Future Research

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.

Similarity Functions for Face Recognition

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.

Errors for Face Recognition

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.

Hausdorff Distance for Face Recognition

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.

Foreword

This book addresses a fundamental step in face recognition research answering, among other issues, the following questions: how to properly measure the distance between surfaces representing faces, what are the pros and contras of each algorithms and how they compare with each other, what are their computational costs. In this respect, this book represents a reference point for PhD students and researchers who want to start working not only at face recognition problems but also at other applications dealing with the recognition of three-dimensional shapes. The need for such a book was particularly evident when we presented to our multidisciplinary team of the High Polytechnic School the topic to be studied that was aimed at the development of a diagnostic tool of prenatal syndromes from three-dimensional ultrasound scans (SYN DIAG). A book, easy to use, putting order and organizing the scientific significance of similarity measures applied to face recognition problems was missing. This aspect was crucial to support the choice of measures to be selected and tested. Coming to the topic of the book, face recognition has several applications, including security, such as authentication and identification of suspects, and medical ones, such as corrective surgery and diagnosis. So, I think that this book is going to be a valuable tool for all scientists 'facing face'.

Other Measures for Face Recognition

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.

Other Distances for Face Recognition

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.

Mahalanobis Distance for Face Recognition

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.