Affine Subspace Models and Clustering for Patch-Based Image Denoising

2025-12-08

AI Summary

Conventional linear subspace models suffer from geometric mismatch when modeling image patches, as patches are nonnegative and not centered at the origin, violating the core assumptions of linear subspaces. Method: This paper systematically introduces affine subspace modeling—replacing linear subspaces for the first time—to more accurately capture the intrinsic clustering geometry of image patches in vector space. We propose an affine subspace-based block clustering framework, integrating least-squares projection for joint patch modeling and denoising, and incorporate multiple robust optimization strategies to enhance solution stability. Contribution/Results: Experiments demonstrate significant improvements in both block clustering accuracy and denoising performance over state-of-the-art linear subspace methods on standard benchmarks, empirically validating that affine modeling better aligns with the geometric priors inherent in natural image patches.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Develop affine subspace models for image patch clustering.
• Improve geometric matching in non-negative image vector spaces.
• Enhance denoising via affine subspace clustering and projection.

Innovation

• Affine subspace models for image patch clustering
• Least squares projection for denoising algorithm
• Geometric structure matching in tile vector space