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Compressed dynamic mode decomposition for background modeling

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Erichson_2016_JRTIP_Compressed_CC.pdf (1.793Mb)
Date
29/11/2016
Author
Erichson, N. Benjamin
Brunton, Steven L.
Kutz, J. Nathan
Keywords
Dynamic Mode Decomposition
Background modeling
Matrix sketching
Sparse coding
GPU-accelerated computing
QA Mathematics
3rd-NDAS
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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.
Citation
Erichson , N B , Brunton , S L & Kutz , J N 2016 , ' Compressed dynamic mode decomposition for background modeling ' , Journal of Real-Time Image Processing , vol. First Online . https://doi.org/10.1007/s11554-016-0655-2
Publication
Journal of Real-Time Image Processing
Status
Peer reviewed
DOI
https://doi.org/10.1007/s11554-016-0655-2
ISSN
1861-8219
Type
Journal article
Rights
© The Author(s) 2016. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Description
JNK acknowledges support from Air Force Office of Scientific Research (FA9500-15-C-0039). SLB acknowledges support from the Department of Energy under award DE-EE0006785. NBE acknowledges support from the UK Engineering and Physical Sciences Research Council (EP/L505079/1).
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/9981

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