Manifold Constrained Low-Rank Decomposition
This work addresses visual data reconstruction for applications like face recognition and digit analysis, but it is incremental as it builds on existing low-rank decomposition methods.
The paper tackled the problem of low-rank decomposition for visual data under challenging conditions like occlusion and misalignment by embedding manifold priors into the framework, resulting in a consistent performance increase compared to state-of-the-art methods across various image datasets.
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.