Face Recognition Image Understanding Xuejin Chen Face Recogntion

Face Recognition Image Understanding Xuejin Chen

Face Recogntion • Good websites – http: //www. face-rec. org/ • Eigenface [Turk & Pentland] Image Understanding, Xuejin Chen

Eigenface • Projecting a new image into the subspace spanned by the eigenfaces (face space) • Classifying the face by comparing its position in face space with the positions of known individuals Image Understanding, Xuejin Chen

• Face image used as the training set Image Understanding, Xuejin Chen

• Average face • 7 eigenfaces calculated from the training images Image Understanding, Xuejin Chen

Calculating Eigenfaces • Face image : intensity matrix -D vector • PCA: to find the vectors that best account for the distribution of face images within the entire image space – Training images – Average face – Each face differs from the average by – Seeks a set of M orthogonal vectors that best describe the distribution of the data • The kth vector is chosen such that Image Understanding, Xuejin Chen

Calculating Eigenfaces • The vector and scalar are the eigenvectors and eigenvalues, respectively, of the covariance matrix Intractable task for typical image size Need a computationally feasible method to find these eigenvectors Image Understanding, Xuejin Chen

Calculating Eigenfaces • If image number M < N^2, only M meaningful eigenvectors Solve Mx. M matrix 16 16384*16384 (an 128 x 128 image) • Consider eigenvectors vi of A’A such that Image Understanding, Xuejin Chen

Calculating Eigenfaces • Construct Mx. M matrix • Compute M eigenvectors of L • The M eigenfaces is the linear combination of the M eigenvectors The computations are greatly reduced Image Understanding, Xuejin Chen

• Average face • 7 eigenfaces calculated from the training images Image Understanding, Xuejin Chen

Classify a Face Image • 40 eigenfaces are sufficient for a good description for an ensemble of M=115 images [Sirovich and Kirby 1987] • A smaller M’ is sufficient for identification • C • hoose M’ significant eigenvectors of L matrix (M=16, M’=7) Image Understanding, Xuejin Chen

Classify a Face Image • New image : transformed into its eigenface components Image Understanding, Xuejin Chen

Classify a Face Image • describe the contribution of each eigenface in representing the input image, treating the eigenfaces as a basis set for face image • Find a class of the face – A simple distance Average of a class or individual Image Understanding, Xuejin Chen

Classify a Face Image • Creating the weight vector is: projecting the original face image onto the low-D face space • Distance from image to face space Image Understanding, Xuejin Chen

Four possibilities for an image and pattern vector • Near face space and near a face class • Near face space but not near a known face class • Distant from face space but near a face class • Distant from face space and not near a known face class Image Understanding, Xuejin Chen

Distance to face space (a) 29. 8 (b) 58. 5 (c) 5217. 4 Image Understanding, Xuejin Chen

Summary of Eigenface Recognition 1. Collect a set of characteristic face image of the known individuals. – The set should include a number of images for each person, with some variation in expression and lighting (M=40) 2. Calculate the 40 x 40 matrix L, find its eigenvalues and eigenvectors, choose M’(~10) eigenvectors with highest eigenvalues 3. Compute eigenfaces 4. For each known individual, calculate the class vector averaging the eigenface pattern vector. – – by Choose a threshold that defines the maximum allowable distance from any face class and a threshold that defines the maximum allowable distance from face space Image Understanding, Xuejin Chen

Summary of Eigenface Recognition 5. For each new face image to be identified, calculate – – • – • • • its pattern vector , the distance to face space , the distance to each known class if the minimum distance . Classify the input face as the individual associated with class vector If the minimum distance The image may be classified as unknown, and Optionally used to begin a new face class Optionally, if the new image is classified as a known individual, the image may be added to the original set of familiar face image, and the eigenfaces may be recalculated (steps 1 -4) Image Understanding, Xuejin Chen

Locating and Detecting Faces • Assume a centered face image, the same size as the training images and the eigenfaces • Using face space to locate the face in image • Images of faces do not change radically when projected into the face space, while the projection of nonface images appears quite different – > detect faces in a scene Image Understanding, Xuejin Chen

Use face space to locate face • At every location in the image, calculate the distance between the local subimage and face space, which is used as a measure of ‘faceness’ a face map Expensive calculation Image Understanding, Xuejin Chen

Face Map • A subimage at (x, y) Image Understanding, Xuejin Chen

Face Map • : linear combination of orthogonal eigenface vectors Image Understanding, Xuejin Chen

Face Map Correlation operator Image Understanding, Xuejin Chen

Face Map L+1 correlations Precomputed Can be implemented by a simple neural networks Image Understanding, Xuejin Chen

Learning to Recognize New Faces • An image is close to face space, but not classified as one of the familiar faces, labeled as “unknown” • If a collection of “unknown” pattern vectors cluster in the pattern space, a new face is postulated • Check similarity: the distance from each image to the mean is smaller than a threshold • Add the new face to database (optionally) Image Understanding, Xuejin Chen

Background Issue • Eigenface analysis can not distinguish the face from background • Segmentation? • Multiply the image by a 2 D Gaussian window centered on the face – Deemphasize the outside of the face – Also practical for hairstyle changing Image Understanding, Xuejin Chen

Scale and Orientation Issue • Recognition performance decreases quickly as the size is misjudged • Motion estimation? • Multiscale eigenfaces / multiscale input image • Non-upright faces – Orientation estimation using symmetry operators Image Understanding, Xuejin Chen

Distribution in Face Space • Nearest-neighbor classification assumes Gaussian distribution of an individual feature vector • No prior to assume any distribution • Nonlinear networks to learn the distribution by example [Fleming and Cottrell, 1990] Image Understanding, Xuejin Chen

Multiple Views • Define a number of face classes for each person – Frontal view – Side view at ± 45° – Right and left profile views Image Understanding, Xuejin Chen

Experiments • Database – Over 2500 face images under controlled conditions – 16 subjects • All combinations of 3 head orientations, 3 head sizes, 3 lighting conditions • Construct 6 -level Gaussian pyramid from 512 x 512 to 16 x 16 Image Understanding, Xuejin Chen

Variation of face images for one individual Image Understanding, Xuejin Chen

Experiments with Lighting, Size, Orientation • Training sets – One image of each person, under the same lighting condition, size, orientation – Use seven eigenfaces • Mean accuracy as the difference between the training conditions, test conditions – Difference in illumination – Image size, – Head orientation – Combinations of illumination, size, orientation Image Understanding, Xuejin Chen

• Changing lighting conditions --- few errors (a) Lighting 96% (b) Size 85% (c) Orientation 64% • Image size changing -performance dramatically drops – Need multiscale approach (d) Orientation & lighting (e) Orienation & Size 1 (g) Size & Lighting 1 (f) Orientation & Size 2 (h) Size & Lighting 2 Image Understanding, Xuejin Chen

Experiments with varying thresholds • Smaller threshold: – Few errors, but more false negative • Larger threshold – More errors • To achieve 100% accurate recognition, boost unknown rate to – 19% while varying lighting – 39% for orientation – 60% for size • Set the unknown rates to 20%, the correct recognition rate – 100% for lighting – 94% for orientation – 74% for size Image Understanding, Xuejin Chen

Neural Networks • Can be implemented using parallel computing elements Image Understanding, Xuejin Chen

Collection of networks to implement computation of the pattern vector, projection into face space, distance from face space, and identification Image Understanding, Xuejin Chen

Image Understanding, Xuejin Chen

Conclusion • • Not general recognition algorithm Practical and well fitted to face recognition Fast and simple Do not require perfect identification – Low false-positive rate – A small set of likely matches for user-interaction Image Understanding, Xuejin Chen

Eigenface • Tutorial Image Understanding, Xuejin Chen

Bayesian Face Recognition Baback Moghaddam, Tony Jebara and Alex Pentland Pattern Recognition 33(11), Nov. 2000

Novelty • • A direct visual matching of face images Probabilistic measure of similarity Bayesian (MAP) analysis of image differences Simple computation of nonlinear Bayesian similarity

A Bayesian Approach • Many face recognition systems rely on similarity metrics – nearest-neighbor, cross-correlation – Template matching • Which types of variation are critical in expressing similarity?

Probabilistic Similarity Measure • Intensity difference • Two classes of facial image variations – Intrapersonal variations – Extrapersonal variations Non-Euclidean similarity measure • Similarity measure Can be estimated using likelihoods given by Bayes rule

A Bayesian Approach • First instance of non-Euclidean similarity measure for face recognition • A generalized extension of – Linear Discriminant Analysis – Fisher. Face • Has computational and storage advantages over most linear methods for large database

Probabilistic Similarity Measures • Previous Bayesian analysis of facial appearance • 3 different inter-image representations were analyzed using the binary formulation – XYI-warp modal deformation spectra – XY-warp optical flow fields – Simplified I-(intensity)-only image-based difference

Probabilistic Similarity Measures • Intrapersonal variations – Images of the same individual with different expression, lighting conditions. . • Extrapersonal variations – Variations when matching two individuals • Both are Gaussian-distributed, learn the likelihoods

Probabilistic Similarity Measures • Similarity score – The priors can be set as the portion of image number in the database or specified knowledge • Maximum Posterior (MAP)

Probabilistic Similarity Measures • M individuals: M classes – Many classification -> binary pattern classification • Maximum likelihood measure • Almost as effective as MAP in most cases

Subspace Density Estimation • Intensity difference vector: high dimensional – No sufficient independent training examples – Computational cost is very large – Intrinsic dimensionality or major degree-of-freedom of intensity difference is significantly smaller than N • PCA – Divides the vector space R^N into two complementary subspaces [Moghaddam & Pentaland]

Subspace Density Estimation • Two complementary subspaces A typical eigenvalue spectrum

Subspace Density Estimation • Likelihood estimation True marginal density in F Estimated marginal density in F’

Dual Eigenfaces Variations mostly due to expression changes Intrapersonal Extrapersonal Variations such as hair, facial hair, glasses…

Dual Eigenfaces • Intensity differences of extrapersonal type span a larger vector space • Intrapersonal eigenfaces corresponds to a more tightly constrained subspace • The key idea of probability similarity measure

Efficient Similarity Computation • Two classes: one intrapersonal and the other as extrapersonal variations with Gaussian distribution Use the principal components Zero-mean since the pair

Bayesian Face Recognition CSE 576, Spring 2008 Face Recognition and Detection 55

Computation • To get the similarity – Subtracting – Project to principal eigenfaces of both extrapersonal and intrapersonal Gaussians – Expotentials for likelihood – Iterated all the operations over all members of the database (many I-k images) until find the maximum score

Offline Transformations • Preprocess the I_k images with whitening transformations • Consequently every image is stored as two vectors of whitened subspace coefficients

Offline Transformations • Euclidean distances are computed for each similarity times • Likelihood • Avoid unnecessary and repeated image differencing and online projection

Experiments • ARPA FERET database – Images taken at different times, location, imaging conditions (clothes, lighting) • Training Set – 74 pairs of images (2/person) • Test set – 38 pairs of images

(a) Training Set (b) Test Set • Differences in clothing, hair, lighting. .

Face Alignment (Detection)

Bayesian Matching • Training data – 74 intrapersonal differences – 296 extrapersonal differences – Separate PCA analysis on each • How they distribute? – Completely enmeshed distributions with the same principle components Hard to distinguish low-amplitude extrapersonal difference from intrapersonal difference

Separate PCA • Dealing with low-D hyper-ellipsoids with are intersecting near the origin of a very high-D space • Key distinguishing factor is their relative orientation

Dual Eigenfaces Variations mostly due to expression changes Intrapersonal Extrapersonal Variations such as hair, facial hair, glasses…

Dual Eigenfaces • Intensity differences of extrapersonal type span a larger vector space • Intrapersonal eigenfaces corresponds to a more tightly constrained subspace • The key idea of probability similarity measure

Dual Eigenfaces • Compute two sets of , compute likelihood estimates • Use principal dimensions • Set the priors as equal

Performance • Improvement over the accuracy obtained with a standard eigenface nearest-neighbor matching rule • Maximum likelihood gets a similar result with MAP – 2~3% deficit on recognition rate – Computational cost is cut by a factor of 2

Performance

Computation Simplification • Exact mapping of the probabilistic similarity score without requiring repeated imagedifferencing and eigenface projections • Nonlinar matching simple Euclidean norms of their whitened feature vectors which can be precomputed offline

Discussion • Model larger variations in facial appearance? – Pose, facial decorations? • Regular glasses • Sunglasses, significant changes in beards, hair – Add more variation in interpersonal training? … – Views • View-based multiple model

Bayesian Face Recognition CSE 576, Spring 2008 Face Recognition and Detection 72

Conclusions • Good performance of probabilistic matching • Advantageous in intra/extra density estimates explicitly characterize the type of appearance variations – Discovering the principle modes of variations • Optimal non-linear decision rule – Do not need to compute and store eigenfaces for each individual – One or two global eigenfaces are sufficient • Maximum Likelihood vs. MAP

View-Based and Modular Eigenspaces for Face Recognition Alex Pentland, Baback Moghaddam and Thad Starner CVPR’ 94

Part-based eigenfeatures • Learn a separate eigenspace for each face feature • Boosts performance of regular eigenfaces CSE 576, Spring 2008 Face Recognition and Detection 75

Morphable Face Model • Use subspace to model elastic 2 D or 3 D shape variation (vertex positions), in addition to appearance variation Shape S Appearance T CSE 576, Spring 2008 Face Recognition and Detection 76

Morphable Face Model • 3 D models from Blanz and Vetter ‘ 99 CSE 576, Spring 2008 Face Recognition and Detection 77

Project 3 Eigenfaces • Given a skeleton, you need to fill the functions – PCA to compute eigenfaces – Projection into the face space – Determining if a vector represents a face – Verifying a user based on a face, finding a face match given a set of user face information – Finding the size and position of a face in an image Image Understanding, Xuejin Chen

Project 3 Eigenfaces • Skeleton code is large, please take time to get familiar with the classes and methods – Vector – Image operations – Minimum modification: faces. cpp, eigenfaces. cpp Image Understanding, Xuejin Chen