Sparse Representation based Anomaly. Detection with Enhanced Local Dictionaries. Sovan Biswas and R. Venkatesh Babu. Vid
Sparse Representation based Anomaly Detection with Enhanced Local Dictionaries Sovan Biswas and R. Venkatesh Babu Video Analytics Lab, Indian Institute of Science, Bangalore, India Quantitative Results: ROC
Generally, anomaly (e) is defined as e ∝ dist(X , y ) ◮ In sparse framework, the anomaly is defined as e ∝ ky − Dαk2 where, dictionary is defined as D = f (X ) ◮ So, if data Xi is related to Xj by Ψji X˜j = Ψji Xi T T ˜ ˜ subject to Xj Xj = Xj Xj ◮ Then, Xi ≈ Di α ⇒ Ψji Xi ≈ Ψji Di α ˜jα ⇒ ˜ j = Ψji Di X˜j ≈ D D Dictionary Enhancement Ψji has the following properties det(Ψji ) = 1 or −1 −1 ◮ Ψij = Ψ ji ◮
As,
T Xj Xj T Xj Xj T Qj Λj Qj
T ˜ ˜ = Xj Xj T = (Ψji Xi )(Ψji Xi ) T T = Ψji Qi Λi Qi Ψji
Estimating Ψji ,
Qj = Ψji Qi −1 Ψji = Qi Qj subject to kΛi − Λj k2 ≤ ǫ ˜ j ] where D ˜ j = Ψji Di ◮ Enhanced dictionary Dj = [Dj , D ◮
The Proposed Approach Features for each dense space-time cubes ◮ Foreground pixel occupancy ◮ Histogram of optical flow (HOF) ◮ Flow magnitude ◮ Learn local dictionary for each region during ◮ Dictionary enhancement from neighborhood dictionaries ◮ l1-minimization solving to obtain sparse α 1 λ2 2 2 min ky − Dαk2 + λ1kαk1 + kαk2 α 2 2 ◮ Final anomaly is obtained as: e = w1 ∗ ky − Dαk2 + w2 ∗ ky − Dαk2 + w3 ∗ kWαk1 where, w3 ≤ w1 ≤ w2.
True Positve Rate (recall)
0.6 0.4 0.2
The Proposed Approach Sparse LSA MDT MPPCA Social Force
0.5 False Positve Rate
1
True Positve Rate (recall)
ROC (AUC: 85.95%, EER: 20.38%) 1 0.8 0.6 0.4 0.2 0 0
With Dictionary Enhancement Without Dictionary Enhancement
0.5 False Positve Rate
ROC (AUC: 85.95%, EER: 20.38%) 1 0.8 0.6 0.4 0.2 0 0
Ped1: Frame level anomaly
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0.8
0 0
Proposed Framework
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ROC (AUC: 85.85%, EER: 19.22%) 1
Ped1: Effect of enhancement
0.5 False Positve Rate
1
ROC (AUC: 50.63%, EER: 48.92%) 1 The Proposed Approach Sparse MDT MPPCA
0.8 0.6 0.4 0.2 0 0
1
The Proposed Approach MDT MPPCA Social Force
Ped2: Frame level anomaly True Positve Rate (recall)
Motion based anomaly detection using sparse representation over normal dictionary. ◮ Enhancing the local dictionaries based on the similarity of usual behavior with its spatial neighbors. ◮
True Positve Rate (recall)
Objective
0.5 False Positve Rate
1
Ped1: Pixel level anomaly
Quantitative Results: Detection Accuracy Approaches Ped1 (EER) Ped2 (EER) SF 31% 42% MPPCA 40% 30% SF-MPPCA 32% 36% MDT 25% 25% Sparse 19% LSA 16% Ours (No Enhancement) 19.53% 21.26% Ours (With Enhancement) 19.22% 20.38%
Frame Level Comparison Approaches
RD
Detection Speed AUC (frame per sec.) 17.9% 20.5% 44% 0.04 fps 46.1% 0.25 fps
SF 21% MPPCA 18% MDT 45% Sparse 46% Our (With 51.02% 50.63% Enhancement)
∼ 3 fps
Pixel Level Comparison on Ped1
Qualitative Results
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E-mail:
[email protected],
[email protected]
(a) Video Sequence Ped1 Test 001
(b) Video Sequence Ped1 Test 019
Conclusion Proposed enhancing the local dictionaries with the help of spatial neighbors to improve anomaly detection. Website: val.serc.iisc.ernet.in
