MATCHED MANIFOLD DETECTION FOR GROUP-INVARIANT REGISTRATION AND CLASSIFICATION OF IMAGES

Consider the set of possible observations turned out by geometric and radiometric transformations of an object. In those cases where the geometric deformations are affine and the radiometric deformations are monotonic, the radiometry invariant universal manifold embedding (RIUME) provides a mapping from the orbit of deformed observations to a single low dimensional linear subspace of Euclidean space. This linear subspace is invariant to the geometric and radiometric transformations and hence is a representative of the orbit. In the unsupervised detection problem, subspaces evaluated from two observations are tested for the similarity of the observed object and their relative transformation is estimated from the RIUME matrix representation. In the presence of observation noise the resulting RIUME subspaces are noisy. We derive a method for estimating the mean subspace representation of a manifold of deformed observations. To optimize the performance of the matched manifold detector, an analytic solution for choosing the RIUME nonlinear operators is derived. The invariant representation of the object is the basis of a matched manifold detection and tracking framework for objects that undergo complex geometric and radiometric deformations. Experimental results on natural scenes demonstrate the generality and applicability of the RIUME framework for classification, detection, and dense registration.