Similarity Measures for Face Recognition

Face recognition is a growing-up branch of pattern recognition in the context of image and vision. Conferences have arisen and brand new technologies have been coming to light providing more and more accurate recognition rates. But what is face recognition? The problem statement could be formulated this way: “Given still or video images of a scene, identify or verify one or more persons in the scene using a stored database of faces” [1]. Face recognition branch is core inasmuch the applications involving recognition algorithms for human face are aimed at different applications such as biometrics, authentication, identification of suspects. This chapter offers an overview of what are similarity and similarity measures.

Minkowski distances really deserve a whole chapter for theirselves. Depending on the value choice of parameter p, explained here below in the introduction, the concept of Minkowski distance is split up in different distance measures, which are typically known as taxicab (p=1), Euclidean (p=2), and Chebyshev distances (

If two vectors originate from the same underlying distribution, the distance between them could be computed with the Mahalanobis distance, a generalization of the Euclidean one. Also, it can be defined as the Euclidean distance computed in the Mahalanobis space. Moreover, there exist also the city block-based Mahalanobis distance and other versions including the angle- and cosine-based ones. Largely employed for face recognition with bi-dimensional facial data, Mahalanobis gains very good performances with PCA algorithms.

When two sets are differently sized, the Hausdorff distance can be computed between them, even if the cardinality of one set is infinite. Different versions of this distance have been proposed and employed for face verification, among which the modified Hausdorff distance is the most famous. The important point to be noted is that, among the most commonly used similarity measures, the Hausdorff distance is the only one that has been widely applied to 3D data.

The cosine distance compares the feature vectors of two images by returning the cosine of the angle between two vectors. Other cosine- and angle-based measures are here presented, including Tanimoto dissimilarity and Jaccard index, together with other correlations; they have been employed in algorithms relying on PCA, ICA, NN, and Gabor wavelets, especially on bi-dimensional facial data. Only correlation coefficients have been applied on three-dimensional point clouds.

Other distances are employed for face recognition, but their usage within the field is less preponderant than the previous ones. This chapter collects these measures, which are known as bottleneck, Procrustes, Earth mover’s, and Bhattacharyya distances. A subsection dealing with performances is only presented for the Bhattacharyya distance, which, although a non-extensive application in the field of face recognition, is one of the most efficient measures of the branch.

Distances between faces may also be seen as errors. Error types are various and may differ depending on the application, but have been used for face recognition. The main outcomes have been collected and are reported in this brief but key chapter.

Similarity functions are not distances, but functions aimed to evaluate the similarity between two objects. Some of them relate to some other previously explained measures, such as cosine distance. Others are statistical or probabilistic, or rely on fuzzy logic. It has not been possible to provide a comprehensive table with recognition rates, as the data were to different to be compared.

Other measures are employed to compute similarity between faces. Although some of them are very popular, such as edit distance or turning function distance, they may be more frequently used for object, vectors or shape comparison and less for faces. This paragraph collects all these measures and the works in which they are used for face recognition. Among them, Dynamic Time Warping (DTW), Hidden Markov Models (HMM), and Fréchet distance have been applied to 3D data.

A thorough organized treatise of similarity measures for face recognition was presented. All these measures were applied to different typologies of recognition algorithms, so a direct and synoptic comparison of their performances is not possible. Nevertheless, many authors used many of these measures for their algorithms and compared the results, depending on the distances. These kinds of works are precious for making an evaluation and efficiency comparison of these measures, in order to give an overview on the way that can be used and employed for face recognition. This is the aim of the chapter. An analysis of requirements of face recognition algorithms is also provided for the applications of authentication and identification of suspects.

This essential chapter is devoted to the hints of future research that this work has inspired. Embracing 3D is the main outcome of this brief analysis.