Face recognition based on texture information and geodesic distance approximations between multivariate normal distributions

Abstract

Geodesic distance is a natural dissimilarity measure between probability distributions of a specific type, and can be used to discriminate texture in image-based measurements. Furthermore, since there is no known closed-form solution for the geodesic distance between general multivariate normal distributions, we propose two efficient approximations to be used as texture dissimilarity metrics in the context of face recognition. A novel face recognition approach based on texture discrimination in high-resolution color face images is proposed, unlike the typical appearance-based approach that relies on low-resolution grayscale face images. In our face recognition approach, sparse facial features are extracted using predefined landmark topologies, that identify discriminative image locations on the face images. Given this landmark topology, the dissimilarity between distinct face images are scored in terms of the dissimilarities between their corresponding face landmarks, and the texture in each one of these landmarks is represented by multivariate normal distributions, expressing the color distribution in the vicinity of each landmark location. The classification of new face image samples occurs by determining the face image sample in the training set which minimizes the dissimilarity score, using the nearest neighbor rule. The proposed face recognition method was compared to methods representative of the state-of-the-art, using color or grayscale face images, and presented higher recognition rates. Moreover, the proposed texture dissimilarity metric also is efficient in general texture discrimination (e.g. texture recognition of material images), as our experiments suggest.

Some Information Geometric Aspects of Cyber Security by Face Recognition

“…Using the results in Section 2 from [15], we investigated in [2,3] the following possible choices for approximating the geodesic distance between two k-variate Gaussians F 1 , F 2 with arbitrary means:…”

“…Experimentally, the optimally small landmark topology, interpolated landmark number L and vicinity size were determined, leading to the landmark number L = 25 and square patches with size 11 × 11 pixels. Therefore, by representing each face image as an ordered sequence of probability distributions as in previous approaches [2,3], dissimilarities between distinct face images were scored by summing geodesic distances between 3-variate Gaussians representative of corresponding landmarks of pairs of face images x and y. Differently here, we obtained an improved score function for dissimilarities between face images by multiplying the geodesics between corresponding landmarks as follows.…”

“…The k -variate Gaussian distributions have the parameter space with probability density functions given by: where is a possible value for the random variable, a k -dimensional mean vector, and is the positive definite symmetric covariance matrix, for features with k -dimensional representation [ 4 ]. In such cases the parameters are obtained using maximum likelihood estimation, as was the case for face recognition applications [ 3 ]. The Riemannian manifold of the family of k -variate Gaussians for a given k is well understood through information geometric study using the Fisher information metric.…”

“…Using the results in Section 2 from [ 15 ], we investigated in [ 2 , 3 ] the following possible choices for approximating the geodesic distance between two k -variate Gaussians with arbitrary means: and, From ( 8 ), between the covariances at fixed mean is given by: This led to two distinct ways to approximate the geodesic distance between k -variate Gaussians, …”

“…In the context of data represented via probability distributions, multivariate Gaussian distributions are a common choice in representing features in complex large datasets, in consequence of their maximal entropy for given mean and covariance; we outline their geometry in Section 2 . We described in [ 2 , 3 ] an efficient method for colour face image recognition using information geometry in such a way that each face image was represented by a set of 3-variate Gaussians, one for the vicinity of each landmark point in the face. The three variables are the RGB colours of pixels and we used sums of geodesic distance approximations between them at corresponding landmarks of distinct images to measure dissimilarities between face images.…”