DECOLOR: A challenger to PCP

The authors of the following paper decided to change the penalty for the error term from an L_1 term in the PCP implementation into an L_0 one. They did not touch the proxy for the rank functional and came up with DECOLOR as featured in Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation by Xiaowei Zhou, Can Yang, Weichuan Yu. The abstract reads:

Object detection is a fundamental step for automated video analysis in many vision applications. Object detection in a video is usually performed by object detectors or background subtraction techniques. Often, an object detector requires manually labeled examples to train a binary classifier, while background subtraction needs a training sequence that contains no objects to build a background model. To automate the analysis, object detection without a separate training phase becomes a critical task. People have tried to tackle this task by using motion information. But existing motion-based methods are usually limited when coping with complex scenarios such as nonrigid motion and dynamic background. In this paper, we show that above challenges can be addressed in a unified framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). This formulation integrates object detection and background learning into a single process of optimization, which can be solved by an alternating algorithm efficiently. We explain the relations between DECOLOR and other sparsity-based methods. Experiments on both simulated data and real sequences demonstrate that DECOLOR outperforms the state-of-the-art approaches and it can work effectively on a wide range of complex scenarios.

The results look impressive. The DECOLOR algorithm is here and was added to the Matrix Factorization Jungle.

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