Shape-Tailored Local Descriptors

Traditional Descriptors aggregate data from some fixed neighborhoods around a pixel, the problem with such descriptors is that they aggregate data across different regions when we are close to the boundary and results in poor segmentation. An ideal descriptor would be tailored to the region of interest and would aggregate data only within the region of interest.

We introduce Shape-Tailored local descriptors which are given by scale spaces defined by Poisson-like partial differential equations. The key property of this descriptor is that it aggregate data only within the region of interest is immune to the problem of aggregating data across boundaries.

equation 1: Shape-Tailored local descriptor defined on region of interest 'R'

Since the region of interest is not know a priori the problem for segmentation and descriptor needs to solved jointly. The step for this joint optimization are summarized below.