Double nuclear norm-based matrix decomposition for occluded image recovery and background modeling.

Area of Science:

• Computer Vision
• Machine Learning
• Matrix Decomposition

Background:

• Robust Principal Component Analysis (RPCA) is effective for low-rank matrix recovery with sparse errors.
• Existing methods struggle with continuous occlusion, often using L1, L2, or M-estimators for error measurement.

Purpose of the Study:

• To develop a novel matrix decomposition method (DNMD) for image data corrupted by continuous occlusion.
• To propose a more intuitive low-rank assumption for characterizing both image data and occlusion.
• To extend the transductive DNMD into an inductive version (IDNMD).

Main Methods:

• Introduced Double Nuclear Norm-based Matrix Decomposition (DNMD) with a unified low-rank assumption for data and occlusion.
• Characterized occlusion-induced error using the nuclear norm.
• Solved DNMD using the alternating direction method of multipliers (ADMM) involving a singular value shrinkage operator.
• Extended DNMD to an inductive version (IDNMD).

Main Results:

• DNMD provides a more intuitive low-rank characterization of occlusion compared to RPCA.
• The proposed methods (DNMD and IDNMD) effectively remove occlusion from face images.
• Demonstrated effectiveness in background modeling from surveillance videos.

Conclusions:

• DNMD and IDNMD offer a robust and effective approach for handling continuous occlusion in image data.
• The nuclear norm is a suitable measure for occlusion-induced error in this context.
• The methods show significant promise for applications in image restoration and video analysis.