Beyond pairwise clustering

We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms

FACE RECOGNITION BY LINEAR DISCRIMINANT ANALYSIS

Linear Discriminant Analysis (LDA) has been successfully applied to face recognition which is based on a linear projection from the image space to a low dimensional space by maximizing the between class scatter and minimizing the within-class scatter. LDA allows objective evaluation of the significance of visual information in different features of the face for identifying the human face. The LDA also provides us with a small set of features that carry the most relevant information for classification purposes. LDA method overcomes the limitation of Principle Component Analysis method by applying the linear discriminant criterion. This criterion tries to maximize the ratio of determinant of the between-class scatter matrix of the projected samples to the determinant of the within-class scatter matrix of the projected samples. Linear discriminant groups the images of the same class and separate images of different classes. Here to identify an input test image, the projected test image is compared to each projected training, and the test image is identified as the closest training image. The experiments in this paper we present to use LDA for face recognition. The experiments in this paper are performed with the ORL face database. The experimental results show that the correct recognition rate of this method is higher than that of previous techniques

Face set classification using maximally probable mutual modes

In this paper we consider face recognition from sets of face images and, in particular, recognition invariance to illumination. The main contribution is an algorithm based on the novel concept of maximally probable mutual modes (MMPM). Specifically: (i) we discuss and derive a local manifold illumination invariant and (ii) show how the invariant naturally leads to a formulation of "common modes" of two face appearance distributions. Recognition is then performed by finding the most probable mode, which is shown to be an eigenvalue problem. The effectiveness of the proposed method is demonstrated empirically on a challenging database containing the total of 700 video sequences of 100 individual

Shape-from-shading using the heat equation

This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x - y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces

A new look at filtering techniques for illumination invariance in automatic face recognition

Illumination invariance remains the most researched, yet the most challenging aspect of automatic face recognition. In this paper we propose a novel, general recognition framework for efficient matching of individual face images, sets or sequences. The framework is based on simple image processing filters that compete with unprocessed greyscale input to yield a single matching score between individuals. It is shown how the discrepancy between illumination conditions between novel input and the training data set can be estimated and used to weigh the contribution of two competing representations. We describe an extensive empirical evaluation of the proposed method on 171 individuals and over 1300 video sequences with extreme illumination, pose and head motion variation. On this challenging data set our algorithm consistently demonstrated a dramatic performance improvement over traditional filtering approaches. We demonstrate a reduction of 50-75% in recognition error rates, the best performing method-filter combination correctly recognizing 96% of the individuals

Face recognition with image sets using manifold density divergence

In many automatic face recognition applications, a set of a person\u27s 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, semi-parametric 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