A probabilistic definition of intrinsic dimensionality for images

Abstract

In this paper we address the problem of appropriately representing the intrinsic dimensionality of image neighborhoods. This dimensionality describes the degrees of freedom of a local image patch and it gives rise to some of the most often applied corner and edge detectors. It is common to categorize the intrinsic dimensionality (iD) to three distinct cases: i0D, i1D, and i2D. Real images however contain combinations of all three dimensionalities which has to be taken into account by a continuous representation. Based on considerations of the structure tensor, we derive a cone-shaped iD-space which leads to a probabilistic point of view to the estimation of intrinsic dimensionality. © Springer-Verlag Berlin Heidelberg 2003.