Mixture of SVMs for Face Class Modeling J.Meynet, V.Popovici, J.-Ph. Thiran MLMI 04

Outline Introduction Presentation of the Work Context The face detection task Principal Component Analysis Classification with Support Vector Machines Mixture of Support Vector Machines With independent subsets With k-means clustering Experiments and Results Conclusions and Future Work

Face Detection Methods Image-Based Detection Consider face as a whole object Eigenfaces Fisher’s Linear Discriminant Neural Network, SVM HMM SNoW Geometrical-based methods Find precise parts of the face and reassemble them for the final decision Top-down Bottom-up …

Principle of the detection Pre-processing with a cascade of boosted Haar-Like Features =>Real-time face detector Principal Component Analysis (PCA) Dimensionality reduction Classification with a Mixture of SVM Random sampling or k-means clustering + - P.Viola, M.Jones, ”Robust real-time object detection.” International Journal of computer Vision, 2002.

Eigenfaces Space PCA and Eigenfaces PCA … Sirovich, Kirby, ”Low-dimensional procedure for the characterization of human faces, 1987

Distance From Feature Space DFFS F DIFS DFFS Construction of the classification vector:

Support Vector Machines (SVM) Find the hyperplane that correctly separates the data while maximising the margin. Optimisation: Lagrange multipliers i: Kernels: V. Popovici, J.-Ph. Thiran, "Face Detection using SVM Trained in Eigenfaces Space", 4th International Conference on Audio- and Video-Based Biometric Person Authentication, Surrey, UK, 2003

Mixture of SVMs (MSVM) Why? Building a face detection system requires a large amount of examples => make the training easier Principle 1- Split initial dataset into N+1 subsets By random sampling Or by K-means clustering 2- Train N first SVMs 3- Pass the N+1th subset through the SVMs, train the 2nd layer SVM on the margins. X 1 2 N N+1 SVM-1 SVM-N m SVM-L2

Mixture of SVMs 2 Sampling techniques: 1- Random partitioning M+1 independent subsets 2- Clustering - Draw 1 random subset for the SVM-L2 - K-means clustering on the remaining examples M clusters for training the SVM-L1-i SVM-L1-i are trained using cross-validation, with RBF kernels: SVM-L2 trained on the margins: It learns a function that assembles the confidences of each individual expert.

Mixture of SVMs Output of the mixture: Advantages: Single SVM: problem of complexity MSVM: problems of complexity => clearly advantageous

Experiments and Results I Database Face images from Banca and XM2VTS Non faces chosen by bootstrapping on randomly selected images Estimation of a correct dimensionality for the eigenfaces space 900000 14000 non faces 7822 8256 faces Validation Training 20x15 images Number of eigenfaces needed to keep 85% of total variation

Experiments and Results II Random sampling or clustering (x5) SVM-L1-i (x5) 1000 F 2000 NF 8256 F 14000 NF SVM-L2 2256 F 4000 NF Random sampling: Reduce the importance of outliers or unusual examples Clustering: Each SVM-L1-i performs like an expert on its own domain 98.86 99.00 76.47 86.23 SVM-L1-1 K-Means R.S Non Faces(%) Faces(%) Classifier 97.68 90.00 82.32 84.91 SVM-L1-2 98.77 99.02 81.23 85.13 SVM-L1-3 99.12 99.13 77.12 84.64 SVM-L1-4 74.29 85.66 SVM-L1-5 96.43 98.14 95.37 93.60 SVM-L2

Experiments and Results III Generalisation Classifier Faces(%) Non Faces(%) Total N° SV MSVM, RS MSVM, KM Single SVM 93.60 95.37 92.8 99.42 96.43 98.14 1673 1420 2504 Better generalisation capabilities than a single SVM; MSVM improves the training time and the true positive rate; Less Support Vectors => lower computation complexity. Results on Banca images pre-processed by boosted Haar-Like features

Conclusions - Future Work Boosted local feature-based classifiers pre-pocessing real-time processing Dimensionality reduction by PCA ( + DFFS) Decrease the complexity of the classification task Extension to the SVM technique which performs well on large datasets. Decrease the training and classification time Improve discrimination capabilities Try other clustering techniques in eigenfaces space based on more appropriate metrics.