Stochastic Texture Difference for Scale-Dependent Data Analysis
This work addresses the problem of scale-dependent texture analysis for researchers in image processing and data science, but it appears incremental as it builds on existing kernel-based and random walk techniques.
The paper introduces the Stochastic Texture Difference method for analyzing data at specific spatial and value scales by using constrained random walks to represent textures as probability distributions and defining differences via distances in a reproducing kernel Hilbert space. It demonstrates the method's ability to infer characteristic scales in signals and images, though no concrete numerical results are provided.
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.