In this paper, we present novel ridge regression (RR) and kernel ridge regression (KRR) techniques for multivariate labels and apply the methods to the problem efface recognition. Motivated by the fact that the regular simplex vertices are separate points with highest degree of symmetry, we choose such vertices as the targets for the distinct individuals in recognition and apply RR or KRR to map the training face images into a face subspace where the training images from each individual will locate near their individual targets. We identify the new face image by mapping it into this face subspace and comparing its distance to all individual targets. An efficient cross-validation algorithm is also provided for selecting the regularization and kernel parameters. Experiments were conducted on two face databases and the results demonstrate that the proposed algorithm significantly outperforms the three popular linear face recognition techniques (Eigenfaces, Fisher faces and Laplacian faces) and also performs comparably with the recently developed Orthogonal Laplacian faces with the advantage of computational speed. Experimental results also demonstrate that KRR outperforms RR as expected since KRR can utilize the nonlinear structure of the face images. Although we concentrate on face recognition in this paper, the proposed method is general and may be applied for general multi-category classification problems.

We present an algorithm that uses a low resolution 3D sensor for robust face recognition under challenging conditions. A preprocessing algorithm is proposed which exploits the facial symmetry at the 3D point cloud level to obtain a canonical frontal view, shape and texture, of the faces irrespective of their initial pose. This algorithm also fills holes and smooths the noisy depth data produced by the low resolution sensor. The canonical depth map and texture of a query face are then sparse approximated from separate dictionaries learned from training data. The texture is transformed from the RGB to Discriminant Color Space before sparse coding and the reconstruction errors from the two sparse coding steps are added for individual identities in the dictionary. The query face is assigned the identity with the smallest reconstruction error. Experiments are performed using a publicly available database containing over 5000 facial images (RGB-D) with varying poses, expressions, illumination and disguise, acquired using the Kinect sensor. Recognition rates are 96.7% for the RGB-D data and 88.7% for the noisy depth data alone. Our results justify the feasibility of low resolution 3D sensors for robust face recognition.