The Monogenic Scale Space on a Rectangular Domain and its Features.

In this paper we present a novel method to implement the monogenic scale space on a rectangular domain. The monogenic scale space is a vector valued scale space based on the Poisson scale space, which establishes a sophisticated alternative to the Gaussian scale space. Previous implementations of the monogenic scale space are Fourier transform based, and therefore suffer from the implicit periodicity in case of finite domains. The features of the monogenic scale space, including local amplitude, local phase, local orientation, local frequency, and phase congruency, are much easier to interpret in terms of image features evolving through scale than in the Gaussian case. Furthermore, applying results from harmonic analysis, relations between the features are obtained which improve the understanding of image analysis. As applications, we present a very simple but still accurate approach to image reconstruction from local amplitude and local phase and a method for extracting the evolution of lines and edges through scale. [ABSTRACT FROM AUTHOR]