Detecting edges is a fundamental problem in computer vision with many applications, some involving very noisy images. While most edge detection methods are fast, they perform well only on relatively clean images. Indeed, edges in such images can be reliably detected using only local filters. Detecting faint edges under high levels of noise cannot be done locally at the individual pixel level, and requires more sophisticated global processing. Unfortunately, existing methods that achieve this goal are quite slow. In this paper we develop a novel multiscale method to detect curved edges in noisy images. While our algorithm searches for edges over a huge set of candidate curves, it does so in a practical runtime, nearly linear in the total number of image pixels. As we demonstrate experimentally, our algorithm is orders of magnitude faster than previous methods designed to deal with high noise levels. Nevertheless, it obtains comparable, if not better, edge detection quality on a variety of challenging noisy images.
@cite_5: This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.
@cite_14: Abstract : The report developes a parametric model for a computer-controlled moveable camera on a pan-tilt head. The model expresses the transform relating object space to image space as a function of the control variables of the camera. We constructed a calibration system for measuring the model parameters which has a demonstrated accuracy more than adequate for our present needs. We have also identified the major source of error in model measurement to be undesired image motion and have developed means of measuring and compensating for some of it and eliminating other parts of it. The system can measure systematic image distortions if they become the major accuracy limitation. It has been shown how to generalize the model to handle small systematic errors due to aspects of pan-tilt head geometry not presently accounted for. The report demonstrates the model's application in stereo vision and have shown how it can be applied as a predictive device in locating objects of interest and centering them in an image. (Author)
@cite_8: A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of ∇ 2 G(x, y) * I(x, y) for image I, where G(x, y) is a two-dimen­sional Gaussian distribution and ∇ 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination bound­aries, and these all have the property that they are spatially localized. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the opera­tion of forming oriented zero-crossing segments from the output of centre-surround ∇ 2 G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).
In this paper we focus on the problem of detecting step edges at high levels of noise. As mentioned in the introduction, this is an important task in a variety of imaging domains. One of the first proposed methods for step edge detection was the Sobel operator @cite_14 , which does so by thresholding the gradient magnitude at each pixel separately. Marr & Hildreth @cite_8 proposed to detect edges by identifying the zero crossings of a 2D Laplacian of a Gaussian filter applied to the image. These local approaches for edge detection are very efficient, essentially with linear-time complexity in the total number of pixels. However, due to their local nature, they are sensitive to noise and exhibit poor performance at low SNR. One exception is the algorithm suggested by Canny @cite_5 , which extends Sobel by hysteresis thresholding of the local gradient magnitudes. This post-processing operation significantly improves its robustness to noise. We thus choose the Canny algorithm as a baseline for comparison to our work.