Geometry and Radiometry Invariant Matched Manifold Detection and Robust Homography Estimation

Abstract

We elaborate on the problem of robust homography estimation based on a novel framework of geometry and radiometry invariant matched manifold detection: Any two observations on the same planar surface are related through a geometric transformation described by a homography, and some radiometric transformation. Using the proposed approach the surface image is tessellated into tiles, such that locally on each tile, the geometric transformation is approximately affine, and the radiometric transformation is monotone. Applying to each of the observations on a surface tile, the radiometry invariant universal manifold embedding (RIUME) operator, the set of all possible observations on that tile is mapped to a single linear subspace of some high dimensional Euclidean space - invariant to monotonic amplitude transformations, and to affine geometric transformations. Thus, by tessellating the observed surface into a set of tiles and matching each tile using the RIUME matched manifold detector to the hypothesized corresponding tile in the other observation on that surface, an efficient method for robust and dense matching of large patches on different observations of the surface is established. Due to the high accuracy of the obtained tile matches, the outliers problem is eliminated. Hence a linear algorithm like the DLT yields accurate estimates of the homography parameters.