Qualitative Descriptions of Image in the Gaussian Scale-Space

Abstract

This article addresses qualitative descriptions of image which characterise hierarchy and configuration of image structure. The qualitative descriptions are derived from trajectories of stationary points in the Gaussian scale-space and the gradient field of the scale-space image, which are called respectively “stationary curves” and “figure field”. The stationary curves and figure-field fluxes define the scale-space hierarchy, which is explicitly described as a single tree by introducing a point at infinity. The configuration of image structure at fixed scale is represented by a pseudograph which is obtained from the figure field. The Voronoi tessellation is also employed to extract boundaries of image segments.