Localization and Shape Normalization for Face Recognition

The concept presented in this work attempts to nd a solution for the localization and normalization problem in the context of recognition of human faces by computers. It is the rst elementary step in the chain of recognition steps to obtain the number, size and exact positions of faces in one image. This is a challenging and rarely examined eld in the area of face recognition, so the expectations concerning the results cannot be too high in the beginning. The approach to localize and normalize human faces in an image is structured in a modular way. The nal output information is found by a coarse to ne search in di erent modules. This allows to modify and improve single modules or to insert additional new modules without modifying other modules. First, a representation of the input image at di erent resolutions is generated by building a Gaussian image pyramid. Next, some invariant rules de ning human head and eye characteristics are applied to detect possible eye pair regions. Then, starting with these regions, which still contain a number of false eyes the correct ones are selected and the exact eye positions are determined. The eyes are also veri ed to suppress false detections. After an additional third xed point below the middle of the upper lip is found, an a ne transformation is performed. The nal results are human faces, segmented from the background, which are normalized concerning their size, rotation and position. These centered and normalized faces can then be given to a recognition system as input data. So far the system works with frontal views of uncovered human faces. Moreover there is no restriction for the number of faces or the size in one image, as long as it stays in acceptable resolution limits. 2 Notation The notation used generally follows the standard conventions of mathematics. A bold letter denotes a vector, soX = (xi) is a vector with components xi; i = 1:::m, withm being deduced from context. The variables that have been used are listed by chapters. Some of them are used as local variables. Chapter 3: xc(t) time-continuous input signal x[n]; xe[k]; xi[k]; xd[m] time-discrete signals T; T 0; T sampling periods ! normalized angular frequency angular frequency rational number L sampling rate is increased by this value M sampling rate is decreased by this value f downsampling factor Nyquist Nyquist frequency (= 1 2 sampling frequency) h impulse response of low pass lter H Fourier transform of h !cut cuto frequency of lowpass lter H ; K0 Gauss function parameters K1; K2 constants for determination of lter attenuation r lter radius of Gaussian lter mask D image dimension in xor y-direction l pyramid level Fourier transformation inverse Fourier transformation Chapter 4: VFC; di values for comparison with thresholds Ti rule threshold mi; mo inner and outer mean gray value Gi gray value at position i of the rule mask Ho head size in pixels at original level 3 Hl head size in pixels at level l lH correct level for head rule Eo eye distance in pixels at original level El eye distance in pixels at level l lE correct level for eye rule ld level distance U number of thresholds Ts threshold vector for strictest rule interpretation TDS threshold di erence sum value i standard deviation of the values for the ith threshold of a rule i mean value of the values for the ith threshold of a rule W number of entries in TDS list NI number of face images SDS squared di erence sum value Z number of entries in SDS list ^ logical AND operation Chapter 5: s position on Quicksearch scanning line q(s) Quicksearch gradient at position s g gray value ndist vertical distance of a line in the search frame to the bottom of the frame w weighting factor FitT (x; y) tting value for gray value template matching at position x; y T set of all points of the template region gI gray value of the image at position x; y gT gray value of the template at position x; y BT best tting value for gray value template matching gold gray value before normalization gnew gray value after normalization Imin; Imax minimal and maximal occuring gray value in the area that will be normalized l ej gradient vector in polar notation c(t) signal function r(t) function used for gradient calculation, here Gauss function C(f) Fourier transform of c(t) R(f) Fourier transform of r(t) FitG(x; y) tting value for gradient template matching at position x; y NG number of gradient vectors in gradient template limg module of a gradient vector computed from the image img phase of a gradient vector computed from the image tem phase of a gradient vector computed from the template S template size B(S) best template matching result for template size S 4 "q(T ) relative quality of the gray value template matching minimum "s(T ) size of the template with the minimal gray value template matching result "q(G) relative quality of the gradient template matching minimum "s(G) size of the template with the minimal gradient template matching result M1; M2 matching values of neighboring maxima Mmin matching value of the examined minimum Sest estimated template size after "q(T ); "q(G) comparison TN normalization value g gray value n(g) occuring number of gray values of g a; b image dimensions N number of pixels of face image image representation as 1D vector M number of images in image set average image i di erence images A matrix with M images i C covariance matrix L matrix ATA ui eigenvectors of C (Eigenface) vi eigenvectors of L M 0 number of images in subset of Eigenfaces with biggest eigenvalues new face image vector of characteristic weighting parameters for face p image projected into face-space "2R squared distance measure for face-like image "2N squared distance measure for non-face-like image Chapter 6: x;y source and destination point of coordinate transformation K transformation matrix b translation vector of transformation Si point in source image Di point in destination image DX; DY dimension of the output image after shape normalization E value in transformation output image, computed by interpolation A:::D edge points used to compute E FA:::FD weighting factor for interpolation 5 Chapter