Manifold Constrained Low-Rank Decomposition

TL;DR

This paper introduces a manifold constrained low-rank decomposition framework that enhances visual data reconstruction by incorporating manifold priors, effectively handling occlusions, noise, and misalignments in images.

Contribution

It proposes a novel framework embedding manifold priors into low-rank decomposition and an ADMM-based optimization method for improved image modeling under challenging conditions.

Findings

Improved reconstruction accuracy over state-of-the-art methods.

Robustness to occlusions, noise, and misalignments.

Effective on face, handwritten digit, and planar surface images.

Abstract

Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and misalignment from rotation or viewpoint changes. We leverage the specific structure of data in order to improve the performance of LRD when the data are not ideal. To this end, we propose a new framework that embeds manifold priors into LRD. To implement the framework, we design an alternating direction method of multipliers (ADMM) method which efficiently integrates the manifold constraints during the optimization process. The proposed approach is successfully used to calculate low-rank models from face images, hand-written digits and planar surface images. The results show a consistent increase of performance when compared to the state-of-the-art over a wide range of realistic image misalignments and corruptions.