On Estimation of Fundamental Matrix in Computational Stereo

We address the problem of estimating a fundamental matrix from a given set of corresponding pixels in two perspective images of a 3D scene that form a stereopair. The 3x3 fundamental matrix of rank 2 determines the corresponding epipolar lines in both images. Experiments with real stereo pairs have established the main reasons for instabilities of the well-known linear estimation based on the 8-parameter representation of a matrix. We compare three alternative 8-parameter representations and propose an enhanced estimation scheme that combines the linear estimation of the six parameters with the subsequent non-linear minimisation of the total distance between the corresponding pixels and relevant epipolar lines. The latter non-linear minimisation is done first by the direct exhaustion of the remaining two parameters and then by the local minimisation of the total distance in a vicinity of the minimum found by the exhaustion. 1 The University of Auckland, Computer Science Department, CITR, Tamaki Campus (Building 731), Glen Innes, Auckland, New Zealand On Estimation of Fundamental Matrix in Computational Stereo Yuping Li and Georgy Gimel'farb CITR, Department of Computer Science Tamaki Campus, The University of Auckland Private Bag 92019, Auckland, New Zealand Abstract: We address the problem of estimating a fundamental matrix from a given set of corresponding pixels in two perspective images of a 3D scene that form a stereopair. The 3 3 fundamental matrix of rank 2 determines the corresponding epipolar lines in both images. Experiments with real stereo pairs have established the main reasons for instabilities of the well-known linear estimation based on the 8-parameter representation of a matrix. We compare three alternative 8-parameter representations and propose an enhanced estimation scheme that combines the linear estimation of the six parameters with the subsequent non-linear minimisation of the total distance between the corresponding pixels and relevant epipolar lines. The latter non-linear minimisation is done rst by the direct exhaustion of the remaining two parameters and then by the local minimisation of the total distance in a vicinity of the minimum found by the exhaustion. We address the problem of estimating a fundamental matrix from a given set of corresponding pixels in two perspective images of a 3D scene that form a stereopair. The 3 3 fundamental matrix of rank 2 determines the corresponding epipolar lines in both images. Experiments with real stereo pairs have established the main reasons for instabilities of the well-known linear estimation based on the 8-parameter representation of a matrix. We compare three alternative 8-parameter representations and propose an enhanced estimation scheme that combines the linear estimation of the six parameters with the subsequent non-linear minimisation of the total distance between the corresponding pixels and relevant epipolar lines. The latter non-linear minimisation is done rst by the direct exhaustion of the remaining two parameters and then by the local minimisation of the total distance in a vicinity of the minimum found by the exhaustion.