Differential matching constraints

Abstract

We introduce a finite difference expansion for closely spaced cameras in projective vision, and use it to derive differential analogues of the finite-displacement projective matching tensors and constraints. The results are simpler, more general and easier to use than Astrom & Heyden's time-derivative based 'continuous time matching constraints'. We suggest how to use the formalism for 'tensor tracking'-propagation of matching relations against a fixed base image along an image sequence. We relate this to non-linear tensor estimators and show how 'unwrapping the optimization loop' along the sequence allows simple 'linear n point' update estimates to converge rapidly to statistically near-optimal, near-consistent tensor estimates as the sequence proceeds. We also give guidelines as to when difference expansion is likely to be worthwhile as compared to a discrete approach.