The maximal scale ridge: Incorporating scale into the ridge definition

Abstract

The maximal convexity ridge is not well suited for the analysis of medial functions or, it can be argued, for the analysis of any function that is created via convolution with a kernel based on the Gaussian. In its place one should use the maximal scale ridge, which takes scale’s distinguished role into account. We present the local geometric structure of the maximal scale ridge of smooth and Gaussian blurred functions, a result that complements recent work on scale selection. We also discuss the subdimensional maxima property as it relates to the maximal scale ridge, and we prove that a generalized maximal parameter ridge has the subdimensional maxima property as well.