Object triangulation, 3-D object tracking, feature correspondence, and camera calibration are key problems for estimation from camera networks. This paper addresses these problems within a unified Bayesian framework for joint multi-object tracking and sensor registration. Given that using standard filtering approaches for state estimation from cameras is problematic, an alternative parametrisation is exploited, called disparity space. The disparity space-based approach for triangulation and object tracking is shown to be more effective than non-linear versions of the Kalman filter and particle filtering for non-rectified cameras. The approach for feature correspondence is based on the Probability Hypothesis Density (PHD) filter, and hence inherits the ability to update without explicit measurement association, to initiate new targets, and to discriminate between target and clutter. The PHD filtering approach then forms the basis of a camera calibration method from static or moving objects. Results are shown on simulated data.
@cite_15: The problem considered involves the use of a sequence of noisy monocular images of a three-dimensional moving object to estimate both its structure and kinematics. The object is assumed to be rigid, and its motion is assumed to be smooth. A set of object match points is assumed to be available, consisting of fixed features on the object, the image plane coordinates of which have been extracted from successive images in the sequence. Structure is defined as the 3-D positions of these object feature points, relative to each other. Rotational motion occurs about the origin of an object-centered coordinate system, while translational motion is that of the origin of this coordinate system. In this work, which is a continuation of the research done by the authors and reported previously (ibid., vol.PAMI-8, p.90-9, Jan. 1986), results of an experiment with real imagery are presented, involving estimation of 28 unknown translational, rotational, and structural parameters, based on 12 images with seven feature points. >
@cite_36: The error sensitivity in the estimation of the 3-D motion and the normal of a planar surface from an instantaneous motion field is studied. The statistical theory or the Cramer-Rao lower bound is used for error covariance in the estimated motion and structure parameters. This enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion field. The obtained lower-bound-matrix is studied analytically with respect to measurement noise, size of the field of view, and the motion-geometry configuration. The coupling between translation and rotation is exacerbated if the field of view and the slant of the plane become smaller, and the deviation of the translation from the viewing direction becomes larger. The relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the plane-normal, the size of the field of view, and the distance from the perceived plane and the translation magnitude are discussed. >
@cite_6: 
@cite_2: The present state-of-the-art in computing the error statistics in three-dimensional (3-D) reconstruction from video concentrates on estimating the error covariance. A different source of error which has not received much attention is the fact that the reconstruction estimates are often significantly statistically biased. In this paper, we derive a precise expression for the bias in the depth estimate, based on the continuous (differentiable) version of structure from motion (SfM). Many SfM algorithms, or certain portions of them, can be posed in a linear least-squares (LS) framework Ax=b. Examples include initialization procedures for bundle adjustment or algorithms that alternately estimate depth and camera motion. It is a well-known fact that the LS estimate is biased if the system matrix A is noisy. In SfM, the matrix A contains point correspondences, which are always difficult to obtain precisely; thus, it is expected that the structure and motion estimates in such a formulation of the problem would be biased. Existing results on the minimum achievable variance of the SfM estimator are extended by deriving a generalized Cramer-Rao lower bound. A detailed analysis of the effect of various camera motion parameters on the bias is presented. We conclude by presenting the effect of bias compensation on reconstructing 3-D face models from rendered images.
@cite_46: One of the major areas in research on dynamic scene analysis is recovering 3-D motion and structure from optical flow information. Two problems which may arise due to the presence of noise in the flow field are examined. First, motion parameters of the sensor or a rigidly moving object may be extremely difficult to estimate because there may exist a large set of significantly incorrect solutions which induce flow fields similar to the correct one. The second problem is in the decomposition of the environment into independently moving objects. Two such objects may induce optical flows which are compatible with the same motion parameters, and hence, there is no way to refute the hypothesis that these flows are generated by one rigid object. These ambiguities are inherent in the sense that they are algorithm-independent. Using a mathematical analysis, situations where these problems are likely to arise are characterized. A few examples demonstrate the conclusions. Constraints and parameters which can be recovered even in ambiguous situations are presented. >
@cite_10: 
The fact that image measurements are inherently noisy, and hence estimation from them requires statistical methodology, has been recognised by many researchers. Statistical methods for estimating the uncertainty in 3-D, such as finding the Cramer-Rao Lower Bound (CRLB), have previously been investigated @cite_15 @cite_2 @cite_10 , though researchers often transform the measurement or linearise the system before estimating the uncertainty, thereby losing the underlying statistical sensor characteristics in the process. There is a consensus in that the uncertainty in triangulated estimates from stereo cameras, or monocular sequences, is non-Gaussian and not trivially estimated @cite_6 . Furthermore, the importance of fusing the estimates given by several complementary cameras is recognised as an instrumental way of reducing the uncertainty in triangulated estimates @cite_46 @cite_36 .