Geometry-Aware Neighborhood Search for Learning Local Models for Image Superresolution

Area of Science:

• Computer Vision
• Machine Learning
• Image Processing

Background:

• Local learning of sparse image models is crucial for solving inverse problems in computer vision.
• Traditional K-means clustering with Euclidean distance may fail for data on non-Euclidean manifolds.
• Effective local model learning requires appropriate dissimilarity measures that respect data geometry.

Purpose of the Study:

• To develop novel algorithms for selecting optimal local training subsets for sparse image models.
• To address the limitations of Euclidean distance in capturing data manifold geometry.
• To improve the accuracy of reconstructing input test samples by learning geometry-aware local models.

Main Methods:

• Proposed adaptive geometry-driven nearest neighbor search (AGNN) algorithm, an extension of replicator graph clustering.
• Introduced geometry-driven overlapping clusters (GOCs) as a simpler, non-adaptive alternative for subset selection.
• Evaluated AGNN and GOCs on image superresolution tasks.

Main Results:

• AGNN and GOCs demonstrated superior performance in image superresolution compared to spectral clustering, soft clustering, and geodesic distance-based methods.
• The proposed methods effectively leverage the underlying data geometry for improved local model learning.
• Geometry-aware subset selection leads to better reconstruction of input test samples.

Conclusions:

• AGNN and GOCs offer effective solutions for local learning of sparse image models by incorporating data geometry.
• These geometry-driven approaches provide significant improvements over traditional clustering and subset selection methods.
• The proposed algorithms enhance the performance of inverse problem solutions in computer vision, particularly in image superresolution.