Algorithmic Advances in Riemannian Geometry and Applications

Dr. Hà Quang Minh is a researcher in the Pattern Analysis and Computer Vision (PAVIS) group, at the Italian Institute of Technology (IIT), in Genoa, Italy.Dr. Vittorio Murino is a full professor at the University of Verona Department of Computer Science, and the Director of the PAVIS group at the IIT.

“The book under review consists of eight chapters, each introducing techniques for solving problems on manifolds and illustrating these with examples. … reading this book would add to my collection of tools for working with data on manifolds and expose me to new problems treatable by these tools. … In each case an effort has been made to provide enough of the underlying theory supporting the techniques, with explicit references where the interested reader can go for further details.” (Tim Zajic, IAPR Newsletter, Vol. 39 (3), July, 2017)

• Introduction.- Bayesian Statistical Shape Analysis on the Manifold of Diffeomorphisms.- Sampling Constrained Probability Distributions using Spherical Augmentation.- Geometric Optimization in Machine Learning.- Positive Definite Matrices: Data Representation and Applications to Computer Vision.- From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings.- Dictionary Learning on Grassmann Manifolds.- Regression on Lie Groups and its Application to Affine Motion Tracking.- An Elastic Riemannian Framework for Shape Analysis of Curves and Tree-Like Structures.