of Face Recognition The Eigenface Approach Relationship to Biology and Neutral Networks Conclusion Introduction of Face Recognition The
human ability to recognize faces is remarkable So, why do we need computational models of face recognition for Computers? Could be applied to a wide variety of problems: Criminal Identification, Security systems, Image and Film Processing, Human-Computer Interaction
Introduction of Face Recognition Developing a computational model is very difficulty Because they a natural class of objects
Introduction of Face Recognition Background and Related Work Much of the work in computer recognition of faces has focused on detecting individual features such as the eyes, nose, mouth and head outline. Eigenvalue and
Eigenvector is Eigenvalue of square matrix A is is Eigenvalue of square matrix A Eigenvalue is Eigenvalue of square matrix A of is Eigenvalue of square matrix A square is Eigenvalue of square matrix A matrix is Eigenvalue of square matrix A A is Eigenvalue of square matrix A x is Eigenvalue of square matrix A is is Eigenvalue of square matrix A Eigenvector is Eigenvalue of square matrix A of is Eigenvalue of square matrix A square is Eigenvalue of square matrix A matrix is Eigenvalue of square matrix A A is Eigenvalue of square matrix A corresponding is Eigenvalue of square matrix A to is Eigenvalue of square matrix A specific is Eigenvalue of square matrix A PCA: Principal Component Analysis Dimension
reduction to a few dimensions Find low-dimensional projection with largest spread PCA: Projection in 2D The Eigenface Approach Introduction
of Engenface Calculating Eigenfaces Using Eigenfaces to Classify a Face Image Locating and Detecting Faces Learning to Recognize New Faces Introduction of Eigenface Eigenvectors
of covariance matrix of the set of face images, treating an image as a point in a very high dimensional space Each image location contributes more or less to each eigenvector, so that we can display the eigenvector as a sort of ghostly face which we call an Eigenface.
Operations for Eigenface Acquire an initial set of face image (training set) Operations for Eigenface Calculate
the eigenfaces from the training set, keeping only the M images that correspond to the highest eigenvalues. These M images define the face space. Calculate the corresponding distribution in M-dimensional weight space for each known individual, by projecting their face image onto the face space
Calculating Eigenfaces Let a face image be a twodimensional by array of (8-bit) intensity values An image may also be considered as a vector of dimension , so that a typical image of size 256 by 256 becomes a vector of
dimension 65,536, equivalently, a point in 65,536-dimensional space Calculating Eigenfaces PCA to find the vectors that best account for the distribution of face images within the entire
image space. These vectors define the subspace of face images, which we call face space Each vector is of length , describes an by image, these vectors are called eigenfaces Calculating Eigenfaces Let
the training set of face images be , is Eigenvalue of square matrix A , is Eigenvalue of square matrix A , is Eigenvalue of square matrix A , is Eigenvalue of square matrix A . Average is Eigenvalue of square matrix A face is Eigenvalue of square matrix A is Eigenvalue of square matrix A = is Eigenvalue of square matrix A is Eigenvalue of square matrix A Each is Eigenvalue of square matrix A face is Eigenvalue of square matrix A differs is Eigenvalue of square matrix A from is Eigenvalue of square matrix A the is Eigenvalue of square matrix A average Calculating Eigenfaces Subject
to principal component analysis, which seeks a set of M orthonormal vectors, , which best describes the distribution of the data. The vector, , is chosen such that is Eigenvalue of square matrix A is a maximum, subject to Calculating Eigenfaces
The vectors and scalars are the eigenvectors and eigenvectors and eigenvalues, respectively, of the covariance matrix Matrix
is by , and determining the eigenvectors and eigenvalues Intractable is Eigenvalue of square matrix A Calculating Eigenfaces If the number of data points in the image space is less than the
dimension of the space , there will be only , rather than , meaningful eigenvectors Multiplying both sides by , we have are the eigenvectors of Calculating Eigenfaces
We construct the by matrix where Find the eigenvectors, of These vectors determine linear combinations of the training set face images to form the Eigenfaces to Classsify a Face
Image A smaller is sufficient for identification. The significant eigenvectors of the L matrix are chosen as those with the largest associated eigenvalues. A new face image is transformed
into its eigenface components (projected into face space) by Eigenfaces to Classsify a Face Image The weights form a vector Determine
the face class of input image Where is a vector describing the kth face class. Face Space difference Eigenfaces to Classsify a Face
Image Near face space and near a face class Near face space but not near a known face class Distant from face space and near a face class
Distant from face space and not near a known face class Locating and Detecting Faces To locate a face in a scene to do the recognition At every location in the image,
calculate the distant between the local subimage and face space Distance from face space at every point in the image is a face map Locating and Detecting Faces Since
Because is a linear combination of the eigenfaces and the eigenfaces are orthonormal vectors Locating and Detecting Faces
The second term is calculated in practice by a correlation with the L eigenfaces Locating and Detecting Faces Since
the average face and the eigenfaces are fixed, the terms and may be computed ahead of time correlations over input image and the computation of Locating and Detecting Faces
Relationship to Biology and Neutral Networks There are a number of qualitative similarities between our approach and current understanding of human face recognition Relatively small changes cause the recognition to degrade
gracefully Gradual changes due to aging are easily handled by the occasional recalculation of the Conclusion Eigenface approach does provide a practical solution that is well
fitted to the problem of face recognition. It is fast, relatively simple, and has been shown to work well in a constrained environment. It can also be implemented using modules of connectionist or neural networks
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