The document discusses the comparison of matrix completion algorithms for initializing background models in video surveillance, focusing on traditional and advanced background subtraction methods. It presents a proposed approach that uses motion detection and frame selection to reduce the number of relevant frames for matrix completion, demonstrating its effectiveness through experimental results on the scene background initialization dataset. The findings indicate the potential for improving background model recovery and suggest future research directions in real-time video analysis.

1. Comparison of Matrix Completion Algorithms
for Background Initialization in Videos
Andrews Sobral, Thierry Bouwmans and El-hadi ZahZah
Ph.D. Student, Computer Vision
Lab. L3I/MIA – University of La Rochelle, France

2. Summary
▪ Context
▪ Understanding an Intelligent Video Surveillance Framework
▪ Introduction to Background Subtraction
▪ Background Model Initialization Problem
▪ Matrix Completion
▪ Proposed Approach
▪ Experimental results
▪ Conclusions

3. !
Video Content Analysis
(VCA) or Video Analytics
Behavior
Analysis
Image
acquisition and
preprocessing
Object
Detection
Object
Tracking
event location
Intrusion
detection
Collision
prevention
Target detection
and tracking
Anomaly
detection
Target behavior
analysis
Traffic data
collection and
analysis
activity report
Understanding an Intelligent Video Surveillance Framework
supervisor
Behind the Scenes of an Intelligent Video Surveillance
Framework
!
Example of automatic
incident detection
our focus

4. Introduction to Background Subtraction
Initialize
Background Model
frame model
Foreground
Detection
Background Model
Maintenance
our focus

5. Background subtraction methods
Traditional methods:
• Basic methods, mean and variance over time
• Fuzzy based methods
• Statistical methods
• Non-parametric methods
• Neural and neuro-fuzzy methods
Matrix and Tensor Factorization methods:
• Eigenspace-based methods (PCA / SVD)
• RPCA, LRR, NMF, MC, ST, etc.
• Tensor Decomposition, NTF, etc.
BGSLibrary (C++)
https://github.com/andrewssobral/bgslibrary
A large number of algorithms have been proposed for background subtraction
over the last few years:
LRSLibrary (MatLab)
https://github.com/andrewssobral/lrslibrary
our focus
Andrews Sobral and Antoine Vacavant. A comprehensive review of background subtraction algorithms
evaluated with synthetic and real videos. Computer Vision and Image Understanding (CVIU), 2014.
http://dx.doi.org/10.1016/j.cviu.2013.12.005

6. Introduction to Matrix Completion (MC)
▪ MC can be formulated as the problem of o recover a low rank matrix (L) from the partial
observations of its entries:
L
Underlying low-rank matrix
A
Matrix of partial observations
http://perception.csl.illinois.edu/matrix-rank/home.html

7. Applying MC for Background Model Initialization
▪ Proposed approach:

8. Motion Detection and Frame Selection
92 relevant frames are selected from a total of 296 frames (68,92% of reduction).

9. Matrix Completion Process
Illustration of the matrix completion process. From the left to the right: a) the
selected frames in vectorized form (our observation matrix), b) the moving
regions are represented by non-observed entries (black pixels), c) the moving
regions filled with zeros (modified version of the observation matrix), and d) the
recovered matrix after the matrix completion process.

10. Experimental results
Scene Background Initialization (SBI) data set
SBI data set provide 7 image sequences and corresponding ground truth
backgrounds. Matlab scripts are provided for evaluating results in terms of eight
metrics that include those used in the literature for background estimation.
Lucia Maddalena and Alfredo Petrosino, Towards Benchmarking Scene Background Initialization, arXiv:1506.04051
http://sbmi2015.na.icar.cnr.it/

11. Matrix Completion Algorithms
The algorithms were implemented in MATLAB (R2014a) running on a laptop
computer with Windows 7 Professional 64 bits, 2.7 GHz Core i7-3740QM
processor and 32Gb of RAM.

12. Quantitative results on SBI data set

13. Quantitative results on SBI data set

14. Visual results on SBI data set

15. Conclusions
▪ The key idea is to eliminate the redundant frames, and consider its moving regions as
non-observed values. This approach results in a matrix completion problem, and the
background model can be recovered even with the presence of missing entries.
▪ The experimental results on the SBI data set shows the comparative evaluation of these
recent methods, and highlights the good performance of LRGeomCG method over its
direct competitors.
▪ Future research may concern to evaluate incremental and real-time approaches of
matrix completion algorithm applied in streaming videos.
▪ MATLAB codes available: https://sites.google.com/site/mc4bmi/