Comparative Study Of Face RecognitionFinal Project,ECE847 : Digital Image Processing,Department of Electrical Engineering, Clemson University,South Carolina, USAComparative Study of Face Recognition AlgorithmsPavan k. Yalamanchili and Bhanu Durga PaladuguAbstractIn this project, we implemented eigenface based face recognition and tried to compare the results with fisherface algorithm. The process required preprocessing. the images had to be resized to a consistent size. The database used included cropped faces of various sizes. Hence the need for face detection was eliminated. But the faces being of various sizes,they had to be resized to a smaller and consistent size. The face recognition process works quickly and consistently throughout a range of test images.We tried to compare two of the most frequently used algorithms; eigenface and fisherface. We compared the performance of each algorithm against two constraints. Pose and the size of training data. Our study has shown us that fisherface algorithm is robust in both cases. This leads us conclude that the eigenface algorithm is beneficial when the database is large. But given the robustness of the fisherface algorithm, it would be the algorithm of choice if the resources are not a problem.In this project we implemented our own resizing algorithm, which resizes the input image to a constant size no matter what the dimensions are, i.e. an algorithm which performs both interpolation and extrapolation. We also tried exploring the possibility of limiting the average image to that of just 3-4 poses in fisherface method. But this gave good results only when the 3 images represented 3 profiles (and hence vary too much).IntroductionFace recognition is an application area where computer vision research is utilized in both military and commercial products. It is a process of identifying or verifying a person from an image and comparing the selected features from the image with a given database. Most commonly used facial recognition techniques / algorithms include eigenface, fisherface, hidden Markov model & dynamic link matching. Using 3-D facial recognition higher accuracy is being achieved lately.1Comparative Study Of Face RecognitionThe process of getting the features from the face involves extracting the face from the rest of the image. Then the features (Nodal Points) such as the distance between the eyes, the shape of the cheekbones, width of the nose, depth of the eye sockets and other distinguishable features are obtained. These nodal points are then compared to the nodal points computed from a database of pictures in order to find a match. Figure 1:Example of a Training SetThe original training set includes multiple poses of 50 individuals.This image only shows 1 pose for 49 individuals. The rest are not shown due to space constraintsThe Eigenface approachIn this approach, the face images are decomposed into a small set of characteristic feature images called “eigenfaces” (which contain the common features in a face) which are extracted from the original training set of images by means of principal component analysis. An 2Comparative Study Of Face Recognitionimportant feature of PCA is that any original image can be reconstructed from the training set by a linear combination of the eigenfaces. Each eigenface represents only certain features of the face. However, the losses due to omitting some of the eigenfaces can be minimized by choosing only the most important features (eigenfaces).The eigenface approach involves the following initialization operations:1. An initial set of images (training set, Figure 1) is acquired.2. The eigenfaces from the training set are calculated and only M images that correspond to the highest eigenvalues (see Figure 2)define the face space. 3. By projecting the face images onto the face space, the corresponding distribution in M-dimensional weight space for each individual image is found.With these weights, any image in the database can be reconstructed using the weighted sum of the eigenfaces. (see Figure 3).In order to recognize face images, the following steps are to be followed1. A set of weights based on the input image and the M eigenfaces are calculated by projecting the input image onto each of the eigenfaces. 2. Nearest neighbor classification is used in order to find out the unknown image in the training set. (see Figure 5a, Figure 5b)InitializationLet the training set of face images be T1,T2,T3,….TM. This training data set has to be mean adjusted before calculating the covariance matrix or eigenvectors. The average face is calculated as Ψ = (1/M) Σ1MTi Each image in the data set differs from the average face by the vector Ф = Ti – Ψ. This is actually mean adjusted data. The covariance matrix is 1) C = (1/M) Σ 1M Φi ΦiT = AAT where A = [ Φ1, Φ2, …. ΦM]. The matrix C is a N2 by N2 matrix and would generate N2 eigenvectors and eigenvalues. With image sizes like 256 by 256, or even lower than that, such a calculation would be impractical to implement. A computationally feasible method was suggested to find out the eigenvectors. If the number of images in the training set is less than the no of pixels in an image (i.e M < N2), then we can solve an M by M matrix instead of solving a N2 by N2 matrix. Consider the covariance matrix as ATA instead of AAT. Now the eigenvector vi can calculated as follows, 2) ATAvi = μivwhere μi is the eigenvalue. Here the size of covariance matrix would be M by M. Thus we can have m eigenvectors instead of N2. Premultipying equation 2 by A, we have 3) AATAvi = μi Avi3Comparative Study Of Face RecognitionThe right hand side gives us the M eigenfaces of the order N2 by 1.All such vectors would make the image space of dimensionality M. The M’ eigenfaces which have the largest associated eigenvalues are selected. These eigenfaces now span a M’-dimensional subspace instead of N2.RecognitionA new image T is transformed into its eigenface components (projected into ‘face space’) by a simple operation, 4) wk = ukT (T – ψ)where k = 1,2,….M’. The weights obtained as above form a vector ΩT = [w1, w2, w3,…. wM’] that describes the contribution of each eigenface in representing the input face image. The Euclidean distance of the weight vector of the new image from the face class weight vector