Compressed dynamic mode decomposition for background modeling

N. Benjamin Erichson, Steven L. Brunton, J. Nathan Kutz

Research output: Contribution to journalArticlepeer-review

67 Citations (Scopus)
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Abstract

We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition is a regression technique that integrates two of the leading data analysis methods in use today: Fourier transforms and singular value decomposition. Borrowing ideas from compressed sensing and matrix sketching, cDMD eases the computational workload of high-resolution video processing. The key principal of cDMD is to obtain the decomposition on a (small) compressed matrix representation of the video feed. Hence, the cDMD algorithm scales with the intrinsic rank of the matrix, rather than the size of the actual video (data) matrix. Selection of the optimal modes characterizing the background is formulated as a sparsity-constrained sparse coding problem. Our results show that the quality of the resulting background model is competitive, quantified by the F-measure, recall and precision. A graphics processing unit accelerated implementation is also presented which further boosts the computational performance of the algorithm.
Original languageEnglish
Number of pages14
JournalJournal of Real-Time Image Processing
VolumeFirst Online
Early online date29 Nov 2016
DOIs
Publication statusE-pub ahead of print - 29 Nov 2016

Keywords

  • Dynamic Mode Decomposition
  • Background modeling
  • Matrix sketching
  • Sparse coding
  • GPU-accelerated computing

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