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Statistical Estimation Theory for Computer Vision

Multi-Object Stereo Filtering in Disparity Space
S. Ivekovic and D. Clark

Stereo tracking refers to the problem of tracking a three-dimensional system from a pair of cameras. The majority of stereo tracking algorithms track the system in 3-D Euclidean space, since the operator is generally interested in knowing the position of the object in the world coordinate system. Unfortunately, the projection from the 3-
D co-ordinate space onto the image planes is non-linear and the noise is dependent on the position of the system. These facts can seriously impede the reliability of tracking algorithms. We propose a fundamentally different approach by stereo tracking in disparity space for optimal 3-D object state estimation.

The Cramer-Rao Lower Bound for 3-D State Estimation from Rectified Stereo Cameras
D. Clark and S. Ivekovic

It is well known that any 3-D state estimate computed from stereo camera measurements is corrupted by heteroscedastic noise due to the nature of the perspective projection. It is also well understood that the image measurements used to estimate the 3-D state are inherently noisy. Despite the wealth of research in this area, the accurate statistical characterisation of the uncertainty for any 3-D state estimation from stereo algorithm is less well understood. This paper presents the Cramer-Rao Lower Bound (CRLB) for 3-dimensional state estimation from a rectified stereo pair of cameras. The paper also presents a method for efficient stereo estimation via Bayesian triangulation that achieves the CRLB. These results provide a basis for 3-D statistical estimation for camera-based sensor measurements.