worth ¥15.5 billion ($137.5 million) to the prefecture in free…

subset: commoncrawl


text:
The BenQ MX501 Multimedia Projector is a comprehensive projector, flexible enough for most applications. It offers plenty of control, letting you easily navigate menu screens to change settings. To ensure you'll have smooth presentations and adaptability, the MX501 Multimedia Projector has integrated various display functions and multiple inputs. It's highlighted by XGA resolution, a brightness of 2700 ANSI lumens and a 4000:1 contrast ratio. Considering the MX501 has features that ensure high-quality picture performance in several conditions, it's hard to think of an application that would be out of its range.
The MX501 is also prepared for presentations and entertainment that require 3D technology. With 3D capabilities, it can project images in lifelike 3D and make your entertainment more exciting and your presentations more interactive. All you have to do is add the 3D glasses, content and video card along with the MX501.
BenQ has integrated several inputs, control terminals and audio jacks with the MX501. You can use the USB, S-video and component video inputs to satisfy all different scenarios. Network connection is achievable through the RS-232 terminal. The dual PC inputs give you the power to connect multiple computers to one projector, which is a plus for presentations. The more options you have, the more you'll get out of each presentation. The audio jacks facilitate mic input and audio output to an external source. There is also a 2W stereo speaker built into the projector which is loud enough for most presentations.
The projector integrates high-performance optical engine projection and a user-friendly design to deliver high reliability and ease of use.
- Long Lamp Life
- Enjoy a lamp life performance of up to 6000 hours - twice the lamp life expectancy of average projector lamps on the market. This certainly lowers the number of lamp changes and keeps all maintenance to a minimum
- Reliable Picture Quality with True-to-Life Color Performance
- BenQ projectors that use DLP technology are virtually immune to color decay - the yellow/green tint that some projector images develop over extended periods of usage. This is one technological advantage that you'll get to enjoy - year after year
- Filter-Free Design
- BenQ DLP projectors feature a filter-free design which could reduce the need for filter cleaning and filter replacement. This reduces the labor as well as the budget for filter maintenance and replacement
- 2700 ANSI Lumens
- A 2700 ANSI lumens projection lamp ensures great viewing even in a location with low ambient light. The MX501 is ideal for a small-sized meeting room with under 25 people
- Sharpen Up with High Contrast Ratios
- The MX501 boasts a high contrast ratio with 4000:1. High contract ratios translate to razor-sharp detail definition and a broader range of subtle color differences, which makes text sharper, cleaner, and easier to read
- Go 3D with DLP Link
- MX501 is equipped with 3D projection technology to bring you the same amazing 3D effects you get in 3D movies. Offered for no added cost, the 3D feature on 3D-ready BenQ projectors gives your audience an immersive real-life experience. All you have to do is add the 3D glasses, content and video card along with the MX501
- Keystone Adjustment
- With up to ±40° keystone adjustment, a perfect square is all you'll see. So go ahead and say goodbye to misshaped images, graphics, and charts
- Built-In Speaker
- With a built-in 2W speaker for the MX501, not only do you get the vivid visual performance, you get the same audio satisfaction, too


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22 year old woman | Lynnwood, WA, USA | Seeking men 22-30 within 50 miles of Monroe, WA
Active within 24 hours
Live simply, Love generously, Care deeply, Speak kindly.
Let's see where to start….Well, I am a very outgoing person and I try to enjoy life to the fullest! I am very honest and I tend to speak my opinions. I can be stubborn but who can't, Right? I am one that sets goals high and is driven to complete the tasks that have been placed in front of me. I would say that I can also be a very kindhearted person that truly wants to help those in need. I believe that is why I have chosen to become an Emergency Medical Technician. I love the outdoors, camping, hiking, kayaking, fishing and I am always up for trying something I haven't done before. I would love to go white water rafting, scuba diving and much more! Maybe even skydiving one of these days but I still haven't decided whether or not I could actually make myself do it! I love adventures and would like to find someone who enjoys that to. I am a very family oriented person and I would like to find someone who is that way to. I love to laugh and have fun but I also enjoy being able to sit and have good quality conversations. I'm looking for someone that will enjoy the same things I do and right now I'm looking for friendship but if it turns into something more that's just a bonus! If you want to know more about me shoot me an email!
Camping , Coffee and conversation , Cooking , Fishing/Hunting , Gardening/Landscaping , Hobbies and crafts , Movies/Videos , Music and concerts , Exploring new areas , Travel/Sightseeing
Cycling, Other types of exercise, Walking / Hiking, Yoga
I exercise 3-4 times per week.
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Everett Community College, Everett, WA
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text:
Telling the Truth about History
W. W. Norton & Company, Feb 14, 2011 - History - 336 pages
"A fascinating historiographical essay. . . . An unusually lucid and inclusive explication of what it ultimately at stake in the culture wars over the nature, goals, and efficacy of history as a discipline."—Booklist
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Review: Telling the Truth About HistoryUser Review - Dan Gorman - Goodreads
Not the most exciting book ever, but the prose is very clear, and the authors give a good overview of the various stages of evolution in historical research. They're writing just as postmodernism ... Read full review
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Review: Telling the Truth About HistoryUser Review - Joel Zartman - Goodreads
Adequate if uninspiring, ending somewhat tediously. One wishes historians to have a bit more humane learning. Read full review
Selected pages
Scientific History and the Idea of Modernity
History Makes a Nation
Absolutisms Dethroned
Competing Histories of America
Discovering the Clay Feet of Science
Postmodernism and the Crisis of Modernity
A New Republic of Learning
Truth and Objectivity
The Future of History
Common terms and phrases
absolute American Annales school argued became believed Christian Cold War colonial contemporary critics cultural cultural war Darwin democracy democratic Derrida Descartes discipline discourse E. P. Thompson economic eighteenth century ence Enlightenment Europe experience explained Foucault French Revolution Hegel hermeneutics heroic model heroic science historians history of science human ical idea identity ideology imagination individual industrial inquiry insisted intellectual interpretation Jefferson knowledge language laws liberal linguistic lives Marx Marxism meaning ment meta-narratives methods Michel Foucault model of science modern moral narrative national history nature Newton Newtonian nineteenth century objectivity past perspective philosophical political Popper postmodernism postmodernist practice progress Protestant Puritans questions realism reality reform relativism religious scholars scientific model scientists secular sense seventeenth century skepticism social history society story struggle theory tion tory tradition truth truth-seeking understanding United universal values Western white Americans women words writing


text:
CCISD officials to have tax rate hearing Aug. 20
CCISD trustees have marked Aug. 20 as the date of the district's public budget and tax rate hearing.
Trustees have discussed the 2007-2008 budget several times this year, but are expected to have a budget workshop on Aug. 2 to discuss the district's $265,000 budget. Among Superintendent Scott Elliff's priorities for funding in the 2007-2008 school year are employee salary increases, a curriculum management plan, major maintenance and technology needs.
The district also will have to consider adopting a new tax rate. Legislation passed in 2006 required districts across the state to lower their maintenance and operation portion of the tax rate by 17 cents last year and by an additional 33 cents for the 2007-2008 school year.
Trustees must adopt a budget by Aug. 31.
Contact Adriana Garza or 886-3618 at firstname.lastname@example.com
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Need Help? Call us at 1-800-566-8098.
Monday-Friday: 6am-3pm / Saturday: 7am-11am / Sunday: 7am-11am


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We offer discount to nonprofits, government agencies, and federal contractors
In just the last two weeks, congressional calls to #EndFamilyDetention have turned the tide of momentum significantly.
AILA Doc No. 12083060 | Dated August 30, 2012
The nonimmigrant visa (NIV) section at the U.S. Consulate in Ciudad Juarez (CDJ) has indicated to AILA liaison that it will annotate TN visas with the anticipated length of stay indicated in the employer's support letter. The consulate suggests that TN applicants have the employer's letter ready for presentation to CBP at the port of entry to facilitate admission for the proper period of time.
Cite as AILA Doc. No. 12083060.
American Immigration Lawyers Association
1331 G Street NW, Suite 300
Washington, DC 20005
Copyright © 1993-2015
American Immigration Lawyers Association.


text:
Originally written on Celtics Life | Last updated 1/11/13
The Kevin Garnett - Carmelo Anthony feud was already headline news, but now KG's trash-talking exploits have come before the judgement of the ultimate media power: Stephen Colbert. Colbert gives a "Tip of the Hat" to KG for (reportedly) telling Melo that his wife tastes like Honey Nut Cheerios. He goes on to advocate more product placement be incorporated into players' trash talk. Nice to see Stephen respecting the C's. The Colbert ReportMon - Thurs 11:30pm / 10:30c Tip/Wag - HAPIfork & Kevin Garnett www.colbertnation.com Colbert Report Full EpisodesPolitical Humor & Satire BlogVideo Archive What do you think? Did Colbert nail it or what? Follow Jacob @TheReelJZ
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A method and apparatus for generating views of an environment with proper perspective and parallax. This invention captures panoramic views at many points in the environment, preferably by using fisheye lenses with subhemispherical fields of views to yield overlapping fisheye images that are seemed together, and stores them as planar polygons, which have been extended to include imagery occluded at their viewing position but visible at nearby points. Three-dimensional information on the environmental source of these polygons is determined and stored, enabling the playback system to simulate parallax as well as to produce stereographic images. Given a location and orientation in the environment, the playback system finds a nearby capture point and translates the polygons at that point to the specified location, producing an image. It then rotates that image to the desired orientation which it then displays.
1. A method for simulating movement within a multidimensional CG or natural environment by displaying an image at a specified viewpoint and orientation within said environment, where said viewpoint and orientation specify the location and direction of a point of view, the method comprising the steps of:
(A) forming a database of the environment in a computer-readable storage medium by:
i) determining a set of k-points in the environment, each k-point within said set having a domain within the environment and playback data associated therewith, said k-point domain forming a range of supported viewpoints and orientations, each of said k-points being defined as a center of projection;
ii) projecting the environment onto a planar surface at a predetermined orientation to form a corresponding k-projection, the step of projecting the environment including:
a) capturing a fisheye image with a camera having a subhemispherical fisheye lens;
b) mapping said fisheye image to a sphere to form a mapped fisheye image; and
c) projecting said mapped fisheye image onto a planar surface at a predetermined orientation to form a corresponding k-projection; and
iii) segmenting said corresponding k-projection into one or more k-polygons;
iv) for each said k-polygon, determining an e-polygon, said e-polygon being a planar polygon that approximates an area in the environment, said k-polygon being a projection of said area;
(B) finding the k-point in the database whose domain supports the specified viewpoint and orientation;
(C) mapping the k-projections at said k-point to said viewpoint and orientation to form said image; and
(D) displaying said image.
2. The method of claim 1, wherein the step of capturing a fisheye image includes the step of capturing a second and a third subhemispherical image, mapping said second and third images to a sphere, and seaming said second and third image with said fisheye image on said sphere to form a panoramic image.
3. The method of claim 1, further including manually determining k-polygons known to be projections of approximately planar areas in the environment, segmenting the k-projections into the determined k-polygons.
4. The method of claim 1, the e-polygons being based on a three-dimensional polygon-based model, wherein the segmentation step further includes:
a) associating an e-polygon with a model polygon;
b) consolidating the e-polygons when the resulting parallax error is lower than a predetermined limit;
c) continuing said consolidation step at least until the number of consolidated e-polygons is reduced to a predetermined limit; and
d) projecting the e-polygons onto a planar surface to form the corresponding k-polygons.
5. The method of claim 1, further including registering a k-polygon at one or more nearby k-points to determine the corresponding e-polygon.
6. The method of claim 1, wherein the k-polygons of a k-point are extended to support the domain of said k-point by:
a) determining an occluded area in the environment that is visible at a viewpoint in said domain but occluded at said k-point;
b) finding a nearby k-point containing said occluded area; and
c) mapping said occluded area from said nearby k-point to said k-point.
7. The method of claim 1, wherein the mapping step further includes translating the k-polygons of a k-projection to the specified viewpoint.
8. The method of claim 1, wherein the mapping step further includes rotating the orientations of said k-polygons or k-projections to the specified orientation.
9. The method of claim 1, wherein the mapping step further includes translating the k-polygons to the specified viewpoint and rotating the orientations of said k-polygons or k-projections to the specified orientation.
10. The method of claim 9, further including consolidating the e-polygons and their corresponding k-polygons.
11. The method of claim 9, further including translating a second time to produce stereographic images.
12. The method of claim 1, further including compressing said k-polygons or said k-projections.
13. The method of claim 1, further including identifying the list-priority order of the k-polygons in said database.
14. The method of claim 1, wherein mapping further includes using nearby k-images to compensate for occlusion.
15. The method of claim 1, wherein the environment is projected to a non-planar surface, such as that of a cylinder.
16. The method of claim 1, wherein the segmentation is into curved areas.
17. The method of claim 1, wherein all information is determined from a CG model.
18. The method of claim 1, wherein the step of projecting the environment includes capturing said k-projection with a planar camera.
19. The method of claim 1, wherein the step of projecting the environment includes:
a) capturing a planar projection with a planar camera; and
b) rotating said planar projection to a predetermined orientation to form a corresponding k-projection.
20. A method for simulating movement within a multidimensional CG or natural environment by displaying an image at a specified viewpoint and orientation within said environment, where said viewpoint and orientation specify the location and direction of a point of view, the method comprising the steps of:
(A) forming a database of the environment in a computer-readable storage medium by:
i) determining a set of k-points in the environment, each k-point within said set having a domain within the environment and playback data associated therewith, said k-point domain forming a range of supported viewpoints and orientations, each of said k-points being defined as a center of projection;
ii) projecting the environment onto a planar surface at a predetermined orientation to form a corresponding k-projection, the step of projecting the environment including:
a) capturing a fisheye image with a camera having a non-hemispherical fisheye lens;
b) mapping said fisheye image to a sphere to form a mapped fisheye image; and
c) projecting said mapped fisheye image onto a planar surface at a predetermined orientation to form a corresponding k-projection; and
iii) segmenting said corresponding k-projection into one or more k-polygons;
iv) for each said k-polygon, determining an e-polygon, said e-polygon being a planar polygon that approximates an area in the environment, said k-polygon being a projection of said area;
(B) finding the k-point in the database whose domain supports the specified viewpoint and orientation;
(C) mapping the k-projections at said k-point to said viewpoint and orientation to form said image; and
(D) displaying said image.
This application is a continuation-in-part of U.S. application Ser. No. 08/552,299 which was filed Nov. 2, 1995, now U.S. Pat. No. 5,694,531.
A. Field of the Invention
This invention relates generally to digital image processing and computer graphics. More particularly, it is concerned with generating full-sphere panorama views using subhemispherical images and simulating free movement within a multidimensional environment, which can be either computer-generated or real.
B. Description of the Related Art
Computer-generated (CG) environments are typically created by representing objects with polygons and associated computer-generated or photographic surfaces, or texture maps. Rendering, the construction of an image from a CG model, can be done from any point of view. See Foley [J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics: principles and practice, 2nd ed., Addison-Wesley, 1987]. As such, it provides unrestricted simulated movement within the environment. However, the temporal resolution of unrestricted movement within a realistic CG environment that one can achieve on today's personal computers is severely limited by the computational requirements and by the labor of constructing realistic imagery.
U.S. Pat. No. 4,807,158 to Blanton, et. al discloses a method for reducing the computational requirements of rendering CG images, which could also be applied to natural images. First they build a database of images at selected positions, or "keypoints", within the environment by rendering them in an off-line process. They store these panoramic images as conic projections. Then in real time, the application approximates the image at any position from that at the nearest keypoint. This approach works well when all objects are about the same distance from the viewer. This is a good assumption in their application, a flight simulator, but the loss of parallax would be a severe limitation in many environments. Objects at different distances move as a unit within the domain of a keypoint, and parallax is only evident when the keypoint changes.
U.S. Pat. No. 5,396,583 to Chen, et. al captures panoramas and project them onto cylindrical surfaces for storage. They are able to rapidly project images from a cylinder to a plane using "scanline coherence". Unfortunately, like Blanton, their method does not support parallax.
McMillan, et. al. [L. McMillan and G. Bishop, Plenoptic Modeling: An Image-Based Rendering System, Siggraph '95 Proceedings, 1995], report a method that supports parallax, and apply it to natural images. They also produce a series of reference images off-line, which are captured with a video camera and re-projected to cylinders for storage. To support parallax, they calculate the image flow field between adjacent reference images. Now, when an image is approximated from a nearby reference image, different parts will move differently. Unfortunately, artifacts are quite apparent unless the image flow field is extremely accurate. Occluded regions cause additional artifacts.
The cylindrical surface (Chen and McMillan) is very inefficient for storing panoramic imagery near the vertical. Other panorama projections do not suffer from the limitations of the cylindrical projection. These include spherical, fisheye and cubic representations.
U.S. Pat. No. 5,185,667 to Zimmerman discloses a system for translating a selected portion of a hemispherical fisheye image into a planar projection for display on a CRT. The Zimmerman reference does not disclose how such hemispherical images can be seemed together by edge-to-edge abutment to form a 360 degree panoramic image. Additionally, such hemispherical fisheye images have been found to include several drawbacks that degrade the quality of the resulting translated image portion.
Accordingly, the need remains for providing improved panoramic imagry for simulating free movement within a multidimensional environment.
It is the object of this invention to simulate movement in a multidimensional space by approximating views at any viewpoint and orientation, with correct perspective and parallax. An additional object of this invention is to support stereography. It is a further object of this invention to provide an efficient method for storing panoramic imagery, especially for orientations near the vertical.
This invention captures panoramic views at many keypoints in the environment, preferably using fisheye photography. It stores these views as projections, from which one can produce views at any position and orientation. The fisheye photography can come from a variety of different lenses including those which have a maximum view angle that is less than, or greater than, 180 degrees. Most preferably, however, a fisheye lens having a view angle of less than 180 is used to avoid the drawbacks of 180 degree or greater fisheye lenses. For instance, several 150 degree images can be taken, overlapped, and seemed together using such tools as the Smoothmove™ seamer from Infinite Pictures, Inc. to form a full panoramic image.
An example of such seaming technique is disclosed herein. Digitized fisheye images are taken in several predefined directions, depending upon the configuration of the lens, to capture the entire image sphere. For instance, in a "bipyramidal" configuration consisting of five fisheye images, a fisheye lens having a view angle of at least approximately 127 degrees is used at 0�, 120� and 240� around the horizontal, straight up, and straight down to define the image sphere.
These images are then mapped to a panoramic image. The subhemispherical imagry form overlapping views defining identical imagery in real space. The overlapping pixels defining these portions of real space come from more than one fisheye image. The color and brightness values of the pixel at a particular real space location are a weighted average of such values from overlapping pixels based upon the area of overlap. These overlapped images can then be converted to equirectangular format in an offline intermediate step before ultimately perspectively correcting the view in real time.
In the preferred embodiment, the projections are planar, and consist of polygons that are projections of areas in the environment that are approximately planar. The locations of these areas are stored, giving the playback system the three-dimensional information necessary to infer how the individual polygons move with the viewpoint, and thus simulate parallax.
Because it simulates parallax, the invention can produce stereographic images.
The preferred embodiment solves the occlusion problem in a novel way. Imagery that is occluded at a keypoint but visible at a nearby viewpoint is added to that keypoint, either by extending existing polygons or by creating new ones.
FIG. 1 is a flow chart illustrating an overview of the invention.
FIG. 2 is a flow chart illustrating an overview of the off-line processing of the invention for a CG model that takes advantage of access to that model.
FIG. 3 is a flow chart illustrating how the invention can be used to eliminate off-line processing for a CG model.
FIG. 4 shows a two dimensional arrangement of keypoints (open circles) with a potential viewpoint (closed circle).
FIG. 5 represents both a fisheye projection and a spherical projection of that fisheye projection.
FIG. 6 illustrates the projection from a sphere to a plane.
FIG. 7 shows the relevant parameters in converting origins of a sphere.
FIG. 8 illustrates the projection of an object point to a plane.
FIG. 9 is an equirectangular projection of fisheye images taken in a tetrahedral configuration.
FIG. 10 is an equirectangular projection of fisheye images taken in a bipyramidal configuration.
FIG. 11 is an equirectangular projection of fisheye images taken in a cubic configuration.
FIG. 1 shows the overall operation of the invention. Images are captured either by a fisheye 101 or planar camera 108, and are used to form planar projections 103 at keypoints; fisheye images are first projected to a sphere 102. An analysis 104 is performed to segment these images into polygons that are the projections of approximately planar areas in the environment. These polygons are extended 105 with occluded imagery and then compressed 106. The compressed polygons, together with three-dimensional and other information, are written 107 to computer-readable storage 120.
The playback system, on receiving a view request 130 specifying a position and orientation in the environment, determines the nearest keypoint 131 and reads 132 the relevant data from storage 120. It decompresses 133 the polygons at that keypoint, translates 134 them to the desired position, rotates 135 them to the desired orientation, and displays 136 the resulting image.
CG environments can be handled exactly as in FIG. 1, except that the views are rendered from the model rather than being captured. However, if one has access to the internals of the model, then one can simplify the analysis, and even eliminate off-line processing. FIG. 2 shows the off-line processing that takes advantage of the model. After the model is created 21, this processing tailors the model 22 for the keypoint by eliminating detail that is too fine to be realized at that keypoint. It then extends and renders 23 and compresses 24 the polygons, and writes the k-point data 25 to computer-readable storage 26.
FIG. 3 shows a self-contained playback system, one that does not require off-line processing. It is similar to the playback system in FIG. 1, except that it generates keypoint data as needed. It does this using the methods illustrated in FIG. 2. In particular, on receiving a view request 321, it determines the nearest k-point 322. If this k-point is close enough 323 to the viewpoint, it reads the k-point data 324 from computer-readable storage 310, decompresses the polygons 325, translates the polygons to the desired position 326, rotates them to the desired orientation 327, and displays the resulting image 328. If it is determined 323 that no k-point is sufficiently close to the viewpoint, then the CG model is tailored to the viewpoint 301, to make it a new k-point. It then extends and renders the polygons 302, compresses them 303, and writes the k-point data 304 to computer-readable storage 310.
FIG. 4 shows a possible two-dimensional environment with open circles 41, 42, 43 representing keypoints, and a closed circle 45 representing a viewpoint. The view at the viewpoint 45 is preferably based on that of the nearest keypoint 41.
The invention consists of the panoramic database, its creation, and its use to map images to arbitrary positions and orientations.
A. Notation
CG, or Computer Graphics, refers to artificial environments.
A projection of the environment is specified by an orientation, or axis of projection, a projection surface normal to that axis, and by the center of projection. The center of projection, or point of view, is the viewpoint; it corresponds to the nodal point of a camera. Unless otherwise specified, the projection surface is planar. Other possibilities include cylindrical, conic, spherical, and fisheye projections. The distance from the center of projection to the plane of projection is the focal length, and is measured in pixels.
Polygons, unless otherwise qualified, are projections of approximately planar areas of the environment. These planar approximations are also polygonal, and are called e-polygons (e is for environment). The e-polygons form a "wire-frame model", and the polygons form the "texture maps". In contrast to conventional CG modeling, however, the environment description is redundant, with multiple e-polygons and polygons instead of one.
Images are projections that are large enough to fill a display. Images may be segmented into polygons.
Projections may be produced directly from the environment or from a CG model, or they may be approximated from previously calculated k-projections (key projections) by a mapping process. The viewpoints of the k-projections are called k-points (keypoints). A k-polygon is a k-projection that is a polygon, and a k-image is a k-projection that is an image. We will sometimes omit the "k-" prefix when the context makes it obvious.
The domain of a k-point is the range of viewpoints and orientations to which its projections can be mapped. The domain of a k-projection is that of its k-point. K-polygons with occluded areas may be extended to support their domains. The domain of a k-point is supported when its k-polygons contain all of the imagery needed to map to any viewpoint in that domain.
Domains can overlap. Non-overlapping domains of k-points can be constructed as Voronoi regions, also known as Dirichlet and nearest neighbor regions, or in other ways.
The mapper produces an image that can be displayed, and is part of the playback system.
B. Description of the panoramic database
The database, which is in a computer-readable storage medium, consists of a set of k-projections, together with their k-points, predetermined key orientations, domains, and other information useful for the creation of views of the environment. All of the data associated with a k-point is collectively referred to as k-point data. The k-projections may be uncompressed, or may be compressed with any of a variety of techniques, such as MPEG or JPEG. For CG environments, the k-projections that are rendered at a k-point might be compressed using a graphic representation. (This is less compression than one could achieve by simply storing the original CG model, but it leads to faster playback.)
The k-points may be arranged on a two or three dimensional lattice, may be concentrated in areas of high detail, or may follow some other arrangement.
In the preferred embodiment, the projections are all planar. However, alternate embodiments use cylindrical, conic, spherical, or fisheye projections. One embodiment uses a cylindrical projection for the "equatorial" region and conic projections for the "poles"; the mathematics for these projections is described by Blanton and McMillan.
There are many different ways to store the k-projections as planar projections at a k-point. In the preferred embodiment, one stores a large number of k-polygons at various orientations. In an alternate embodiment, one stores one or more k-images at various orientations. The way this is done will depend on the needs of the application, such as the importance of the "polar regions". As few as four k-images, arranged tetrahedrally, provide a full panorama. However, the more k-images, the fewer the total number of pixels. An obvious arrangement consists of six k-images around the equator (horizon), three to six k-images about 60� above the equator, and three to six below. Another possibility is four k-images about 45� above the equator, and four below.
There is a useful advantage in storing the panorama as planar images, as opposed to, say, cylindrical ones: the images at the k-points can be directly displayed without mapping. When one moves rapidly through the environment, it may be sufficient to display an existing image that has approximately the correct viewpoint and orientation. This benefit is somewhat reduced when the k-projections are similarly oriented polygons rather than images, and reduced more if their orientations are independent.
When the k-projections are stored as k-images, then these images are completely segmented into non-overlapping polygons. Whether the polygons are stored as units or as subunits of an image, each polygon represents the projection of an area of the environment that is approximately planar. The planar approximation of this area is also polygonal, and is known as an e-polygon. The database records the planar equation of each e-polygon. (Alternately, one can specify the coordinates of its vertices, or calculate them from the planar equation, the coordinates of the vertices of the k-polygon, and Eq. 5 and Eq. 10 below.) This permits the mapper to translate the polygon to another viewpoint in its domain.
It is desirable for storage and computational efficiency that the k-polygons and their corresponding e-polygons be large and few in number. However, the larger they are, the worse the planar approximation becomes, and the larger will be the parallax distortion when a polygon is mapped to a viewpoint in its domain. This distortion limits their sizes. This implies that an area of the environment represented by a single e-polygon (and a single k-polygon) at a distant k-point will likely be represented by multiple e-polygons at one nearby.
The e-polygons form a three-dimensional model for a k-point and its domain. In the preferred embodiment only one k-polygon is stored for each e-polygon. The k-polygon can be formed as a projection of the e-polygon at any orientation; a convenient orientation is the one pointing to the center of gravity of the e-polygon. In an alternate embodiment, an e-polygon is represented by k-polygons at several orientations to minimize the magnitude of the scale changes and shearing of a mapping, and thus to minimize aliasing.
In the preferred embodiment, the polygons of a k-point are extended to include parts of the environment that are occluded at that k-point but are visible at some point in their domain. (The k-projections cannot be stored as k-images in this embodiment because the extended polygons would overlap if placed in a single plane.) Without this embodiment, the mapper must use k-projections at more than one k-point to map the occluded areas.
In an alternate embodiment, the k-polygons are replaced by curved areas that more naturally represent the environment.
To minimize the complexity of mapping, the polygons (or curved areas) at each k-point are described in "list-priority" order. They are split as necessary to preserve this order over their domain, as described by Foley in chapter 15.
C. Preparation of the panoramic database for CG environments
One can calculate the k-projections for CG environments using the standard graphics rendering techniques described by Foley. However, clipping will be disabled, or at least relaxed, in order to extend the polygons to support their domain. Similarly, the e-polygons follow directly from the CG model. This assumes that the embodiment of the invention has access to the CG model, and that it can control the rendering of that model. Otherwise, some of the techniques described below for natural environments will be needed here.
CG models tend to use a large number of e-polygons. These e-polygons are important for mapping images at nearby viewpoints, but their numbers are excessive for distant viewpoints. For those viewpoints, it is necessary to consolidate e-polygons; a good criterion is to consolidate when the resulting parallax error is below a predetermined limit, preferably 1 pixel. However, merging continues at least until the number of e-polygons is reduced to a predetermined limit.
In the preferred embodiment the database is built off-line, as shown if FIG. 2. In an alternate embodiment, projections are rendered from the CG model as needed, as shown if FIG. 3. The viewer-selected viewpoints, or a subset of them, become k-points. This alternate embodiment reduces bandwidth and/or storage requirements, and is important when it is not practical to pre-calculate the database, or to transmit it dynamically. Suppose, for example, a game player enters a new environment. Because some delay can be expected in this case, it may be acceptable to render the first several projections dynamically. These projections and associated information are saved as k-point data. As the number of k-points increases, it will become increasingly likely that one can map k-projections from existing ones, and response will improve.
D. Preparation of the panoramic database for natural environments
1. Construction of k-projections
There are various ways to construct panoramic views. One embodiment combines the projections from a video camera (McMillan). The preferred embodiment uses a camera with a fisheye lens. A single fisheye camera, pointed forward, will capture about half of the panorama at a k-point, which will be adequate for some applications, and two may provide a full panorama. The preferred embodiment uses three horizontal fisheye projections with 120� between their axes, which provide a full panorama with ample overlap to minimize boundary artifacts. An alternate embodiment uses a single fisheye projection pointed upward; a 220� lens can capture everything except for imagery about 20� or more below the horizon.
Conceptually, one produces planar projections from the fisheye image by using a spherical projection as an intermediary. The mapping to a sphere can be understood from FIG. 5, which represents both the fisheye image and the sphere, with slightly different interpretations. Subscripts will distinguish these cases: f for the fisheye and s for the sphere. The point to be mapped, p, is represented by h, its distance to the origin, O, and θ, the angle from the vertical. H is the maximum value of h.
Hf is the radius of the fisheye image. The units of hf and Hf are pixels.
For the sphere, the view in FIG. 5 is along the axis of the camera, with the viewpoint, or center of projection, at the center of the sphere. The origin, Os, is at the intersection of the axis and the surface of the sphere; it is NOT the center of the sphere. hs is the angle of the arc of the great circle between Os and ps, and Hs is the maximum angle of view, measured from Os. For example, for a 180� lens, Hs =90�=π/2. θs is the dihedral angle between 2 axial planes, one through the vertical and one through ps.
A preferred method for obtaining a fisheye image is to use a fisheye lens which has a maximum viewing angle that is "subhemispherical", e.g. less than 180 degrees. For instance, one could use a fisheye lens with a maximum view angle of 150 degrees to capture several images by aiming the camera around the horizon and then aiming it up and down. These pictures could then be used to construct a full panorama representing the entire spherical view. The mathematics are the same as in the case of a traditional 180 degree fisheye.
To capture a full spherical image, several methods are envisioned using subhemispherical views. FIG. 9 illustrates an equirectangular projection of fisheye images in a tetrahedral configuration. Each fisheye image has a view angle of at least approximately 142�. All overlapping portions of the projection are shown in cross-hatching. Shown in FIG. 9 are four images 50, 52, 54 and 56. To gain full coverage of the image sphere, image 50 is taken straight upward from a keypoint and remaining images 52, 54 and 56 are taken at 0�, 120� and 240� around a vertical axis and in a direction tilted downward by about 19.5� below horizontal.
FIG. 10 illustrates an equirectangular projection of fisheye images in a bipyramidal configuration consisting of five fisheye images 60, 62, 64, 66 and 68. Each fisheye image of the bipyramidal configuration has a view angle of at least approximately 127�. To gain full coverage of the image sphere, image 60 is taken straight upward and image 68 is taken straight downward from a keypoint. The remaining images 62, 64 and 66 are taken at 0�, 120� and 240� around a vertical axis.
FIG. 11 illustrates an equirectangular projection of fisheye images in a cubic configuration consisting of six fisheye images 70, 72, 74, 76, 78 and 80. Each fisheye image of the cubic configuration has a view angle of at least approximately 109.5�. To gain full coverage of the image sphere, image 70 is taken straight upward and image 80 is taken straight downward from a keypoint. The remaining images 72, 74, 76 and 78 are taken at 0�, 90�, 180�, and 270� (or East, North, West and South) about a vertical axis.
seaming of subhemispherical views to obtain a panoramic image is preferred because of inherent optical drawbacks with 180� or greater images. For instance, lower quality 8 mm fisheye lenses tend to have extreme circular fisheye distortion near the edges of the image. Furthermore, more information needs to be packed into the same image frame. These two factors combined have been found to produce low quality panoramas.
Other drawbacks of 180� or greater fisheye photography is the general requirement of manual touchup of images to eliminate such artifacts as a capture of the tripod supporting the camera. Additionally, lens glare is common in 180� or greater fisheye images because direct light is difficult to avoid. The 180� field of view also tends to cover very wide dynamic ranges of lighting, especially in interior shots, and produce highly contrasted pictures. Finally, panoramas created with 180� fisheye lenses devote a lot of pixels to the top and the bottom regions of the image which tend to have little information while the compressed middle region tend to have more details. To achieve similar quality for displaying information in the middle region, the panorama size will need to be much bigger (about 2� or more). This results in bigger file sizes for any computer downloads.
The mapping to the sphere is simply (see, e.g., R. Kingslake, Optical System Design, p. 87, Academic Press, 1983, for a discussion of the fisheye):
θs =θf
hs /Hs =hf /Hf Eq. 1
One can readily project from a sphere to a plane at any orientation. FIG. 6 shows a plane in cross section tangent to the sphere at point O', which specified the orientation. For any point in the plane, one finds the corresponding point in the sphere by extending the radial line from the sphere to the plane. Then, with f being the focal length and (hp, θp) being the polar coordinates of a point in the plane (see FIG. 5), the point on the sphere is:
hs '=tan-1 (hp /f)
θs '=θp Eq. 2
It is desirable to express this in terms of (hs, θs) so that Eq. 1 can be used to get the fisheye coordinates. FIG. 7 shows the quantities used to express the conversion, where all of the curves are arcs of great circles, and the lengths are measured as angles. The "North Pole" defines the vertical, and l and l' are the compliments of the "latitudes" of O and O', respectively. φ is the azimuth angle between O and O'.
From l, l', and φ, which are independent of p and are assumed known, we find the intermediate quantities: φ, φ', and d from spherical trigonometry:
cos d=cos l cos l'+sin l sin l' cos φ
sin φ'/sin l=sin φ/sin l'=sin φ/sin d Eq. 3
cos hs =cos hs ' cos d+sin hs ' sin d cos (φ'+θs ')
sin (φ-θs)=sin (φ'+θs ') sin hs '/sin hs Eq. 4
Note when hs =0, that θs is irrelevant.
Of course, the entire panorama requires more than one fisheye, and each fisheye will have its own origin, O. Typically one will select the O closest to the tangent point, O'.
2. Analyzing images to find the k-polygons and e-polygons
The analysis is more difficult for natural environments. The analysis, which is individually optimized for each k-point, determines the three-dimensional environment in sufficient detail to accurately map k-projections from the k-point to viewpoints in its domain. The three-dimensional environment is specified by specifying the e-polygons and their corresponding k-polygons. Since the three-dimensional environment determines how the k-polygons move with the viewpoint, one can determine the e-polygons, which approximate this environment, by observing this motion.
In the preferred embodiment the analysis uses k-images, and one selects a target image for each reference image being analyzed. The target and reference images will be assumed to have the same orientation, and will be associated with nearby k-points. Normally, the nearby k-point will be an adjacent one; however, occlusion or other reasons may reduce the value of the adjacent k-points, forcing the use of other ones. In FIG. 4, 42 is a k-point adjacent to k-point 41, and 43 is a nearby k-point that is not adjacent to 41.
One then segments the reference image into (non-degenerate) polygons that are the projections of approximately planar areas in the environment. This segmentation can be done manually using human understanding of the environment. Alternatively, one can base it on a three-dimensional model of the environment, which could be built using a commercially-available three-dimensional modeling package. One would then have to consolidate polygons, as with CG environments above.
Each polygon in the reference image is registered with the target image, and the registration is fitted to a planar model. The following describes this analysis.
First we need to know how a point in the environment projects to the two k-points. In particular, we need to know how the two image points are related. The coordinate system has x and y in the image plane and z perpendicular to it. Then:
O=origin of the reference image; i.e., its k-point.
O'=origin of the target image
M=O'-O=the displacement between the k-points
m=(Mx, My, 0)=components of M in the plane of projection
Q=object point in the O coordinate system
q=(Qx, Qy, 0)=components of Q in the plane of projection
p=image point of Q in the reference image
where boldface indicates a vector or point in two or three dimensions, and quantities with a prime refer to the target image. Then (see FIG. 8):
p/f=q/Qz Eq. 5
and similarly
p'/f=q'/Q'z Eq. 6
Also, from the definition of M, it follows:
Q'=Q-M Eq. 7
From these equations, it follows:
p'=p+(Mz p-fm)/(Qz -Mz) Eq. 8
It is useful to rewrite this as:
1/Qz =(p'-p)/(Mz p'-fm) Eq. 9
The vector division in Eq. 9 implies that the numerator and denominator must be parallel, which is guaranteed by Eq. 8.
For Q in an e-polygon, which is assumed planar, we can write:
a Qx +b Qy +c Qz =1 Eq. 10
This equation explicitly constrains the constant term to be non-zero. When zero, the plane of the e-polygon passes through O, and the e-polygon projects as a line, or degenerate polygon, contradicting the segmentation. It follows that 1/Qz is linear in p:
1/Qz =a Qx /Qz +b Qy /Qz +c=a px /f+b py /f+c Eq. 11
using Eq. 5. Combining Eq. 9 and Eq. 11:
a px /f+b py /f+c=(p'-p)/(Mz p'-fm) Eq. 12
The next step is to determine p' as a function of p over the polygon. There are various ways of doing this. In the preferred embodiment, the polygon is broken into 8�8 blocks, and each block is compared with the target to find the best match; e.g., the minimum mean-square-difference. This is a well-known registration procedure in image coding and analysis. The possible values of p' are subject to epipolar constraints; in particular, the direction of p'-p is fixed by Eq. 8.
Eq. 12 is a system of linear equations in a, b, and c. If p' is known for at least four points in the polygon, this system is over-determined, and one can readily find the least-squares solution using standard techniques in linear algebra.
In the preferred embodiment, weighting is first applied to these points to reflect our confidence in them. One possibility is
weight=<quality of fit>*<reliability of fit>
<quality of fit>=activity/(RMSE+noise)
<reliability of fit>=<useful edge strength> Eq. 13
A quality fit has low RMSE (root-mean-square-error) relative to what is possible; for various reasons, one cannot expect a very low RMSE for a very "active" block, even with a very good vector. Activity measures the roughness of the block.
Furthermore, one cannot find a reliable fit for a block without any structure. If there is a strong edge, then the component of the vector p'-p normal to direction of the edge will be reliable, but the parallel component may not be. Since the direction of this vector is determined by the epipolar constraint (Eq. 8), the useful edge strength is the component of the edge direction normal to the constrained direction.
3. Extending the polygons
The polygon is then extended to support the viewpoints in its domain. This is done by:
finding imagery that is not visible at the k-point because of occlusion, but that is visible at some viewpoint in the domain;
finding a nearby k-point at which that imagery is visible; and
mapping that imagery from said nearby k-point to said k-point.
In the preferred embodiment, one analyzes the relative motion of adjacent k-polygons by using Eq. 8 to examine pixels along their common border. If the polygons separate for any vector M, occlusion results, and the k-polygon corresponding to the more distant e-polygon must be extended. This can be done by mapping imagery to it from a k-point in the M direction. If that k-point does not have the occluded imagery, then it will be necessary to find a nearby k-point that does. The amount the k-point must be extended depends on the extent of the domain in the M direction. In some cases, an additional k-polygon must be created to support the occluded area.
In the embodiment that stores the polygons without extension, the extension is done dynamically as needed. This is the case when the k-projections are stored as k-images.
a) Mapping images to viewpoints
There are several steps in mapping an image at a viewpoint and orientation:
Select the appropriate k-point.
Translate the projections at that k-point to the viewpoint.
Rotate the orientations of the projections to the desired orientation.
Rotation and translation can be done be done in either order. If it is likely that the viewer will stay at one location for a while and look around, it is most efficient to translate first, to avoid repeating the translation. Otherwise, if the application supports stereographic images, rotation should probably be done first. The two stereographic images will have the same orientation but slightly different translations.
Of course, rotation and translation can be done at the same time.
The polygons are mapped in list-priority order, with the most distant one mapped first. Then the mapper needs not determine which pixels will actually be displayed. Alternatively, the polygons could be mapped in reverse order, with the mapper taking care not to overwrite previously mapped pixels. The extra logic prevents any pixel from being mapped more than once.
This order is obviously only important when the polygons are combined into an image. If all of the polygons have the same orientation, it is desirable to combine then in the translation phase. Otherwise, they should be combined in the second phase.
i) K-projection selection
The domain of the k-point must contain the viewpoint. If domains overlap, the mapper will normally select the nearest one. However, if the mapper has adequate resources, it may map the image more than once and calculate a weighed average. This will reduce the discontinuity when the viewpoint moves between domains.
For the embodiment in which k-projections are k-images, it is likely that the domain of a k-image at a k-point will not cover the entire image at the viewpoint, and that k-images with different orientations will be required.
For the embodiment in which an e-polygon at a k-point is represented by multiple polygons at various orientations, the closest orientation will be preferable. However, the mapper can map more than once and average.
ii) Translation
Translation requires the use of polygons to achieve correct parallax. The mapping of any point, p, in a k-polygon to p' at the viewpoint is given by Eq. 8. M and m now refer to the displacement to the viewpoint, and Qz is given by Eq. 11. When necessary to reduce computation, the mapper will first consolidate polygons into larger ones.
In the preferred embodiment, Eq. 8 and Eq. 11 are only used to translate the k-polygon's vertices to the viewpoint. Then for each pixel at that viewpoint, p', the corresponding source pixel, p, is found from the inverses of these equations:
p=p'-(Mz p'-fm)/(Qz '+Mz) Eq. 14
1/Qz '=a' px '/f+b' py '/f+c' Eq. 15
k=1-a Mx -b My -c Mz Eq. 16
iii) Rotation of orientation
If the orientation at a viewpoint changes, then the projection will change. This orientation change can be represented as a rotation of the coordinate system. As is well known, the corresponding change in the planar projection can be readily expressed in homogeneous coordinates (Foley, McMillan). If R is the rotation matrix that changes the coordinates of an object point Q to Q': Q'=R Q, then using Eq. 5:
(Qx ', Qy ', Qz ')T =R (Qx, Qy, Qz)T =Qz R (Qx /Qz, Qy /Qz, 1)T =Qz R (px /f, py /f, 1)T
so that:
R (px /f, py /f, 1)T =(Qx ', Qy ', Qz ')T /Qz =(Qx '/Qz ', Qy '/Qz ', 1)T Qz '/Qz =(px '/f, py '/f, 1)T w Eq. 17
where w=Qz '/Qz is the third component of R(px /f, py /f, 1)T.
Note this transformation is independent of the three-dimensional structure of the environment, since there is no parallax change. If all of the polygons have the same orientation and have been combined into an image, then the image can be transformed as a unit. Otherwise, the polygons must be rotated individually.
Rotations about an axis in the plane of projection is simpler. For example, for a rotation of ω about the y axis is:
px /f=((px '/f) cos ω+sin ω)/D
py /f=(py '/f)/D Eq. 18
D=-(px '/f) sin ω+cos ω
This can be done fairly fast if done column-wise: to find all of the pixels in the rotated projection for a column defined by fixed px ', first calculate D and px using the above formulas. Then, for each pixel in that column, calculate py, which is a (non-integer) multiple of py ', and interpolate the value from the original projection at (px, py). This is analogous to Chen's scanline coherence.
Non-Patent Citations
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text:
A label of "leadoff hitter"...top of the order, get on base so that the middle of the order can drive them in with extra base hits. Is there a prototype for that other than "gets on base?"
Can't win with 'em
Can't win without 'em
Last edited by Mario-Rijo; 12-23-2010 at 09:19 AM.
"You can't let praise or criticism get to you. It's a weakness to get caught up in either one."
--Woody Hayes
I want my leadoff hitter (or any hitter) to avoid outs and acquirer bases.
The more bases he acquirers the better, it leads to run production.
While Rickey had some pop he only hit over 20 home runs 4 times in his career. He really didn't pack a lot of power. Stubbs has light tower power. Not to mention Rickey was an absolute pest when it came to making the pitcher work, and work deep.
Another difference is Rickey spent a majority of his career in the AL, where he was not batting after the pitcher, but was instead batting after another MLB hitter.
"Today was the byproduct of us thinking we can come back from anything." - Joey Votto after blowing a 10-1 lead and holding on for the 12-11 win on 8/25/2010.
If teams had lineups full of Votto's and Pujols' then it would be okay to bat a 25 home run guy leadoff. But teams are full of players with different skills and each spot in the batting order is able to best capitalize on different skills.
The leadoff spot capitalizes on OBP and minimizes the value of home runs and SLG. Spots 3-5 best capitalize on SLG Therefore, it's most productive to put high OBP, low SLG hitters in the top of the lineup, and high SLG guys in the middle.
But all of this depends on who you have available.
"Imagination is more important than knowledge." -- Albert Einstein
What you said here makes the most sense to me and its what managers (even Abner LaRussa) have done throughout the course of baseball history. Put your hitters who are good at getting on base but lack power in front of your hitters that are good at both.
We can bang our head against the wall as long as we want but the Joey Votto's of the world are going to hit 3rd and if your lucky enough to get a Ricky Henderson he is going to first.
If Stubbs leads off the game I want him to avoid makeing an out. If he walks or hits a single that's good.
If he hits a double that's great. If he hits a triple that's better. If he hits a HR that's even better.
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Adam Shankman, Bill Mechanic to produce 2010 Oscars
It's the second year in a row that organizers have picked a pair of rookie Oscar producers to oversee
Academy President Tom Sherak says the Oscars will have a talented team — Mechanic for his producing and management experience and Shankman for his directing and choreography skills.
Oscar organizers are trying to put more razzle-dazzle into the show. Instead of the usual standup comic, the Oscars called on song-and-dance man


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Bodega Calle's mission is to produce high quality wines in a sustainable manner for customers in select markets across the world. The winery also aims to apply the highest international quality standards, helping to develop the prestige of Mendoza's wine and Argentina. Bodega Calle takes strides to preserve the environment and the culture of the region, while maintaining concern and social commitment for the winery's workers, producers and surrounding community. View all Bodega Calle Wines
About ArgentinaView a map of Argentina wineries (ahr-jen-TEE-nah)
Notable FactsUnlike its Chilean neighbor, Argentina's vineyards are spread out around the country. The best known region is Mendoza, almost parallel to Santiago to the west. Mendoza contains the sub-regions of Maipu (pronounced MY-pu) and San Rafael. Grape-wise, the most important white is Chardonnay, making wine similar to California's style on the variety. Another fun white grape to try is Torrontes. Almost only grown in Argentina, Torrontes makes wines that are crisp, aromatic and easy-drinking. Some of the best versions of this wine come from the northern region of Salta, with very high altitude vineyards. As for the reds, Cabernet Sauvignon is the main grape for many wines leaving the country, but Malbec, the grape Argentinians like to call their own, makes very distinctive wines that are structured, dense and velvety. Many more varieties happily grow in the country, but for export, and consistent quality, these are the primary grapes.
About South America
Related Links:
Young, organically farmed Carmenère at Chile's De Martino estate vineyard


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Genre :Fantasy, Adventure, Drama
Release Date :February 14, 2008
MPAA Rating :PG
Director :Mark Waters
Starring :Freddie Highmore, Mary-Louise Parker, Nick Nolte, Joan Plowright, David Strathairn, Seth Rogen, Martin Short, Izabella Miko, Sarah Bolger
REVIEWS RATE: Critics Readers [Rate It]
Reader's Reviews
ZbVTwUposted by Tfvzugbx on Jul 13, 2009 02:58:36
The film is great to watch and to own on DVD. I watched the film when it first got its worldwide release to cinemas, i have to say that i was very happy with the film... even the trailers makes me think but the film have really made me love the film soooooooooooo much! And also, i think that actor Freddie Highmore had done a wonderful job by playing a cool double role! Well done, dude! It should be a Oscar WINNER film! 5 out of 5!posted by Mahinder on Apr 17, 2009 02:16:31
A must see film. Very well done, love the artwork in this film. The double role is cute! 5 out of 5! A must buy film on DVD!posted by Mandip on Apr 17, 2009 02:11:21


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A Detailed Eagle
BC's Larsen A Top Contender In The ODAC
HARRISONBURG — Whether it's on the tennis court or in the classroom, Bridgewater College junior Brandon Larsen prides himself on his attention to detail.
As an information systems major, Larsen –…
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Happy to announce that I have launched the new Projekt19 site. http://projekt19.com
The new website uses the awesome Foundation from Zurb. The main goal was to make the site more personable and easier to understand the business.
Please let me know your thoughts and feedback
More Chad Mueller
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Rated 3.9 out of 5 by 513 reviewers.
Rated 5 out of 5 by jimono Outstanding Convenience What a great place to stay when you have a flight early the next morning. Paris traffic and getting up extra early were eliminated by staying at the Sheraton Paris Airport Hotel Club level is super, with drinks, snacks, breakfast and wifi and large TVs to relax and enjoy. I'll do it again! April 29, 2013
Rated 5 out of 5 by Bill The Hotel Has IT ALL The building is great. Check in perfect -- she gave me a perfect room with nice view. The bell men who both Che led me in and took my baggage up and drove me in the shuttle to Terminal 1 were both outstanding, above and beyond the call of duty .. ! April 25, 2013
Rated 4 out of 5 by Amine Always nice, quiet and clean BUT The front desk staff refused to honor my gold status advantages and simply declined offering free-wifi.... April 25, 2013
Rated 4 out of 5 by Neodoc Excellent location - at the Paris Charles de Gaul Airport! Wonderfully located - no hassel to get to CDG airport - you are basically in Terminal 2! Facility is excellent - large room with nice bath. Of course no " heavenly" bed, like the ones in US and Australia - never had one in The Meridian in Paris or the Sheratons in Amsterdam or Frankfurt or the Westin in Berlin - come on Europe - catch up!! Room service food was poor - sent the orders back once then could not eat their second try! The Staff were very apologetic and took the charges off our bill but no dinner that night was not optimum! April 23, 2013
Rated 4 out of 5 by waxdol Nice and comfortable Really enjoyed my stay in the hotel after long journey. Room ambience make me at home April 21, 2013
Rated 5 out of 5 by Ginger2013 Location location location Arrived at night and was so happy to get to hotel without having to leave airport. Was great next day to just walk to our gate. Could use more signs about location in terminal April 21, 2013
Rated 5 out of 5 by Lena Great location at airport The hotel was very modern and the room was wonderfully appointed and so clean. After 2 weeks traveling in Europe, it was great to have a spacious American size room with king bed and good air conditioning. We were able to catch a train right from the hotel to the airport for our morning flight. It was so convenient and April 19, 2013
Rated 5 out of 5 by Sunny Exceptional Airport Hotel This was an absolutely exceptional airport hotel in every respect. I arrived tired and felt instantly tucked into a cocoon that was peaceful, clean, and comfortable. The bathroom and amenities were superb and the bed so very comfortable. The quietness was such a surprise being right there at CDG--it was so very silent. I will definitely return for another stay. April 19, 2013
Rated 5 out of 5 by rain45 Nice, spacious and clean hotel. We only stayed in this hotel because it was the closest to the airport, but I enjoyed it! Bed and bathroom (with bath and shower) was spacious and clean. The receptionist was friendly, too. April 15, 2013
Rated 3 out of 5 by G007 This Hotel has great location I like the convenience to land at CG and just sleep at Sheraton. What I did not like: the hotel smells smoking and the restaurant was terrible. We order chicken, that come to the table cold; the waiter did not speak English and the service was below expectation. April 10, 2013
Rated 4 out of 5 by naz1 Flying out of CDG Best location to fly out of Charles De Gaulle. Excellent service standard. "NO" outside noise. April 10, 2013
Rated 5 out of 5 by MSous Excellent Accommodations The late evening staff was very nice and the accommodations, for an airport hotel, were EXCELLENT. April 6, 2013
Rated 5 out of 5 by Duper Outstanding hotel for CDG connection The hotel is very conveniently located for RER from Paris to CDG. Room was large and has a spacious bath with both shower and tub. Staff is friendly and helpful. April 5, 2013
Rated 4 out of 5 by Ab07 March 2013 Profesionnal staff - great location - enjoyable stay for 1 night March 31, 2013
Rated 2 out of 5 by rua4102 convient but real expensive This is right at the airport but it is extremely expense for the quality and service received.. The shower barely has any water coming out to conserve on water i assume and the water only gets luke warm , so no hot showers here. i then asked management and was offered 3000 SPG points for inconvience and to still have NOT received the points and i get no responce to emails to the hotel... March 30, 2013
Rated 5 out of 5 by DonnaH Great airport hotel experience What a great hotel in a great airport. The staff was very nice and helpful. The breakfast buffet is well worth getting up for and I love the free internet in the lobby. I will stay here every time I have a long trip that includes CDG. March 29, 2013
Rated 4 out of 5 by MarilynnDW Nice and Convenient I have stayed here several times when passing through Paris. The staff is always pleasant and helpful. The club lounge is nice, but it would help if they would label the snacks. Being France and they do like their fancy foods, it is difficult for those with allergies and when I asked the staff person tending the lounge, she either didn't speak English or chose not to, she could not tell me what the snacks were or their ingredients. I stuck with bread and cheese. March 28, 2013
Rated 1 out of 5 by traveller staff attitude Staff in bar not polite and unwilling to attend clients properly; "just waht is on the list" , als signing for payment took long.. three staff members talking amongst themselves at the bar , not interested in clients March 28, 2013
Rated 4 out of 5 by EP2013 Great sleep! For a airport hotel, the rooms are extremely well sound proofed! It is almost eerie it is so quiet! And the sweet sleeper bed always deliver! The only negative comment, I know it's an airport hotel, but the price of food and drinks is exorbitant! Complete rip off for what you get... I'd recommend buying a bottle of wine, baguette and cheese at a market and enjoy these in the room! March 25, 2013
Rated 3 out of 5 by Richard Sport Sport facility is crowded. Not enough fresh air and too warm inside. March 23, 2013
Rated 5 out of 5 by supatight80 The BEST Starwood Airport Hotel to date.... Located on Terminal 2 of CDG, the property gave me a complimentary Suite upgrade and a personal hand written letter from their manager. Suites were in excellent condition and their staffs were more than welcoming. Makes me forget I am in Paris! March 20, 2013
Rated 4 out of 5 by YULHNLCDG Doesn't get any closer to CDG ...than inside Terminal 2! We needed a simple, convenient, cost effective option for a one night stay before a return flight to Montreal. This Sheraton fit the bill perfectly. Decor was contemporary and stylish, yet practical. Complimentary Evian in our rooms for SPG elite members was appreciated. The check-in process was efficient and courteous, as was check-out. Best of all was avoiding the need to catch a taxi or shuttle to catch our flight in the morning, and instead taking a leisurely 10 minute walk to our airline ticket counter. It made all the difference on our travel day, and ensured a lovely end to our trip to France. March 17, 2013
Rated 4 out of 5 by Buffy13 Good for a quick stop over I have stayed at the Sheraton many times, and it continues to provide a good nights stay. if you do not have the chance to get into Paris this would be the best hotel by far. March 10, 2013
Rated 4 out of 5 by Francois My most recent stay I love the Sheraton at Charles De Gaulle airport and stay there once a month. This time, however, my wake up call never came. Fortunately, I had my own alarm clock. But if I didn't, I could have missed my 8.20 a.m. Air France flight to New York. March 10, 2013
Rated 4 out of 5 by Shinergise Great service, shame about menu choice Had fantastic service from all staff that I interacted with during my brief stay. Only disappointment was that the restaurant and brasserie menus did not offer a wider selection of more reasonably priced food. Even if I had taken the burger it would have cost me EUR 24 even before I added any gratuity and beverage. As a very frequent traveller, I would have preferred a wider choice of more reasonably priced food that did not mean I would have to leave the hotel to seek it out. The fixed menu was 54 EUR and I really did not want that much food. March 10, 2013
Rated 5 out of 5 by Amy72 Surprisingly pleasant Hotel is really clean, staff is really super nice, and you are AT the airport, so you can wake up and walk to security. The most convenient experience. I didn't use the gym or eat at the restaurant - just really slept there. But it was perfect. March 9, 2013
Rated 4 out of 5 by cwimpy Better Signage I have stayed at the hotel a number of times and it seems that whoever wants to pick me up gets lost at the airport. The signage to find the hotel is terrible. I realize that many may use the hotel just for connecting flights, but for the few who actually have meetings outside, it is frustrating for cars having to park because they and even taxi drivers cannot find the driveway for pick-ups March 8, 2013
Rated 2 out of 5 by STM123 This hotel needs help The location is great but service is not good, rooms are poor, and desire to go above is non exisitant. i have stayed at this hotel many times and felt the location merited the high price. This time the poor service and terrible experiece will cause me to go to another brand for CDG overnites. No more. March 6, 2013
Rated 4 out of 5 by IRELANDSMAN JUST A LITTLE MORE ATTENTION Warmly received as a Platinum Lifetime guest. A very pleasant junior suite with airport view. Internet connection--ok Problems with shower--water mixer--has serious problems--HOT-COLD. Some towels/bath robes are grey in colour--no longer white. The most annoying issue was the dining room hostess at Breakfast greeting guests while chewing gum--it was DISGUSTING . Throughout the time we were there she continued to chew ! Breakfast--ok. March 3, 2013
Rated 4 out of 5 by nortraveller Good location, inconsistant service A very good location at the airport. However, inconsistant service, specially at breakfast. The staff were not very attentive to the guests, and I several times had to ask for basic things like someone to staff the egg-station, coffe, juice. There is also no free wifi at this hotel. They charge €19 for one day access, whic is an outrageous price condicering the price you need to pay for a room. March 1, 2013


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Less will lead to more for Hogs lineman
Posted: August 20, 2014 at 2:55 a.m.
Sebastian Tretola arrived at Arkansas shattering stereotypes.
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₦airaland ForumWelcome, Guest: Join Nairaland / Login / Trending / Recent / New
Stats: 1,384,962 members, 2,152,317 topics. Date: Tuesday, 30 June 2015 at 01:44 PM
Nairaland Forum / Nairaland / General / Religion / Help! (503 Views)
|Help! by Fiscobelle: 9:54am On Oct 19, 2007
Help please!!!!!! Iam a muslim and my boyfiend is a Xtian.WE love each other dearly but our parents are against it cos of the difference in Religion.I cant leave this guy for anything in this world.What do i do?Who can help
|Re: Help! by finekid(m): 10:43am On Oct 19, 2007
Are you hermaphrodite?
|Re: Help! by chilla(f): 3:22pm On Oct 19, 2007
I can't leave this guy for anything in this world.
What advice do u need again? Since your mind is made up, do what your heart tells u to do.
Good luck
|Re: Help! by jerrymania(m): 9:10am On Oct 20, 2007
hey posterman, you've been busted. Fake Bloke.
(0) (Reply)
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These are real!
Viewed from one angle you see this…
But from just the right angle you see this…
And so on…
They're so amazing! I can't imagine all the work involved to figure out exactly where to place each part of the design! Check out Felice's website for more.
Via Fraiing.
- -Jan 23, 2009, 10:03PM
Wow! That is truly amazing. It's great to see such a talented individual make art accessible to everyone!
- -Jan 23, 2009, 1:12PM
This is by far one of the coolest things I've ever seen. Aside from those 3D sidewalk chalk designs. http://www.toxel.com/inspiration/2008/05/18/3d-sidewalk-chalk-art/


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Latest Post:
Started By:
65 days ago.
by amos57usa
Letters To Ed :-)
"We've been duped by the Republicans. Kentucky Sen. and minority leader Mitch McConnell in a news conference one day after the election, stated that the single and sole goal of the GOP over the next two years is: to make Barack Obama a single term president. What an arrogant and obnoxious goal and statement. There agenda before the election was to get votes by promising that there first goals were jobs, the economy and health care reform. It seems their goal is to grab power, not to do things for the people that are in need of jobs and or unemployment pay, health care for those that don't have it, and the people losing their homes. This is the same party that wanted the auto plants and their suppliers to go out of business. We are just coming back from what they did to this country, and now we have them back to do the same things to our country again. What a mess the next two years is going to bring to this country. Talk about partisanship." Carl D. Leow Rogers Cit
Member Comments
It's progress, thirty days ago he wouldn't have been able to sign up. As I said, give it time, the bugs will be worked out, that's how it is with major software implementations in The Real World. And he's being pretty quiet about the cost: Why doesn't he be honest if he saved money?
Posted 588 days ago.
So, he signed up but can not actually pay for it.
Not really that funny when you think about it, is it?
Posted 588 days ago.
Read the whole story?
Posted 588 days ago.
Come on jaxspp.
Limited government does not mean NO GOVERNMENT.
That is the biggest load of baloney in the left's arguments.
It's always your way or nothing. If you're against government waste then you're against all government programs.
Keep it real. Goofing up 1/6 of the economy is not a task that the federal government should be engaging in. <-Period
Wait for it.... "that means you think we should go back...blabbah blabbah".
No it does not. Nobody wants to go back to what we had.
We never had to be here. If the democrats were not so*****bent on passing ANYTHING, instead of something with substance that was actually well thought out, then we'd not be discussing this.
Posted 588 days ago.
Boehner successfully signs up for Obamacare. HAHAHAHAHAHAHA! news(dot)yahoo(dot)com/boehner-signs-obamacare-delay-tweet-120640766(dot)html
Posted 588 days ago.
RS: How do you feel about meat inspection? A good thing or a government intrusion?
Posted 588 days ago.
Not my God, just logic and common sense built from working in The Real World that knows America's best days are when the free market and government work hand in hand. I don't want any part of your toxic, polluted world with poisonous food products and companies preying on the vulnerable.
Posted 588 days ago.
I realize that Government is your God Jaxowashingtonworshiper.
I want as little gov. as possible Normindmeldminion. So does the Tea Party. That would, by definition be much less subgjugative, still, I wouldn't expect you to realize that. Don't try to think, that's the Borg's job.
Posted 588 days ago.
I will not tell you again. My malady is still in remission. Your pathetic attempts at subjugating me do not work. Take your own medicine, as in common sense. I have never smoked a cigarette, Mr. Boehner.
Posted 588 days ago.
Fill it buster.
Posted 588 days ago.
Nice imagination Normaryjane. Switch to regular smokes, they tend to leave your brain intact a bit longer.
Posted 588 days ago.
Ah, there he is :-)
Posted 588 days ago.
Maybe you should live on the Moon Jaxie. Government has no "business" in the free market, mmkay(?) unless your country is a commie country. I would not like that. You can imagine liking it if you want to. It's the very reason I think you a fool's fool, and one of our the village idiots.
Speaking of which...where's Normanhole?
Posted 588 days ago.
How naïve! Rshrill, there is quite simply nothing about the present day GOP, in particular the swine Tea Party that suggests even one iota of less subjugative government. You are so far up the ideological arse of the evangelical fundamentalist faction of the GOP that seeks a theocracy with the bible in place of the Constitution that your head simply CANNOT be retrieved. Wake TF up.
Posted 588 days ago.
Do you ever ask yourself how some diseases have been cured? Hint: Government research grants are involved.
Posted 588 days ago.
Do you ever ask yourself how America made it to the moon? Hint: The government was involved.
Posted 588 days ago.
"Here's the alternative: Free Markets...mmkay? "
Pre-existing conditions - not covered. Pre-existing conditions - unable to get insurance, period. Caps. Claims denied. Dangerous jobs - unable to get coverage. Policies cancelled after claims filed - found slight errors in application. Children dropped at 18.
Posted 588 days ago.
If you still have an idealized view that the democrat party is still that of your parents, then perhaps you need to think much deeper below the surface, as your naive views are not merely superficial, they are stuporficial.
Our entire government is virtually an extension of the democrat party, as are much of the courts, and your party seeks to stack the deck even further in their favor.
Living under an all consuming government thumb may seem utopian to you, but it is*****to me. Subjugation beneath that ever-widening thumb does not suit me. It will not suit my progeny either.
You are bogged down in process, along with your lefty media maggots, since you are incapable of thinking with your own brain. I am actually looking at the ingredients of the sausage making apparatus, and I don't like all of the raw sewage flowing into the mix. You are either blissfully OK with it, don't care to look at it, are willfully blind to it, or have no problem eating sewage.
Posted 588 days ago.
Look in Reid's pocket little camper. Oh wait, you're already in that pocket. Just open your peepers.
Here's the alternative: Free Markets...mmkay?
Here's the problem: Marxism.
Get the hint?
Answering questions isn't part of the Borg network is it? Could you at least refer me to someone who might be able to answer something without lying their Never-Lovin' a-s-s off?
And have you anything other than Iraq?
Posted 588 days ago.
Bam! ACA is all I have! Bam! Obstruction is all I do! Bam! I haven't passed one bill this year to create jobs or help the economy in any manner! Bam! I shut down the government I ran to be a part of! Bam! I voted 42 times to repeal the ACA without proposing an alternative.
Posted 588 days ago.
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printable version
Talk amongst yourselves
15 Sep 2013
Right now I am going with KC because of the talent level, but the Carolina matchup seems better. Thoughts?
Posted by: agauntpanda on 15 Sep 2013
0 replies
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GREENVILLE - Two early triples and Eduardo de Oleo's first home run of the season sparked Charleston (6-7), but Brandon Thomas' ninth-inning single was the winner in an 8-7 sweep-clinching victory over the Greenville (7-6) on Wednesday at Fluor Field at the West End in South Atlantic League action.
The RiverDogs' lead grew to 5-0 in the top of the fourth. Thomas led off the frame with a walk and scored during a Gosuke Katoh triple. Katoh scored when de Oleo cleared Greenville's version of the Green Monster in left field for a two-run shot that put Charleston up by five.
Charleston returns home on Thursday to host the Rome Braves at 7:05 p.m.
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Originally written on MyTeamRivals.com | Last updated 9/1/12
The 2012 college football season kicks off tonight, and isportsweb is previewing this year's Heisman Trophy favorites. Each week, we'll update the list with new stats and information as some players make their way into the Heisman conversation and others drop out of the race. 2012 Preseason Heisman Trophy Favorites Matt Barkley – QB, USC According to Vegas odds, Barkley is the favorite to win this year's Heisman Trophy – but we know how well that worked out for Andrew Luck last season. Barkley, a darkhorse candidate by the end of last season, put up numbers comparable to Luck's: the USC quarterback threw for 3,528 yards, 39 touchdowns and just 7 interceptions. He has the best wide receiver duo on the nation in Robert Woods and Marqise Lee, and he should, at the very least, be in New York this December. Montee Ball – RB, Wisconsin Ball was a finalist for the Heisman last season after tying Barry Sanders' single season record of 39 touchdowns. He had a rocky offseason – first he w...
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