Determining Accurate Locations of Edges in Natural Images: A Phase-Based, Nonparametric Framework

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Abstract

We propose a phase-based, nonparametric framework for determining accurate locations of edges in natural images. The basic idea is: we consider the phases of an edge’s positive frequency coefficients lie at the heart of accurately estimating the locations. In the spirit of this idea, we construct a linear representation of images whose phases in multiple bands are almost linear functions of the locations, which guarantees even minuscule location variation be captured by changes in phases. In each of those bands, the fields of phases represent the locations of edges with particular resolution and along particular direction, and thereby the representation offers a nonparametric framework for gathering multi-resolution and multi-directional pieces of evidence about an edge’s locations to jointly locate the edge. Our method quantifies an edge’s spatial shift that is less than 0.01 pixel and demonstrates its periodic movement within 0.35-pixel range in natural images. This remarkable location estimation performance verifies our framework’s ability in identifying accurate locations of edges and opens the door to unveil imperceptible phenomena that are not previously detected.