doi:10.1016/j.imavis.2005.07.023 
Copyright © 2005 Elsevier B.V. All rights reserved.
Face recognition using optimal linear components of range images
Anuj Srivastavaa, 
, 
, Xiuwen Liub and Curt Hesherb
aDepartment of Statistics, Florida State University, Tallahassee, FL 32306, USA
bDepartment of Computer Science, Florida State University, Tallahassee, FL 32306, USA
Received 19 March 2005;
accepted 29 July 2005.
Available online 6 October 2005.
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Abstract
This paper investigates the use of range images of faces for recognizing people. 3D scans of faces lead to range images that are linearly projected to low-dimensional subspaces for use in a classifier, say a nearest neighbor classifier or a support vector machine, to label people. Learning of subspaces is performed using an optimal component analysis, i.e. a stochastic optimization algorithm (on a Grassmann manifold) to find a subspace that maximizes classifier performance on the training image set. Results are presented for face recognition using FSU face database, and are compared with standard component anlyses such as PCA and ICA. This provides an efficient tool for analyzing certain aspects of facial shapes while avoiding a difficult task of geometric surface modeling.
Keywords: Face recognition; Range imaging; Optimal component analysis; Nearest neighbor classifier; Grassmann manifold
Fig. 1. Data capture. Subjects stay in a predetermined position and orientation with respect to the 3D scanner. Each subject was scanned for six different facial expressions.
Fig. 2. The asterisk indicates the tip of the nose and the white line indicates the bridge of the nose. Images show range images before (left panel) and after (middle panel) rotational alignment. Right panel shows the mask imposed on range images to crop periphery.
Fig. 3. Range images of same faces under different facial expressions. Top row shows subject 2, middle row shows subject 13 and bottom row shows subject 19.
Fig. 4. Range images of first 24 subjects under the neutral facial expression.
Fig. 5. Evolution of F(Xt) versus t under Algorithm 1 for different initial conditions. For each case, the top panel plots F on the training data while the lower panel plots F on the test data. The initial conditions are as follows: (a) PCA basis, (b) ICA basis, (c) basis specified by first d Euclidean axes, and (d) a random basis.
Fig. 6. Evolution of the average entropy H(P) as the subspace changes according to Algorithm 1, under four different initial conditions.
Fig. 7. Examples of probabilities before and after optimization.
Table 1.
Recognition performance on the test data before and after using Algorithm 1
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