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![Proposed Work
11/29
How to Choose the Classifier?
Bicego and Figueiredo, 2009 proposed a Weighted version that allow to use weights W = {w1,...,wN } in [0,1]
for the data.
R
R
R
a
wiξi
target
outlier
xi
Weighted One-Class SVM (WOC-SVM)
Minimizing the hypersphere volume implies the
minimization of R2
. To prevent the classifier from
over-fitting with noisy data, slack variables ξi are
introduced to allow some target points (respectively
outliers) outside (respectively inside) the hypersphere.
Therefore the problem is to minimize:
Θ(a,R) = R2
+C
N
∑
i=1
wi ξi (1)
where C is a user-defined parameter that controls the
trade-off between the volume and the number of
target points rejected. The larger C, the less outliers
in the hypersphere.
The BS task requires adjust the learned model to the scene variations over time](https://image.slidesharecdn.com/presentationicpr-170608133851/75/ICPR-2016-11-2048.jpg)
![Proposed Work
13/29
An Incremental Weighted One-Class SVM (IWOC-SVM)
We propose an IWOC-SVM which is closely related to the procedure proposed by Tax and Laskov (2003).
Given new samples Z1 = {x1,x2,...,xs} and its
respective weights not learned by the IWOC-SVM.
Karush-Kuhn-Tucker (KKT) conditions:
αi = 0 ⇒ ||xi −a||2
< R2
(2)
0 < αi < C ⇒ ||xi −a||2
= R2
(3)
αi = C ⇒ ||xi −a||2
> R2
(4)
The mathematical model can be defined as:
R −θ ≤ ||x −a||≤ R (5)
where θ ∈ [0,R] is relative to the distribution of
previous training set.
R
R
R
a
wiξi
target
outlier
xi
Algorithm 2 Incremental Weighted One-Class SVM
1: Require: Previous training set Z0, newly added training set Z1 and its respective weights
2: Train IWOC-SVM classifier on Z0, then split Z0 = SV0 ∪NSV0
3: Input new samples Z1. Put samples that violate KKT conditions in ZV
1 . If ZV
1 = /0, then goto 2.
4: Put samples from NSV0 that satisfy Eq. (5) into NSVS
0 .
5: Set Z0 = SV0 ∪NSVS
0 ∪ZV
1 and train IWOC-SVM classifier on Z0.
6: Output: IWOC-SVM classifier Ω and the new training set Z0.
.](https://image.slidesharecdn.com/presentationicpr-170608133851/75/ICPR-2016-13-2048.jpg)
![Proposed Work
17/29
D. Heuristic approach for Background Model Maintenance
The Small Votes Instance Selection (SVIS) introduced by Guo and Boukir (Guo and Boukir, 2015) consists of an
unsupervised ensemble margin that combines the first c(1) and second most voted class c(2) labels under the
learned model. Let vc(1)
and vc(2)
denote the relative number of votes. Then the margin, taking value in [0,1] is:
m(x) =
vc(1)
−vc(2)
L
(10)
where L represents the number of best base classifiers in the ensemble. The first smallest margin instances are
selected as support vector candidates. The strong model is updated by the first smallest margin instances. This
procedure is presented in the Algorithm 4.
This heuristic significantly reduces the IWOC-SVM training task complexity while maintaining the accuracy of the
IWOC-SVM classification.](https://image.slidesharecdn.com/presentationicpr-170608133851/75/ICPR-2016-17-2048.jpg)
Uploaded byCaroline Pacheco do Espírito Silva
ICPR 2016
The proposed method uses an online weighted ensemble of one-class SVMs for feature selection in background/foreground separation. It automatically selects the best features for different image regions. Multiple base classifiers are generated using weighted random subspaces. The best base classifiers are selected and combined based on error rates. Feature importance is computed adaptively based on classifier responses. The background model is updated incrementally using a heuristic approach. Experimental results on the MSVS dataset show the proposed method achieves higher precision, recall, and F-score than other methods compared.
ICPR 2016
- 1. Online Weighted One-ClassEnsemble for Feature Selection in Background/Foreground Separation Caroline Silva, Thierry Bouwmans, Carl Fr´elicot, Micka¨el Coustaty December 6th, 2016 - Mexico
- 2. Summary 2/29 1 Introduction 2 ProposedWork 3 Experimental Results 4 Conclusion and Future Works
- 3. Introduction 3/29 Background Subtraction Ini$alize Backgrounwd Model Background Model Maintenance Foreground Detec$on Model Input Stream Output Masks Figure:Block diagram of the background subtraction process.
- 4. Introduction 4/29 Background Subtraction Background subtractionis a widely used approach for detecting moving objects from static cameras. Figure: Moving object tracking results.
- 5. Introduction 5/29 Why is itinteresting today X1 X2 X3 X4X5 Figure: Given a complex scene with different regions X1, X2, X3, X4 and X5, each region can be characterized by different features such as: texture, color, texture-color, motion and edge. Common methods Same feature is used globally for the whole scene. Key challenges It requires a deep knowledge of the scene. It is possible to automatically select the most relevant features
- 6. Introduction 6/29 Feature Selection Traditionally, featureselection methods can be categorized into three main groups: Wrapper-based methods • employ a classification algorithm as a “black box” for selecting a set of relevant features. Embedded methods • the feature selection is incorporated as part of the classification algorithm, such as in the decision trees or in neural networks. Filter-based methods • evaluate the relevance of the features based on a statistical measure estimated directly from the data. Ensemble-based approaches for feature selection
- 7. Summary 7/29 1 Introduction 2 ProposedWork 3 Experimental Results 4 Conclusion and Future Works
- 8. Proposed Work 8/29 N u m b e r o f fra m e s 200 150 Frames 100 50 0 Feature Importance Motion Gradient Color+Texture Features Texture Color 0.6 1 0.8 0.4 0 0.2 Importance Figure:Illustration of a complex scene (left) and its features importance over time. The bar-graph (right) shows the feature importance variations for a certain region of the scene along time. The color, texture, cor-texture, gradients and motion features are represented by pink, blue, pale orange, green and dark orange color, respectively. We propose an online weighted ensemble of one-class SVMs (Support Vector Machines) for foreground-background separation. It automatically selects the best features for different regions of the image, and the more relevant features are used for foreground segmentation.
- 9.
- 10. Proposed Work 10/29 An OnlineWeighted One-Class Ensemble for Feature Selection A. Generate multiple base models N u m b e r o f fra m e s This above approach increases the diversity of base classifiers since different weights of each random sub- space are taken to distinguish the decision boundaries computed by the classifiers. Algorithm 1 Generate multiple base background models 1: Require: IWOC-SVM training procedure, training sequence X, subspace dimension p∗, number of base classifiers M, weight distribution δ(x) 2: k ← 1 3: repeat 4: Sk ← SelectRandomSubspace(X,p∗) 5: Train k-th IWOC-SVM on Sk with respect to weights w ∼ δ(x) 6: k ← k+1 7: until k > M 8: Output: trained IWOC-SVM base classifiers Ψ = {Ψ1,Ψ2,...,ΨM }
- 11. Proposed Work 11/29 How toChoose the Classifier? Bicego and Figueiredo, 2009 proposed a Weighted version that allow to use weights W = {w1,...,wN } in [0,1] for the data. R R R a wiξi target outlier xi Weighted One-Class SVM (WOC-SVM) Minimizing the hypersphere volume implies the minimization of R2 . To prevent the classifier from over-fitting with noisy data, slack variables ξi are introduced to allow some target points (respectively outliers) outside (respectively inside) the hypersphere. Therefore the problem is to minimize: Θ(a,R) = R2 +C N ∑ i=1 wi ξi (1) where C is a user-defined parameter that controls the trade-off between the volume and the number of target points rejected. The larger C, the less outliers in the hypersphere. The BS task requires adjust the learned model to the scene variations over time
- 12. 12/29 Why update thebackground model?
- 13. Proposed Work 13/29 An IncrementalWeighted One-Class SVM (IWOC-SVM) We propose an IWOC-SVM which is closely related to the procedure proposed by Tax and Laskov (2003). Given new samples Z1 = {x1,x2,...,xs} and its respective weights not learned by the IWOC-SVM. Karush-Kuhn-Tucker (KKT) conditions: αi = 0 ⇒ ||xi −a||2 < R2 (2) 0 < αi < C ⇒ ||xi −a||2 = R2 (3) αi = C ⇒ ||xi −a||2 > R2 (4) The mathematical model can be defined as: R −θ ≤ ||x −a||≤ R (5) where θ ∈ [0,R] is relative to the distribution of previous training set. R R R a wiξi target outlier xi Algorithm 2 Incremental Weighted One-Class SVM 1: Require: Previous training set Z0, newly added training set Z1 and its respective weights 2: Train IWOC-SVM classifier on Z0, then split Z0 = SV0 ∪NSV0 3: Input new samples Z1. Put samples that violate KKT conditions in ZV 1 . If ZV 1 = /0, then goto 2. 4: Put samples from NSV0 that satisfy Eq. (5) into NSVS 0 . 5: Set Z0 = SV0 ∪NSVS 0 ∪ZV 1 and train IWOC-SVM classifier on Z0. 6: Output: IWOC-SVM classifier Ω and the new training set Z0. .
- 14. Proposed Work 14/29 B. Selectionof the best base classifiers Let λcorrect k (respectively λwrong k ) be the number of times a pixel was correctly (respectively uncorrectly) classified by the k-th (k = 1,...,M) base classifier from given ground truth data. Then, the corresponding error is given by: errork = λwrong k λcorrect k +λwrong k (6) Note that only the base classifiers that have the smallest errors are combined and used to differentiate the moving objects from the background model in the scene.
- 15. 15/29 The Algorithm 3was adapted from the algorithm proposed by (Wozniak, 2013) Algorithm 3 Adaptive Importance (AI) computation 1: Require: Strong classifier H, validation set (t1,y1),...,(tN ,yN ) where ti ∈ T, yi ∈ Y = 0,1 for background and foreground examples respectively, set of L best base classifiers Ψ = {Ψ1,Ψ2,...,ΨL}, learning rate parameter γ 2: Initialize all L best classifiers with importance: βl = 1 3: repeat 4: Classify ti using the strong classifier H according to Eq. (9) 5: for l = 1 : L do 6: Checks response of Ψl and calculates their errorl according to Eq. (6) 7: For each best classifier, Ψl , update the importance βl = βl (i −1)+ Pa(Ψl )−Pa(Ψl (i−1)) (N+γ) 8: where Pa(Ψl ) = 1 −errorl according to Eq.(6). 9: end for 10: until i < N 11: Normalize the importance β of each L best classifier. 12: Output: New importance assigned to the best classifiers β = {β1,β2,...,βL}
- 16. Proposed Work 16/29 C. BackgroundDetection Given an incoming pixel x to be classified, one can define a support function associated to the target class ω for each of the L best base classifiers: ∀l = 1,...,L Fl (x,ω) = 1 s1 exp(−d(x,a)/s2) (7) where d(x,a) is a distance metric from x to the center a of the target class ω, s1 is a normalization factor and s2 is a scale parameter. Each Fl (x,ω) is then compared to a threshold t1 to obtain the positive or negative class labels:∀l = 1,...,L cl (x,ω) = 1 if Fl (x,ω) t1 −1 otherwise (8) Comparing the weighted sum of theses L class labels as in (Tax and Duin, 2001) to another threshold t2 allows to define the strong classifier for x as follows: H(x) = 1 if 1 L ∑L l=1 βl cl (x,ω) t2 0 otherwise (9) A pixel x is classified as a background pixel if H(x) = 0.
- 17. Proposed Work 17/29 D. Heuristicapproach for Background Model Maintenance The Small Votes Instance Selection (SVIS) introduced by Guo and Boukir (Guo and Boukir, 2015) consists of an unsupervised ensemble margin that combines the first c(1) and second most voted class c(2) labels under the learned model. Let vc(1) and vc(2) denote the relative number of votes. Then the margin, taking value in [0,1] is: m(x) = vc(1) −vc(2) L (10) where L represents the number of best base classifiers in the ensemble. The first smallest margin instances are selected as support vector candidates. The strong model is updated by the first smallest margin instances. This procedure is presented in the Algorithm 4. This heuristic significantly reduces the IWOC-SVM training task complexity while maintaining the accuracy of the IWOC-SVM classification.
- 18. Proposed Work 18/29 Algorithm 4Heuristic approach for model maintenance 1: Require: strong classifier H, test set Z = {z1,z2,...,zt }, weight distribution δ(z), user defined parameter time, user defined parameter η. 2: i ← 1 3: repeat 4: if H(zi ) = 1 (background) then 5: Compute the margin m(zi ) by Eq. (10). 6: end if 7: if time is reached then 8: Order all the test instances according to their margin values, in ascending order. 9: The η smallest margin instances are selected as support vectors. 10: H(x) is updated using Z1 and its weight w ∼ δ(x). 11: end if 12: i ← i +1 13: until i > t
- 19. Summary 19/29 1 Introduction 2 ProposedWork 3 Experimental Results 4 Conclusion and Future Works
- 20. Experimental Results 20/29 Dataset MSVS dataset(Benezeth et al., 2014) which consists of a set of 5 video sequences containing 7 multispectral bands and color video sequence (RGB). Parameter Settings IWOC-SVM with RBF (Radial Basis Function) kernel as a base classifier with C = 1. The pool of classifiers was homogeneous and consisted of 10 base classifiers of the same type. The classification threshold t1 was set to 0.9 and t2 to 0.5 for combining the best one-class classifiers. Video sequences were resized to 160 ×120 The p* = 5 for the random subspace dimension from the original p = 26-dimensional. Features: Color features (R,G,B, H,S,V and gray-scale), texture feature (XCS-LBP), color-texture (OC-LBP), edge feature (gradient orientation and magnitude), motion feature (optical flow) and multispectral bands (7 spectral narrow bands).
- 21. Experimental Results 21/29 MSVS dataset Figure:Background subtraction results using the MSVS dataset – (a) original frame, (b) ground truth and (c) proposed method. The true positives (TP) pixels are in white, true negatives (TN) pixels in black, false positives (FP) pixels in red and false negatives (FN) pixels in green.
- 22. Experimental Results 22/29 Table: Performanceof the different methods using the MSVS data set. Videos Method Precision Recall F-score Scene 01 MD (RGB)(Benezeth et al., 2014) 0.6536 0.6376 0.6536 MD (MSB)(Benezeth et al., 2014) 0.7850 0.8377 0.8105 Pooling (MSB)(Benezeth et al., 2014) 0.7475 0.8568 0.7984 Proposed 0.8500 0.9580 0.9008 Scene 02 MD (RGB)(Benezeth et al., 2014) 0.8346 0.9100 0.8707 MD (MSB)(Benezeth et al., 2014) 0.8549 0.9281 0.8900 Pooling (MSB)(Benezeth et al., 2014) 0.8639 0.8997 0.8815 Proposed 0.8277 0.8245 0.8727 Scene 03 MD (RGB)(Benezeth et al., 2014) 0.7494 0.5967 0.6644 MD (MSB)(Benezeth et al., 2014) 0.7533 0.6332 0.6889 Pooling (MSB)(Benezeth et al., 2014) 0.8809 0.5134 0.6487 Proposed 0.9056 0.9953 0.9483 Scene 04 MD(RGB)(Benezeth et al., 2014) 0.8402 0.7929 0.8158 MD (MSB)(Benezeth et al., 2014) 0.8430 0.8226 0.8327 Pooling (MSB)(Benezeth et al., 2014) 0.8146 0.8654 0.8392 Proposed 0.9534 0.8374 0.8997 Scene 05 MD (RGB)(Benezeth et al., 2014) 0.7359 0.7626 0.7490 MD (MSB)(Benezeth et al., 2014) 0.7341 0.8149 0.7724 Pooling (MSB)(Benezeth et al., 2014) 0.7373 0.8066 0.8066 Proposed 0.7316 0.8392 0.8400 *MD = Mahalanobis distance
- 23. Experimental Results 23/29 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Importance Gray Red Green Blue Hue Saturation Value XCS−LBP OCLBPRR OCLBPGG CLBPBB OCLBPRG OCLBPRB OCLBPGB GradientX GradientY GradientMagnitude GradientDirection OpticalFlow MS1 MS2 MS3 MS4 MS5 MS6 MS7 Scene 01 most(+): Gradient Direction with medium contrib. multispectral features less (-): OCLBP-GB 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Importance Gray Red Green Blue Hue Saturation Value XCS−LBP OCLBPRR OCLBPGG CLBPBB OCLBPRG OCLBPRB OCLBPGB GradientX GradientY GradientMagnitude GradientDirection OpticalFlow MS1 MS2 MS3 MS4 MS5 MS6 MS7 most (+): MS1,MS2 and MS6 with Color, Gradient X features less (-): XCS-LBP and MS4
- 24. Experimental Results 24/29 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Importance Gray Red Green Blue Hue Saturation Value XCS−LBP OCLBPRR OCLBPGG CLBPBB OCLBPRG OCLBPRB OCLBPGB GradientX GradientY GradientMagnitude GradientDirection OpticalFlow MS1 MS2 MS3 MS4 MS5 MS6 MS7 most (+):OCLBP-GG,RR with medium contrib. of other OCLBP channels and gradient features less (-): Hue, Optical flow and multispectral features 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Importance Gray Red Green Blue Hue Saturation Value XCS−LBP OCLBPRR OCLBPGG CLBPBB OCLBPRG OCLBPRB OCLBPGB GradientX GradientY GradientMagnitude GradientDirection OpticalFlow MS1 MS2 MS3 MS4 MS5 MS6 MS7 most (+): OCLBP-BB,RR,RG and GG with medium contrib. of gradient features less (-): Multispectral and color features
- 25. Experimental Results 25/29 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Importance Gray Red Green Blue Hue Saturation Value XCS−LBP OCLBPRR OCLBPGG CLBPBB OCLBPRG OCLBPRB OCLBPGB GradientX GradientY GradientMagnitude GradientDirection OpticalFlow MS1 MS2 MS3 MS4 MS5 MS6 MS7 most (+):OCLBP-RR with high contrib. of other OCLBP channels and multispectral features less (-): Gradient Magnitude
- 26. Summary 26/29 1 Introduction 2 ProposedWork 3 Experimental Results 4 Conclusion and Future Works
- 27. Conclusion and FutureWorks 27/29 Conclusion An incremental version of the WOC-SVM algorithm, called Incremental Weighted One-Class Support Vector Machine (IWOC-SVM). An online weighted version of random subspace (OW-RS) to increase the diversity of the classifiers pool. A mechanism called Adaptive Importance Calculation (AIC) to suitably update the relative importance of each feature over time. A heuristic approach for IWOC-SVM model updating to improve speed. Future Works A superpixel segmentation strategy to improve the segmentation performance, increasing the computational efficiency of our ensemble. An unsupervised mechanism to suitably update the importance of each feature discarding insignificantly features over time without ground-truth data.
- 28.
- 29. References 29/29 Benezeth, Y., Sidibe,D., and Thomas, J. B. (2014). Background subtraction with multispectral video sequences. In IEEE International Conference on Robotics and Automation (ICRA). Guo, L. and Boukir, S. (2015). Fast data selection for SVM training using ensemble margin. Pattern Recognition Letters (PRL), 51. Tax, D. and Duin, R. (2001). Combining one-class classifiers. In Proceedings of the Second International Workshop on Multiple Classifier Systems (MCS), pages 299–308. Tax, D. and Laskov, P. (2003). Online SVM learning: from classification to data description and back. In IEEE Workshop on Neural Network for Signal Processing (NNSP), pages 499–508. Wozniak, M. (2013). Hybrid classifiers: methods of data, knowledge, and classifier combination. Springer Publishing Company, Incorporated.