Matches in SemOpenAlex for { <https://semopenalex.org/work/W4302528462> ?p ?o ?g. }
Showing items 1 to 64 of
64
with 100 items per page.
- W4302528462 abstract "We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on the direct methods in the calculus of variation, on $Gamma$-convergence, and on weighted finite element error estimation. The convergence results of the discrete geodesic calculus are experimentally confirmed for a basic model on a two-dimensional Riemannian manifold. This provides a theoretical basis for applications in computer vision: In particular, discrete geodesics offer an effective tool for shape morphing and the computation of a distance between shapes, the discrete logarithm allows a linear representation of strongly nonlinear shape variability, the discrete exponential map provides a robust tool for shape extrapolation, and the discrete parallel transport can be used to transfer geometric details from one shape to another. The basic operations are exemplarily illustrated for two different shape spaces, the space of viscous volumetric objects and the space of discrete viscous shells." @default.
- W4302528462 created "2022-10-06" @default.
- W4302528462 creator A5050613004 @default.
- W4302528462 creator A5063603168 @default.
- W4302528462 date "2012-10-07" @default.
- W4302528462 modified "2023-09-26" @default.
- W4302528462 title "Variational time discretization of geodesic calculus" @default.
- W4302528462 doi "https://doi.org/10.48550/arxiv.1210.2097" @default.
- W4302528462 hasPublicationYear "2012" @default.
- W4302528462 type Work @default.
- W4302528462 citedByCount "0" @default.
- W4302528462 crossrefType "posted-content" @default.
- W4302528462 hasAuthorship W4302528462A5050613004 @default.
- W4302528462 hasAuthorship W4302528462A5063603168 @default.
- W4302528462 hasBestOaLocation W43025284621 @default.
- W4302528462 hasConcept C102224218 @default.
- W4302528462 hasConcept C12520029 @default.
- W4302528462 hasConcept C132459708 @default.
- W4302528462 hasConcept C134306372 @default.
- W4302528462 hasConcept C153782549 @default.
- W4302528462 hasConcept C162269530 @default.
- W4302528462 hasConcept C162324750 @default.
- W4302528462 hasConcept C165818556 @default.
- W4302528462 hasConcept C195065555 @default.
- W4302528462 hasConcept C2524010 @default.
- W4302528462 hasConcept C2777303404 @default.
- W4302528462 hasConcept C28826006 @default.
- W4302528462 hasConcept C33923547 @default.
- W4302528462 hasConcept C42448751 @default.
- W4302528462 hasConcept C50522688 @default.
- W4302528462 hasConcept C73000952 @default.
- W4302528462 hasConceptScore W4302528462C102224218 @default.
- W4302528462 hasConceptScore W4302528462C12520029 @default.
- W4302528462 hasConceptScore W4302528462C132459708 @default.
- W4302528462 hasConceptScore W4302528462C134306372 @default.
- W4302528462 hasConceptScore W4302528462C153782549 @default.
- W4302528462 hasConceptScore W4302528462C162269530 @default.
- W4302528462 hasConceptScore W4302528462C162324750 @default.
- W4302528462 hasConceptScore W4302528462C165818556 @default.
- W4302528462 hasConceptScore W4302528462C195065555 @default.
- W4302528462 hasConceptScore W4302528462C2524010 @default.
- W4302528462 hasConceptScore W4302528462C2777303404 @default.
- W4302528462 hasConceptScore W4302528462C28826006 @default.
- W4302528462 hasConceptScore W4302528462C33923547 @default.
- W4302528462 hasConceptScore W4302528462C42448751 @default.
- W4302528462 hasConceptScore W4302528462C50522688 @default.
- W4302528462 hasConceptScore W4302528462C73000952 @default.
- W4302528462 hasLocation W43025284621 @default.
- W4302528462 hasLocation W43025284622 @default.
- W4302528462 hasOpenAccess W4302528462 @default.
- W4302528462 hasPrimaryLocation W43025284621 @default.
- W4302528462 hasRelatedWork W1963109055 @default.
- W4302528462 hasRelatedWork W1981848768 @default.
- W4302528462 hasRelatedWork W2025452396 @default.
- W4302528462 hasRelatedWork W2044577408 @default.
- W4302528462 hasRelatedWork W2130044423 @default.
- W4302528462 hasRelatedWork W2320549948 @default.
- W4302528462 hasRelatedWork W2793980966 @default.
- W4302528462 hasRelatedWork W2949301327 @default.
- W4302528462 hasRelatedWork W4297988277 @default.
- W4302528462 hasRelatedWork W4298140757 @default.
- W4302528462 isParatext "false" @default.
- W4302528462 isRetracted "false" @default.
- W4302528462 workType "article" @default.