Some Theory for Texture Segmentation

TL;DR

This paper provides theoretical guarantees for texture segmentation methods based on local feature extraction and clustering, demonstrating consistency for both stationary and non-stationary textures with numerical validation.

Contribution

It introduces a theoretical framework proving the consistency of clustering-based texture segmentation methods for stationary and non-stationary textures.

Findings

Consistency of clustering methods for stationary textures with Gaussian Markov models

Consistency of clustering methods for non-stationary textures with location features

Numerical experiments validating theoretical results

Abstract

In the context of texture segmentation in images, and provide some theoretical guarantees for the prototypical approach which consists in extracting local features in the neighborhood of a pixel and then applying a clustering algorithm for grouping the pixel according to these features. On the one hand, for stationary textures, which we model with Gaussian Markov random fields, we construct the feature for each pixel by calculating the sample covariance matrix of its neighborhood patch and cluster the pixels by an application of k-means to group the covariance matrices. We show that this generic method is consistent. On the other hand, for non-stationary fields, we include the location of the pixel as an additional feature and apply single-linkage clustering. We again show that this generic and emblematic method is consistent. We complement our theory with some numerical experiments performed on both generated and natural textures.