An expression-invariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expression-invariant representations of faces using the bending-invariant canonical forms approach. The result is an efficient and accurate face recognition algorithm, robust to facial expressions, that can distinguish between identical twins (the first two authors). We demonstrate a prototype system based on the proposed algorithm and compare its performance to classical face recognition methods. The numerical methods employed by our approach do not require the facial surface explicitly. The surface gradients field, or the surface metric, are sufficient for constructing the expression-invariant representation of any given face. It allows us to perform the 3D face recognition task while avoiding the surface reconstruction stage.

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.

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

We propose a novel 3D face recognition algorithm based on facial range image matching using the complex wavelet structural similarity metric (CW-SSIM) metric. Compared with many existing 3D surface matching methods, CW-SSIM is computationally efficient and is robust to small geometrical distortions. Using a data set that contains 360 3D face models of 12 subjects, we tested the performance of the proposed method and compared it with existing 3D surface matching based face recognition algorithms. Verification and identification performance of each algorithm was evaluated by means of the receiver operating characteristic curve and the cumulative match characteristic curve. Among the algorithms tested, the proposed algorithm based on the CW-SSIM resulted in the best overall performance with an equal error rate of 9.13 % and a rank 1 recognition rate of 98.6%, significantly better than all the other algorithms. Besides the introduction of a novel approach for 3D face recognition, this is also the first attempt to expand the application scope of complex wavelet domain similarity measure to range image matching in general. 1.

Face recognition (FR) is the preferred mode of identity recognition by humans: It is natural, robust and unintrusive. However, automatic FR techniques have failed to match up to expectations: Variations in pose, illumination and expression limit the performance of 2D FR techniques. In recent years, 3D FR has shown promise to overcome these challanges. With the availability of cheaper acquisition methods, 3D face recognition can be a way out of these problems, both as a stand-alone method, or as a supplement to 2D face recognition. We review the relevant work on 3D face recognition here, and discuss merits of different representations and recognition algorithms.

For more than 50 years, the meansquared error (MSE) has been the dominant quantitative performance metric in the field of signal processing. It remains the standard criterion for the assessment of signal quality and fidelity; it is the method of choice for comparing competing signal processing methods and systems, and, perhaps most importantly, it is the nearly ubiquitous preference of design engineers seeking to optimize signal processing algorithms. This is true despite the fact that in many of these applications, the MSE exhibits weak performance and has been widely criticized for serious shortcomings, especially when dealing with perceptually important signals such as speech and images. Yet the MSE has exhibited remarkable staying power, and prevailing attitudes towards the MSE seem to range from “it’s easy to use and not so bad ” to “everyone else uses it.” So what is the secret of the MSE—why is it still so popular? And is this popularity misplaced? What is wrong with the MSE when it does not work well? Just how wrong is the MSE in these cases? If not the MSE, what else can be used? These are the questions we’ll be concerned with in this article. Our backgrounds are primarily in the field of image processing, where the MSE has a particularly bad reputation, but where, ironically, it is used nearly as much as in other areas of signal processing. Our discussion will often deal with the role of the MSE (and alternative methods) for processing visual signals. Owing to the poor performance of the MSE as a visual metric, interesting alternatives are arising in the image processing field. Our goal is to stimulate fruitful thought and discussion regarding the role of the MSE in processing other types of signals. More specifically, we hope to inspire signal processing engineers to rethink whether the MSE is truly the criterion of choice in their own theories and applications, and whether it is time to look for alternatives.

Abstract—We introduce a new measure of image similarity called the complex wavelet structural similarity (CW-SSIM) index and show its applicability as a general purpose image similarity index. The key idea behind CW-SSIM is that certain image distortions lead to consistent phase changes in the local wavelet coefficients, and that a consistent phase shift of the coefficients does not change the structural content of the image. By conducting four case studies, we have demonstrated the superiority of the CW-SSIM index against other indices (e.g., Dice, Hausdorff distance) commonly used for assessing the similarity of a given pair of images. In addition, we show that the CW-SSIM index has a number of advantages. It is robust to small rotations and translations. It provides useful comparisons even without a preprocessing image registration step, which is essential for other indices. Moreover, it is computationally less expensive. Index Terms—Complex wavelet structural similarity index (CW-SSIM), image similarity, structural similarity (SSIM) index. I.

Automated human face recognition is required in numerous applications. While considerable progress has been made in color/two dimensional (2D) face recognition, three dimensional (3D) face recognition technology is much less developed. 3D face recognition approaches based on the appearance of range images and geometric properties of the facial surface have been proposed. Methods that combine 2D and 3D modalities also exist. These innovations have advanced the field and have created novel areas of investigation. The purpose of this chapter is to provide a summary and critical analysis of the progress in 3D and 2D+3D face recognition. The chapter also identifies open problems and directions for future work in the area. 2

Face recognition has rapidly emerged as an important area of research within many scientific and engineering disciplines. It has attracted research institutes, commercial industries, and numerous government agencies. This fact is evident by the existence of large number of face recognition conferences such as the International Conference on Automatic

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