Non-Gaussian Scale Space Filtering with 2 by 2 Matrix of Linear Filters

TL;DR

This paper demonstrates that a non-Gaussian scale space can be constructed using a 2x2 matrix of linear filters, expanding the possibilities beyond traditional Gaussian kernels.

Contribution

It introduces a novel approach using a matrix of filters to create non-Gaussian scale spaces, with derived conditions and numerical demonstrations.

Findings

Non-Gaussian scale space constructed with 2x2 filter matrix

Derived sufficient conditions for filter matrices to form scale spaces

Numerical examples validate the proposed method

Abstract

Construction of a scale space with a convolution filter has been studied extensively in the past. It has been proven that the only convolution kernel that satisfies the scale space requirements is a Gaussian type. In this paper, we consider a matrix of convolution filters introduced in [1] as a building kernel for a scale space, and shows that we can construct a non-Gaussian scale space with a $2\times 2$ matrix of filters. The paper derives sufficient conditions for the matrix of filters for being a scale space kernel, and present some numerical demonstrations.