VIEWS: 70 PAGES: 20 POSTED ON: 1/3/2011 Public Domain
12/14/2010 Face Detection Problem Face Recognition • Scan window over image • Classify window as either: – Face – Non-face Face Window Wi d Cl ifi Classifier Non-face Face Detection: Experimental Results Face Detection now in many Digital Cameras Test set 1: 125 images with 483 faces Test set 2: 20 images with 136 faces Canon Powershot 1 12/14/2010 Face Recognition Problem Face Verification Problem • Face Authentication/Verification (1:1 matching) query image q Query face g y • Face Identification/Recognition (1:N matching) database Application: Access Control Biometric Authentication www.viisage.com www viisage com www.visionics.com 2 12/14/2010 Application: Autotagging Photos in Application: Video Surveillance Facebook, Flickr, Picasa, iPhoto, … Face Scan at Airports www.facesnap.de iPhoto 2009 • Can be trained to recognize pets! http://www.maclife.com/article/news/iphotos_faces_recognizes_cats 3 12/14/2010 iPhoto 2009 Why is Face Recognition Hard? • Things iPhoto thinks are faces The many faces of Madonna Intra-class Variability Recognition should be Invariant to • Faces with intra-subject variations in pose, illumination, expression, accessories, color, occlusions, and brightness • Lighting variation • Head pose variation • Different expressions • Beards, disguises • Glasses, occlusion Gl l i • Aging, weight gain • … 4 12/14/2010 Inter-class Similarity Face Detection in Humans • Different people may have very similar appearance There are cells that detect faces in the “Fusiform Face Area” of brain k d hl www.marykateandashley.com bb news.bbc.co.uk/hi/english/in_depth/americas/2000/us_el k/hi/ li h/i d h/ i /2000/ l ections Twins Father and son Blurred Faces are Recognizable Blurred Faces are Recognizable Michael Jordan, Woody Allen, Goldie Hawn, Bill Clinton, Tom Hanks, Saddam Hussein, Elvis Presley, Jay Leno, Dustin Hoffman, Prince Charles, Cher, and Richard Nixon. The average recognition rate at this resolution is one-half. 5 12/14/2010 by L. Harmon and B. Julesz, Scientific American,1973 S. Dali, Gala contemplating the Mediterranean Sea, 1976 Eyebrows Aid Recognition Richard Nixon and Winona Ryder 6 12/14/2010 Saccadic Eye Movements Field of View • Human vision system uses narrow-field-of-view and wide-field-of-view naturally and intelligently y g y o 2 , high-acuity fovea window of the world 3 saccades per second and gaze moves Human vision can integrate information seamlessly Work by Russian psychophysicist Yarbus who traced saccadic eye movements Challenges Problems of Recognition: Recognition is Easier than Synthesis • Sinha et al [2005] use this example to illustrate the difficulty of Pawan Sinha gave an Id tikit operator P Si h Identikit t finding a suitable “similarity” measure to gauge similarity between a pair of faces. photographs of celebrities and asked him to • In this example, the outer two faces actually belong to the same person while the middle one does not. But conventional pixel-based create the best likenesses he could. He thought measures who say otherwise. he did very well. • Common variations in pose (this case), lighting, expression, distance, aging remain challenges to face recognition. Who are these people? 7 12/14/2010 Illumination and Shading Affect Problems of Recognition Interpretation Bill Cosby, Tom Cruise, Ronald Reagan, Michael Jordan Vision is Inferential: Illumination Vision is Inferential: Illumination Which square is darker, A or B? http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html http://web.mit.edu/persci/people/adelson/checkershadow_illusion.html 8 12/14/2010 Context is Important P. Sinha and T. Poggio, I think I know that face, Nature 384, 1996, 404. P. Sinha and T. Poggio, Last but not least, Perception 31, 2002, 133. Holistic Processing Holistic Processing Who is/are this person? Woody Allen and Oprah Winfrey 9 12/14/2010 NIST’s Face Recognition Grand Challenges • Goal: Advance performance of face recognition 10 fold (20% 2% verification rate @ 0 1% false 10-fold 0.1% alarm rate) • Focus on different scenarios Face Recognition Architecture Feature Classification Image Extraction Face (window) Feature Identity Vector 10 12/14/2010 Image as a Feature Vector Nearest Neighbor Classifier { Rj } are set of training images x2 ID arg min dist ( R j , I ) j I x1 x3 x2 Consider an n-pixel i • C id to be i t in i l image t b a point i an n-dimensional “image space,” x Rn R1 • Each pixel value is a coordinate of x x1 x3 R2 Key Idea Eigenfaces (Turk and Pentland, 91) Pentland, • One or more images for each person (class) • Use Principle Component Analysis Expensive t compute k di t • E i to t distances, especially i ll to d the dimensionality (PCA) t reduce th di i lit when each image is big (n dimensional) • Not all images are very likely – especially when we know that every image contains a face. I.e., images of faces are highly correlated, so compress them into a low-dimensional subspace that retains the key appearance characteristics 11 12/14/2010 Eigenface Representation Eigenface Representation Each face image is represented by a weighted combination of a small number of “component” or “basis” faces Principal Component Analysis (PCA) Principal Component Analysis (PCA) • Pattern recognition in high-dimensional spaces − Problems arise when performing recognition in a high-dimensional − Dimensionality reduction implies information space (“curse of dimensionality”) loss − Significant improvements can be achieved by first mapping the data into a lower-dimensional subspace − How to determine the best lower dimensional subspace? − Maximize information content in the compressed data by finding a set of k orthogonal vectors that account for as much of the data’s variance as possible − The goal of PCA is to reduce the dimensionality of the data − Best dimension = direction in n-D with max variance while retaining the important variations present in the original data − 2nd best dimension = direction orthogonal to first and max variance 64 12 12/14/2010 Principal Component Analysis (PCA) Principal Component Analysis (PCA) • Geometric interpretation − The best low-dimensional space can be − PCA projects the data along the directions where the data varies the most best determined by the “best” eigenvectors of the − These directions are determined by the eigenvectors of the covariance matrix of the data, i.e., the covariance matrix corresponding to the largest eigenvalues eigenvectors corresponding to the largest − The magnitude of the eigenvalues corresponds to the variance of the data along the eigenvector directions eigenvalues – also called “principal components” − Can be efficiently computed using SVD 66 Subspaces Subspaces • Suppose we have points in 2D and we take a • Some lines will represent the data well and line through that space not, others not depending on how well the projection separates the data points • We can project each point onto that 1D line 13 12/14/2010 Subspaces Eigenvectors • An eigenvector is a vector, u, that obeys the • Rather than using a line, we can do a similar following rule: projection onto a vector v vector, i ui Cui where C is a matrix, is a scalar called the eigenvalue • Example: 2 3 3 3 2 3 3 C u 4 2 1 2 2 2 1 2 • Scale the vector to obtain any point on the line • So eigenvalue =4 for this eigenvector Method Method • Each input image, Xi , is an n-D column • Stack all training images together nxM t vector of all pixel values (i raster order) f ll i l l (in t d ) Y [Y1Y2 ...YM ] matirx • Compute “average face image” from all M • Compute n x n Covariance Matrix training images of all people: 1 1 M C YY T YiYi T A Xi M i 1 M i • Compute eigenvalues and eigenvectors of • Normalize each training image, Xi, by C by solving subtracting the average face: i ui Cui Yi X i A 14 12/14/2010 Method Method • Compute eigenvalues and eigenvectors of • Each ui is an n x 1 eigenvector called an by l i C b solving “ i f ” (to b t !) “eigenface” (t be cute!) i ui Cui • The eigenfaces form a “basis,” meaning where the eigenvalues are Yi w1u1 w2u2 ... wn u n 1 2 ... n n X i wi ui A and the corresponding eigenvectors are i 1 u1, u2, …, un • Image is exactly reconstructed by a linear combination of all eigenvectors Method How do you Construct Face Space? [ ] [ ] • Reduce dimensionality by using only the b t k << n eigenvectors (i best i t the (i.e., th ones corresponding to the largest k eigenvalues k X i wi ui A i 1 [ X1 X2 X3 X4 X5 ] [ u1 u2 u3 ] • Each image Xi is approximated by a set of k weights [wi1 , wi2, …, wik ] = Wi where Construct data matrix by stacking vectorized images and then using Singular Value Decomposition (SVD) to compute eigenfaces wij u T ( X i A) j 15 12/14/2010 Eigenspace Representation Face Image Reconstruction • Face X in “face space” coordinates: • Key property: Given 2 images, X1 and X2, d their j ti into i and th i projections i t eigenspace, Z1 and Z2, then = || X 1 X 2 || || Z1 Z 2 || • Reconstruction: is, • That is distance in eigenspace is approximately equal to the correlation = + between the 2 images ^ X = A + w1u1 + w2u2 + w3u3 + w4u4 + … Reconstruction Method The more eigenfaces you use, the better the reconstruction, but even a small number gives good quality for matching • So, image Xi is a point in n-D “image ” that is j t d into i t space” th t i projected i t a point Wi in the k-D subspace called “face space” defined by the “eigenfaces” (i.e., basis vectors) u1, u2, …, uk 16 12/14/2010 Eigenfaces Algorithm Example: Training Images • Modeling (Training) 1. Given a collection of n labeled training images 2. 2 Compute mean image and covariance matrix 3. Compute k eigenvectors (note that these are images) of covariance matrix corresponding to k largest eigenvalues Note: Faces must be 4. Project the training images to the k-dimensional approximately registered (translation, face space rotation, size, pose) • Recognition (Testing) R iti (T ti ) 1. Given a test image, project it into face space 2. Classify it as the class (person) that is closest to [ Turk & Pentland, 2001] it (as long as its distance to the closest person is “close enough”) Example Eigenfaces Training images m=5 eigenface images Average Image, A 94 17 12/14/2010 Example Experimental Results Top eigenvectors: u1,…uk • Training set: 7,562 images of approximately 3 000 people 3,000 Average: A • k=20 eigenfaces computed from a sample of 128 images • Test set accuracy on 200 faces was 95% 95 Limitations Difficulties with PCA • The direction of maximum variance is • Projection may suppress important detail not always good for classification – smallest variance directions may not be unimportant • Method does not take discriminative task into account – typically, we wish to compute features that allow good discrimination – not the same as largest variance 18 12/14/2010 Limitations Limitations • PCA assumes that the data has a Gaussian distribution (mean µ, covariance matrix C) − Background (de-emphasize the outside of the face – e.g., by multiplying the input image by a 2D Gaussian window y py g p g y centered on the face) − Lighting conditions (performance degrades with light changes) − Scale (performance decreases quickly with changes to head size); possible solutions: multi scale − multi-scale eigenspaces − scale input image to multiple sizes − Orientation (performance decreases but not as fast as with scale changes) − plane rotations can be handled The shape of this dataset is not well described by its principal components − out-of-plane rotations are more difficult to handle Limitations Extension: Eigenfeatures • Not robust to misalignment • Describe and encode a set of facial features: eigeneyes, eigennoses, eigenmouths • Use for detecting facial features 102 19 12/14/2010 Recognition using Eigenfeatures 20