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

In many automatic face recognition applications, a set of a person's face images is available rather than a single image. In this paper, we describe a novel method for face recognition using image sets. We propose a flexible, semiparametric model for learning probability densities confined to highly non-linear but intrinsically low-dimensional manifolds. The model leads to a statistical formulation of the recognition problem in terms of minimizing the divergence between densities estimated on these manifolds. The proposed method is evaluated on a large data set, acquired in realistic imaging conditions with severe illumination variation. Our algorithm is shown to match the best and outperform other state-of-the-art algorithms in the literature, achieving 94% recognition rate on average.

This paper presents an online learning algorithm to construct from video sequences an image-based representation that is useful for recognition and tracking. For a class of objects (e.g., human faces), a generic representation of the appearances of the class is learned off-line. From video of an instance of this class (e.g., a particular person), an appearance model is incrementally learned on-line using the prior generic model and successive frames from the video. More specifically, both the generic and individual appearances are represented as an appearance manifold that is approximated by a collection of sub-manifolds (named pose manifolds) and the connectivity between them. In turn, each submanifold is approximated by a low-dimensional linear subspace while the connectivity is modeled by transition probabilities between pairs of sub-manifolds. We demonstrate that our online learning algorithm constructs an effective representation for face tracking, and its use in video-based face recognition compares favorably to the representation constructed with a batch technique. 1

The paper poses video-to-video face recognition as a dynamical system identification and classification problem. Video-to-video means that both gallery and probe consists of videos. We model a moving face as a linear dynamical system whose appearance changes with pose. An autoregressive and moving average (ARMA) model is used to represent such a system. The choice of ARMA model is based on its ability to take care of the change in appearance while modeling the dynamics of pose, expression etc. Recognition is performed using the concept of subspace angles to compute distances between probe and gallery video sequences. The results obtained are very promising given the extent of pose, expression and illumination variation in the video data used for experiments. 1.

Abstract—We address the problem of comparing sets of images for object recognition, where the sets may represent variations in an object’s appearance due to changing camera pose and lighting conditions. Canonical Correlations (also known as principal or canonical angles), which can be thought of as the angles between two d-dimensional subspaces, have recently attracted attention for image set matching. Canonical correlations offer many benefits in accuracy, efficiency, and robustness compared to the two main classical methods: parametric distribution-based and nonparametric sample-based matching of sets. Here, this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations. Motivated by their proven effectiveness, a novel discriminative learning method over sets is proposed for set classification. Specifically, inspired by classical Linear Discriminant Analysis (LDA), we develop a linear discriminant function that maximizes the canonical correlations of within-class sets and minimizes the canonical correlations of between-class sets. Image sets transformed by the discriminant function are then compared by the canonical correlations. Classical orthogonal subspace method (OSM) is also investigated for the similar purpose and compared with the proposed method. The proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views. The method is also applied to object category recognition using ETH-80 database. The proposed method is shown to outperform the state-of-the-art methods in terms of accuracy and efficiency. Index Terms—Object recognition, face recognition, image sets, canonical correlation, principal angles, canonical correlation analysis, linear discriminant analysis, orthogonal subspace method. Ç 1

We propose a novel approach for modeling, tracking and recognizing facial expressions. Our method works on a low dimensional expression manifold, which is obtained by Isomap embedding. In this space, facial contour features are first clustered, using a mixture model. Then, expression dynamics are learned for tracking and classification. We use ICondensation to track facial features in the embedded space, while recognizing facial expressions in a cooperative manner, within a common probabilistic framework. The image observation likelihood is derived from a variation of the Active Shape Model (ASM) algorithm. For each cluster in the lowdimensional space, a specific ASM model is learned, thus avoiding incorrect matching due to non-linear image variations. Preliminary experimental results show that our probabilistic facial expression model on manifold significantly improves facial deformation tracking and expression recognition. 1.

In spite of over two decades of intense research, illumination and pose invariance remain prohibitively challenging aspects of face recognition for most practical applications. The objective of this work is to recognize faces using video sequences both for training and recognition input, in a realistic, unconstrained setup in which lighting, pose and user motion pattern have a wide variability and face images are of low resolution.

In this work we consider face recognition from face motion manifolds. An information-theoretic approach with Resistor-Average Distance (RAD) as a dissimilarity measure between distributions of face images is proposed. We introduce a kernel-based algorithm that retains the simplicity of the closed-form expression for the RAD between two normal distributions, while allowing for modelling of complex, nonlinear manifolds. Additionally, it is shown how errors in the face registration process can be modelled to significantly improve recognition. Recognition performance of our method is experimentally demonstrated and shown to outperform state-of-the-art algorithms. Recognition rates of 97-100% are consistently achieved on databases of 35-90 people.

Illumination and pose invariance are the most challenging aspects of face recognition. In this paper we describe a fully automatic face recognition system that uses video information to achieve illumination and pose robustness. In the proposed method, highly nonlinear manifolds of face motion are approximated using three Gaussian pose clusters. Pose robustness is achieved by comparing the corresponding pose clusters and probabilistically combining the results to derive a measure of similarity between two manifolds. Illumination is normalized on a per-pose basis. Region-based gamma intensity correction is used to correct for coarse illumination changes, while further refinement is achieved by combining a learnt linear manifold of illumination variation with constraints on face pattern distribution, derived from video. Comparative experimental evaluation is presented and the proposed method is shown to greatly outperform state-of-the-art algorithms. Consistent recognition rates of 94-100% are achieved across dramatic changes in illumination. 1