Affine Subspace Models and Clustering for Patch-Based Image Denoising

TL;DR

This paper introduces affine subspace models for clustering image patches in denoising tasks, improving geometric fit and denoising performance over traditional linear subspace methods.

Contribution

It proposes the use of affine subspace models for image patch clustering and presents a simple denoising algorithm based on this approach.

Findings

Affine subspace clustering improves clustering accuracy.

The proposed denoising algorithm outperforms traditional methods.

Experimental results show enhanced denoising quality.

Abstract

Image tile-based approaches are popular in many image processing applications such as denoising (e.g., non-local means). A key step in their use is grouping the images into clusters, which usually proceeds iteratively splitting the images into clusters and fitting a model for the images in each cluster. Linear subspaces have emerged as a suitable model for tile clusters; however, they are not well matched to images patches given that images are non-negative and thus not distributed around the origin in the tile vector space. We study the use of affine subspace models for the clusters to better match the geometric structure of the image tile vector space. We also present a simple denoising algorithm that relies on the affine subspace clustering model using least squares projection. We review several algorithmic approaches to solve the affine subspace clustering problem and show experimental results that highlight the performance improvements in clustering and denoising.