Modern mathematics and applications in computer graphics and vision (Q2844601)

In these days computer graphics, vision and machine learning are ubiquitous. But these areas cannot work without the use of precise and modern mathematics. However, in order to understand the mathematics that is applied to computer science, one has to read many books which treat different areas of mathematics. This book is different. It gathers different areas of mathematics like algebra, geometry, and topology in one place and shows applications of them to computer graphics and vision.NEWLINENEWLINEThis book consists of seventeen chapters grouped in four parts. In the first part, linear, tensor, exterior, and geometric algebras are described. In the second part, projective, differential, and non-Euclidean geometries are presented. The third part treats general topology, manifolds, Hilbert spaces, measure spaces, and probability spaces. The last part is devoted to applications of mathematics to color spaces, perspective, quaternions, and machine learning.NEWLINENEWLINEThis book is written in an accesible fashion with a number of images, examples, and excercices. The chapters can be read quite independently, depending on a reader's needs. The bottom-up approach of the presentation, in which the theory is presented, starting from a concrete system to an abstract one, makes the book easy to follow. The proofs of the theorems are ommited what furthermore facilitates the reading of the text. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, computer vision, and game programming.