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

TL;DR

This paper introduces geometry-aware algorithms for selecting local training samples that improve image reconstruction tasks by respecting data manifold structures, outperforming traditional clustering methods.

Contribution

It proposes two novel algorithms, AGNN and GOC, for geometry-aware neighborhood selection in local models for image reconstruction.

Findings

AGNN and GOC outperform spectral clustering and geodesic distance methods.

Algorithms improve results in super-resolution, deblurring, and denoising.

AGNN adapts to data geometry, enhancing local model accuracy.

Abstract

Local learning of sparse image models has proven to be very effective to solve inverse problems in many computer vision applications. To learn such models, the data samples are often clustered using the K-means algorithm with the Euclidean distance as a dissimilarity metric. However, the Euclidean distance may not always be a good dissimilarity measure for comparing data samples lying on a manifold. In this paper, we propose two algorithms for determining a local subset of training samples from which a good local model can be computed for reconstructing a given input test sample, where we take into account the underlying geometry of the data. The first algorithm, called Adaptive Geometry-driven Nearest Neighbor search (AGNN), is an adaptive scheme which can be seen as an out-of-sample extension of the replicator graph clustering method for local model learning. The second method, called Geometry-driven Overlapping Clusters (GOC), is a less complex nonadaptive alternative for training subset selection. The proposed AGNN and GOC methods are evaluated in image super-resolution, deblurring and denoising applications and shown to outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings.