Stochastic Texture Difference for Scale-Dependent Data Analysis

TL;DR

The paper presents a novel stochastic texture difference method for analyzing data at specific spatial and value scales, capable of handling diverse data types through kernel-based probability distributions.

Contribution

It introduces a scale-dependent texture difference operator based on constrained random walks and kernel methods, applicable to various data types beyond scalar images.

Findings

Effective in inferring spatial and data characteristic scales.

Applicable to diverse data types including images, strings, and graphs.

Demonstrates scale-dependent analysis capabilities.

Abstract

This article introduces the Stochastic Texture Difference method for analyzing data at prescribed spatial and value scales. This method relies on constrained random walks around each pixel, describing how nearby image values typically evolve on each side of this pixel. Textures are represented as probability distributions of such random walks, so a texture difference operator is statistically defined as a distance between these distributions in a suitable reproducing kernel Hilbert space. The method is thus not limited to scalar pixel values: any data type for which a kernel is available may be considered, from color triplets and multispectral vector data to strings, graphs, and more. By adjusting the size of the neighborhoods that are compared, the method is implicitly scale-dependent. It is also able to focus on either small changes or large gradients. We demonstrate how it can be used to infer spatial and data value characteristic scales in measured signals and natural images.