We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the face. The obtained geometric invariants allow mapping 2D facial texture images into special images that incorporate the 3D geometry of the face. These signature images are then decomposed into their principal components. The result is an efficient and accurate face recognition algorithm that is robust to facial expressions. We demonstrate the results of our method and compare it to existing 2D and 3D face recognition algorithms.

This survey focuses on recognition performed by matching models of the three-dimensional shape of the face, either alone or in combination with matching corresponding two-dimensional intensity images. Research trends to date are summarized, and challenges confronting the development of more accurate three-dimensional face recognition are identified. These challenges include the need for better sensors, improved recognition algorithms, and more rigorous experimental methodology.

We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling (MDS)-like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples. For isometry-invariant comparison of surfaces in the case of partially missing data, we present the partial embedding distance, which is computed using a similar scheme. The main idea is finding a minimum-distortion mapping from one surface to another, while considering only relevant geodesic distances. We discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency.

(will be inserted by the editor) A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching

www.elsevier.com/locate/cviu A survey of approaches and challenges in

Abstract—An algorithm is proposed for 3D face recognition in the presence of varied facial expressions. It is based on combining the match scores from matching multiple overlapping regions around the nose. Experimental results are presented using the largest database employed to date in 3D face recognition studies, over 4,000 scans of 449 subjects. Results show substantial improvement over matching the shape of a single larger frontal face region. This is the first approach to use multiple overlapping regions around the nose to handle the problem of expression variation. Index Terms—Biometrics, face recognition, three-dimensional face, facial expression. 1

Abstract—We present a fully automatic face recognition algorithm and demonstrate its performance on the FRGC v2.0 data. Our algorithm is multimodal (2D and 3D) and performs hybrid (feature based and holistic) matching in order to achieve efficiency and robustness to facial expressions. The pose of a 3D face along with its texture is automatically corrected using a novel approach based on a single automatically detected point and the Hotelling transform. A novel 3D Spherical Face Representation (SFR) is used in conjunction with the Scale-Invariant Feature Transform (SIFT) descriptor to form a rejection classifier, which quickly eliminates a large number of candidate faces at an early stage for efficient recognition in case of large galleries. The remaining faces are then verified using a novel region-based matching approach, which is robust to facial expressions. This approach automatically segments the eyesforehead and the nose regions, which are relatively less sensitive to expressions and matches them separately using a modified Iterative Closest Point (ICP) algorithm. The results of all the matching engines are fused at the metric level to achieve higher accuracy. We use the FRGC benchmark to compare our results to other algorithms that used the same database. Our multimodal hybrid algorithm performed better than others by achieving 99.74 percent and 98.31 percent verification rates at a 0.001 false acceptance rate (FAR) and identification rates of 99.02 percent and 95.37 percent for probes with a neutral and a nonneutral expression, respectively. Index Terms—Biometrics, face recognition, rejection classifier, 3D shape representation. 1

We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.

Recent studies on three-dimensional face recognition proposed to model facial expressions as isometries of the facial surface. Based on this model, expression-invariant signatures of the face were constructed by means of approximate isometric embedding into flat spaces. Here, we apply a new method for measuring isometry-invariant similarity between faces by embedding one facial surface into another. We demonstrate that our approach has several significant advantages, one of which is the ability to handle partially missing data. Promising face recognition results are obtained in numerical experiments even when the facial surfaces are severely occluded.

This paper explores the problem of similarity criteria between nonrigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the object and the latter to how it is laid out in the Euclidean space. Both criteria have their advantages and disadvantages: extrinsic similarity is sensitive to nonrigid deformations, while intrinsic similarity is sensitive to topological noise. In this paper, we approach the problem from the perspective of metric geometry. We show that by unifying the extrinsic and intrinsic similarity criteria, it is possible to obtain a stronger topology-invariant similarity, suitable for comparing deformed shapes with different topology. We construct this new joint criterion as a tradeoff between the extrinsic and intrinsic similarity and use it as a set-valued distance. Numerical results demonstrate the efficiency of our approach in cases where using either extrinsic or intrinsic criteria alone would fail.