Many vision problems, such as object recognition and image synthesis, are greatly impacted by deformation of objects. In this paper, we develop a deformation model based on Lie algebraic analysis. This work aims to provide a generative model that explicitly decouples deformation from appearance, which is fundamentally different from the prior work that focuses on deformation-resilient features ...

There is a primitive relationship between Riemannian geometry and classical mechanics: by Newton’s first law, free particles move along straight lines. Consequently, geodesics can be scrutinized by experimenting with the paths of free particles. This brings dynamical concepts to Riemannian geometry, and a recent text in the subject ([3]) also presents classical mechanics, even though its author...

We develop a framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory. Our results connect with and extend ideas developed for higher gauge theories in the framework of 2-connections on 2-bundles. We work with quadrilaterals rather than bigons.

The full-domain “sweep,” in which all angular fluxes in a problem are calculated given previous-iterate values only for the volumetric source, forms the foundation for many iterative methods that have desirable properties [1]. One important property is that iteration counts do not grow with mesh refinement [1]. The sweep solution on parallel machines is complicated by the dependency of a given ...

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports and transports along paths satisfying some additional conditions are constructed. In particular, the equivalence between the concepts “connection” and “(axiomatically defined) parallel transport” is established. Bozhid...

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports and transports along paths satisfying some additional conditions are constructed. In particular, the equivalence between the concepts “connection” and “(axiomatically defined) parallel transport” is established. Bozhid...

The axiomatic approach to parallel transport theory is partially discussed. Bijective correspondences between the sets of connections, (axiomatically defined) parallel transports, and transports along paths satisfying some additional conditions, are constructed. In particular, the equivalence between the concepts “connection” and “(axiomatically defined) parallel transport” is established. Bozh...