Parsing scale-space and spatial stability analysis

Abstract

The scale-space S( x, σ) of a signal I( x) is defined as the space of the zero-crossings from {∇ 2 G(σ)* I( x)}, where G is a Gaussian filter. We present a new method for parsing scale-space, spatial stability analysis, that allows the localization of region boundaries from scale space. Spatial stability analysis is based on the observation that zero-crossings of region boundaries remain spatially stable over changes in filter scale. It is shown that spatial stability analysis leads to an edge detection scheme with good noise resilience characteristics and that it can lead to improvements in “shape from texture” methods.