- - Ref: cds.cern.ch/record/2700089 - This monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Providing a thorough overview of mathematical modeling of physical systems, this book is a useful resource for graduate students and researchers.
- David W. Henderson
- Object recognition requires that you know when two shapes are 'similar'. But what does similar mean? The mathematician says: make the set of all (two dimensional, three dimensional or higher) shapes into the points of an infinite-dimensional space and then put a metric on this space reflecting what 'similar' means. The background image is supposed to suggest this construction: here a certain set of eggs with varying shapes are each put in its own pigeon-hole. If, for example, our 'shapes' are taken to be open subsets of Euclidean space with smooth boundaries, then this space will be a Banach or Frechet manifold, but a highly non-linear one. The question of finding the right mathematical model for the space of such shapes is not unlike moduli problems and I tried to get a grip on this as soon as I looked at vision problems. Around 2004 I met Peter Michor and found that he had systematically developed the foundations of differential geometry of such infinite dimensional spaces. This seemed to be the right tool for studying the above spaces of shapes. Since then, we have been studying various Riemannian metrics on them and their associated completions; the geodesics in these metrics and the curvature of the space; examples and applications to object recognition.

*ACM Transactions on Graphics**39 (2): 1--14*(*April 2020*)*Comput. Graph. Forum**39 (5): 69-80*(*2020*)- (
*2019*)*cite arxiv:1904.00235.* - (
*2004*)*cite arxiv:math/0412421Comment: The textbook, AmSTeX, 132 pages, amsppt style, prepared for double side printing on letter size paper.* *Proc. Conference, Soc. Photo-optical & Ind. Engineers (SPIE)*(*1991*)- (
*July 2008*)