TLS and Constrained TLS Neural Networks for Computer Vision

Abstract

This paper deals with the exploitation of the epipolar constraint information for the construction of the essential matrix (fundamental matrix for uncalibrated images), which, once decomposed, solves the structure from motion problem. This technique has been longly considered inferior to the techniques which use the optical flow information, because of its high sensitivity to noise. The approach used here, which is particularly robust to noise, both demonstrates the validity and presents an extension of the essential matrix approach. Once established the fact that the problem at hand is Total Least Squares (TLS) with a certain structure, a statistical analysis of the problem suggests the use of the Constrained TLS in order to take in account the linear dependences of the noise components in the coefficients. This leads to the CTLS and CTLSn EXIN neurons which are simple variants (change of metrics) of the TLS EXIN linear neuron which solves the basic TLS problem. These neurons are able to yield good results even in the presence of an outlier contamination of half the point matches.