Anuj Srivastava – författare

3D Face Modeling, Analysis and Recognition presents methodologies for analyzing shapes of facial surfaces, develops computational tools for analyzing 3D face data, and illustrates them using state-of-the-art applications. The methodologies chosen are based on efficient representations, metrics, comparisons, and classifications of features that are especially relevant in the context of 3D measurements of human faces. These frameworks have a long-term utility in face analysis, taking into account the anticipated improvements in data collection, data storage, processing speeds, and application scenarios expected as the discipline develops further.

The book covers face acquisition through 3D scanners and 3D face pre-processing, before examining the three main approaches for 3D facial surface analysis and recognition: facial curves; facial surface features; and 3D morphable models. Whilst the focus of these chapters is fundamentals and methodologies, the algorithms provided are tested on facial biometric data, thereby continually showing how the methods can be applied.

Key features: • Explores the underlying mathematics and will apply these mathematical techniques to 3D face analysis and recognition • Provides coverage of a wide range of applications including biometrics, forensic applications, facial expression analysis, and model fitting to 2D images • Contains numerous exercises and algorithms throughout the book

3D Face Modeling, Analysis and Recognition presents methodologies for analyzing shapes of facial surfaces, develops computational tools for analyzing 3D face data, and illustrates them using state-of-the-art applications. The methodologies chosen are based on efficient representations, metrics, comparisons, and classifications of features that are especially relevant in the context of 3D measurements of human faces. These frameworks have a long-term utility in face analysis, taking into account the anticipated improvements in data collection, data storage, processing speeds, and application scenarios expected as the discipline develops further.

The book covers face acquisition through 3D scanners and 3D face pre-processing, before examining the three main approaches for 3D facial surface analysis and recognition: facial curves; facial surface features; and 3D morphable models. Whilst the focus of these chapters is fundamentals and methodologies, the algorithms provided are tested on facial biometric data, thereby continually showing how the methods can be applied.

Key features: • Explores the underlying mathematics and will apply these mathematical techniques to 3D face analysis and recognition • Provides coverage of a wide range of applications including biometrics, forensic applications, facial expression analysis, and model fitting to 2D images • Contains numerous exercises and algorithms throughout the book

Recently, a data-driven and application-oriented focus on shape analysis has been trending. This text offers a self-contained treatment of this new generation of methods in shape analysis of curves. Its main focus is shape analysis of functions and curves—in one, two, and higher dimensions—both closed and open. It develops elegant Riemannian frameworks that provide both quantification of shape differences and registration of curves at the same time. Additionally, these methods are used for statistically summarizing given curve data, performing dimension reduction, and modeling observed variability. It is recommended that the reader have a background in calculus, linear algebra, numerical analysis, and computation.

Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations.

We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in #x211D;, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this frameworkis that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations.

The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L² metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities.

These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis.

This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.