HW2 due Today. Face Recognition: Dimensionality Reduction. Biometrics CSE 190 Lecture 11. Perceptron Revisited: Linear Separators.

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1 HW due Today Face Recognition: Dimensionality Reduction Biometrics CSE 190 Lecture 11 CSE190, Winter 011 CSE190, Winter 011 Perceptron Revisited: Linear Separators Binary classification can be viewed as the task of separating classes in feature space: Linear Separators Which of the linear separators is optimal? w T x + b > 0 w T x + b = 0 w T x + b < 0 f(x) = sign(w T x + b) 3 4 1

2 Classification Margin Distance from example x i to the separator is r = wt x i + b w Training examples closest to the hyperplane are support vectors. Margin ρ of the separator is the distance from the separator to support vectors. ρ r Non-linear SVMs Datasets that are linearly separable with some noise work out great: 0 x But what are we going to do if the dataset is just too hard? 0 x How about mapping data to a higher-dimensional space: x 5 0 x 6 Non-linear SVMs: Feature spaces The Kernel Trick General idea: the original feature space can always be mapped to some higher-dimensional feature space where the training set is separable: Φ: x φ(x) 7 The linear classifier relies on inner product between vectors K(x i,x j )=x it x j If every datapoint is mapped into high-dimensional space via some transformation Φ: x φ(x), the inner product becomes: K(x i,x j )= φ(x i ) T φ(x j ) A kernel function is a function that is eqiuvalent to an inner product in some feature space. Example: -dimensional vectors x=[x 1 x ]; let K(x i,x j )=(1 + x it x j ), Need to show that K(x i,x j )= φ(x i ) T φ(x j ): K(x i,x j )=(1 + x it x j ),= 1+ x i1 x j1 + x i1 x j1 x i x j + x i x j + x i1 x j1 + x i x j = = [1 x i1 x i1 x i x i x i1 x i ] T [1 x j1 x j1 x j x j x j1 x j ] = = φ(x i ) T φ(x j ), where φ(x) = [1 x 1 x 1 x x x 1 x ] Thus, a kernel function implicitly maps data to a high-dimensional space (without the need to compute each φ(x) explicitly). 8

3 Examples of Kernel Functions Linear: K(x i,x j )= x it x j Mapping Φ: x φ(x), where φ(x) is x itself Polynomial of power p: K(x i,x j )= (1+ x it x j ) p Mapping Φ: x φ(x), where φ(x) has dimensions Dual problem formulation: Non-linear SVMs Mathematically Find α 1 α n such that Q(α) =Σα i - ½ΣΣα i α j y i y j K(x i, x j ) is maximized and (1) Σα i y i = 0 () α i 0 for all α i Gaussian (radial-basis function): K(x i,x j ) = Mapping Φ: x φ(x), where φ(x) is infinite-dimensional: every point is mapped to a function (a Gaussian); combination of functions for support vectors is the separator. Higher-dimensional space still has intrinsic dimensionality d (the mapping is not onto), but linear separators in it correspond to non-linear separators in original space. 9 The solution is: f(x) = Σα i y i K(x i, x j )+ b Optimization techniques for finding α i s remain the same! 10 Face Face Recognition Face is the most common biometric used by humans Applications range from static, mug-shot verification to a dynamic, uncontrolled face identification in a cluttered background Challenges: automatically locate the face recognize the face from a general view point under different illumination conditions, facial expressions, and aging effects CSE190, Winter 011 3

4 Authentication vs Identification Applications Face Authentication/Verification (1:1 matching) Face Identification/recognition (1:N matching) Applications Applications Face Scan at Airports Tracking people in games (Kinnect) 4

5 Why is Face Recognition Hard? Face Recognition Home Page Many faces of Madonna CSE190, Winter 011 Graph shows how many items on face recognition were published between 1991 and 006, Who are these people? Why is Face Recognition Hard? [Sinha and Poggio 1996] 5

6 Inter-class Similarity Face Recognition Difficulties Identify similar faces (inter-class similarity) Different persons may have very similar appearance Accommodate intra-class variability due to: head pose illumination conditions expressions facial hair aging effects glasses Twins partial occlusion news.bbc.co.uk/hi/english/in_depth/ americas/000/us_elections Father and son camera variability Artistic renderings Intra-class Variability Faces with intra-subject variations in pose, illumination, expression, accessories, color, occlusions, and brightness Sketch of a Pattern Recognition Architecture Image (window) CS5A, Winter 011 Feature Extraction Classification Feature Vector Object Identity Computer Vision I 6

7 Example: Face Detection Detection Test Sets Scan window over image. Classify window as either: Face Non-face Window Classifier Face Non-face CS5A, Winter 011 Computer Vision I Profile views Schneiderman s Test set Face Detection: Experimental Results Test sets: two CMU benchmark data sets Test set 1: 15 images with 483 faces Test set : 0 images with 136 faces [See also work by Viola & Jones, Rehg, Schneiderman] 7

8 Generative model Learn about faces from examples: P( Window Face) Challenge: High dimensional data, multi-modal Detection: Scan window over image, and classify window if local maximum of P(Window Face) and P(Window Face) > Threshold E.g., mixture of factor analyzers [Yang, Kriegman, Ahuja, 001] Discriminative Model Learn face and nonface models from examples P( Window Face) and P( Window Non-face) Cluster samples of each class to create subclasses, and project the examples to a lower dimensional space based on multi-discriminant analysis. Detect faces in lower-dimensional space when P(Face Window) > P(Non-face Window) Add non-face examples using bootstraping [Sung and Poggio 98] [Sung and Poggio 98] State of the Art Method: Viola Jones Face Detection Variants [Viola and Jones CVPR 01]: A face is modeled as a set of Harrlike features A fast way to compute simple rectangle features Use Adaboost to focus on a small set of features Cascade of simple classifiers Lubomir Bourdev, Jonathan Brandt Robust Object Detection via Soft Cascade, CVPR 005. A Survey of Recent Advances in Face Detection, Cha Zhang and Zhengyou Zhang, MSR Redmond TR, 010. Error rate comparable to the best Fast: 15 Fps, 700Mhz Pentium, half resolution video images 8

9 Example: Finding skin Non-parametric Representation of CCD Skin has a very small range of (intensity independent) colors, and little texture Compute an intensity-independent color measure, check if color is in this range, check if there is little texture (median filter) See this as a classifier - we can set up the tests by hand, or learn them. get class conditional densities (histograms), priors from data (counting) Classifier is Figure from Statistical color models with application to skin detection, M.J. Jones and J. Rehg, Proc. Computer Vision and Pattern Recognition, 1999 copyright 1999, IEEE CS5A, Winter 011 Computer Vision I CS5A, Winter 011 Computer Vision I Face Detection Algorithm Lighting Compensation Color Space Transformation Input Image Skin Color Detection Variance-based Segmentation Connected Component & Grouping Face Localization Eye/ Mouth Detection! Face Boundary Detection" Verifying/ Weighting! Eyes-Mouth Triangles! Facial Feature Detection! Output Image 9