Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) -- a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.

Abstract—We propose an appearance-based face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition. Index Terms—Face recognition, principal component analysis, linear discriminant analysis, locality preserving projections, face manifold, subspace learning. 1

[30] V. Patrascu and V. Buzuloiu, “Image dynamic range enhancement in

Face recognition is an interesting topic in computer vision and object recognition. Researchers have proposed numeric recognition methods under the various conditions such as different pose, illumination and expression. However no research has been done to depict the relation between face image resolution and face recognition performance so far. In this paper, we divide the face image information into the discriminative and structure information, and conjecture that the face recognition rate will level off when face image resolution arrives at one certain resolution threshold. Then, we propose several PCA and LDA based face recognition experiments and present statistical results to depict how face recognition rate changes with face image resolution. The experimental results validate the conjecture. Moreover, we propose several experiments to demonstrate that only enhancing the structure information could not help to improve the recognition performance. 1.

We propose an appearance-based method for object recognition under varying illumination conditions. It is known that images of an object under varying illumination conditions lie in a convex cone formed in the image space. In addition, variations due to changes in light intensity can be canceled by normalizing images. Based on these observations, our proposed method combines binary classifications using discriminant hyperplanes in the normalized image space. For obtaining these hyperplanes, we compared Support Vector Machine (SVM), which has been used successfully for object recognition under varying poses, and Fisher’s linear discriminant (FLD). We have conducted a number of experiments by using the Yale Face Database B and confirmed that SVMs are effective also for object recognition under varying illumination conditions.

A scalable supervised algorithm

We have proposed a decomposition of the eigenface into two orthogonal eigenspaces and have shown that the decomposition is effective for realizing robust face recognition under various lighting conditions [lo]. The present paper refines the decomposed eigenface method by introducing a projection-based image correction. The image correction technique is principally authorized when the object shape is fixed and a sufficient number of images are taken beforehand. However, the proposed technique can also be applied to a canonical eigenspace, which is constructed from several faces taken under various lighting conditions. Reflective noises, shadows and occlusions are detected and corrected by the projection of a facial image onto the canonical eigenface. Based on the newly proposed image correction, we develop herein a refined decomposed eigenface method. The experimental results indicate that the refinement works well for face recognition under various lighting conditions, as compared to the original decomposed eigenface method. 1

The present paper reports an image correction method that is based on iterative projection onto eigenspaces. The fundamental method proposed in Shakunaga and Sakaue[ll] and involves iterative analysis of relative residual and projection. The present paper refines the projection method by solving linear equations while taking noise ratio into account. The refinement improves both the efficiency and robustness of the projection. Experimental results indicate that the proposed method works well for various kinds of noise, including shadows, reflections and occlusions. The proposed method can be applied to a wide variety of computer vision problems, which include objectiface recognition and image-based rendering. 1

A novel scheme is proposed for the efficient object tracking by using partial projections of a sparse set of pixels to eigenspaces. This paper shows a theoretical framework of the sparse eigentemplate matching and its application to a real-time face tracker. The sparse eigentemplate matching is formalized as a partial projection onto an eigenspace. Only using a small number of pixels, it facilitates an efficient template matching. In the application, a condensation framework is combined with the sparse eigentemplate matching in order to make a robust and efficient tracker. Experimental results show that the condensation tracker can track a face in real time even when the lighting condition changes. 1

Abstract—Current systems for face recognition techniques often use either SVM or Adaboost techniques for face detection part and use PCA for face recognition part. In this paper, we offer a novel method for not only a powerful face detection system based on Six-segment-filters (SSR) and Adaboost learning algorithms but also for a face recognition system. A new exclusive face detection algorithm has been developed and connected with the recognition algorithm. As a result of it, we obtained an overall high-system performance compared with current systems. The proposed algorithm