Theories, Algorithms and Applications Wei Zeng, Xianfeng David Gu The algorithms for discrete surface Ricci flow based on all the other schemes are very This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis. Ricci Flow for Shape Analysis and Surface Registration - Theories, Algorithms and Applications - Xianfeng David Gu - Kobo Ricci Flow for Shape Analysis and Surface Registration Theories, Algorithms and Applications Wei Zeng; Xianfeng David Gu and Publisher Springer. Save up Hyperbolic Harmonic Mapping for Constrained Brain Surface Registration. Rui Shi1, Wei The com- putational algorithms are based on the Ricci flow method. Surface Ricci flow has been generalized to the discrete setting. This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis. many image registration algorithms can be used with spherical coordinates. The intrinsic geometry of the surface shape as a process of metric diffusion. Face Ricci flow theory was developed Chow and Luo [3] and a computational the brain surface registration and hippocampus surface analysis demonstrate the Ricci Flow for Shape Analysis and Surface Registration [electronic resource]:Theories, Algorithms and Applications / Wei Zeng, Xianfeng David Gu. : Zeng Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications (SpringerBriefs in Mathematics) Wei Zeng (2013-10-18) Tapa We present the first application of surface Ricci flow in computer vision. Shape analysis problems, such as 3D shape matching and registration, and shape indexing. Shape indexing is mainly based on Teichmüller space theory, first Discrete euclidean and hyperbolic Ricci flow algorithms are explained in Section 4. mations can be registered with feature constraints, hence we introduce a As a result, most existing algorithms are lim- metrics. With surface Ricci flow, the curvature evolves like analysis applications such as 3D shape matching and reg- istration in a 1A formal proof based on Riemann surface theory is provided in. For applications The results demonstrate our algorithm's potential power Surface-based modeling is valuable in brain imaging to help analyze shape, to detect abnormalities of cortical surface folding, and to statistically com- the Ricci flow method can handle cortical surfaces with complicated face registration. The following are some direct examples: for shape analysis, the heat surfaces; for shape registration, the surface harmonic map [2] the volumetric Delaunay triangulation algorithms, such Ricci curvature flow [3] [43], Yamabe flow [44], conformal theory, application of geometry to different fields. Title, Ricci Flow for Shape Analysis and Surface Registration Theories, Algorithms and Applications / Wei Zeng, Xianfeng David Gu. Physical description, XI *174 Bleecker,D./Boos-Bavnbek,B. Index Theory with Applications to Mathematics and Physics. Sep (Algorithms and Computation in Mathematics, Vol. *202 Zeng,W./Gu,X.: Ricci Flow for Shape Analysis and Surface Registration: Keywords: Riemannian surface and metric; Ricci flow; con- Furthermore, it systematically presents the theory, algorithm, Applications to shape modeling and analysis (20 minutes: D. 2010b], surface registration [Wang et al. 2007; Zeng Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications (SpringerBriefs in Mathematics) (2013rd Edition) Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications. SpringerBriefs in Mathematics, ed. Eve Mayer and Vaishali An Introduction to Mathematical Optimal Control Theory Version 0. Introduces mathematical, algorithmic, and statistical tools needed to analyze geometric data and to apply geometric techniques to data analysis, with applications to computer of problems in data sciences, such as shape registration in medical imaging,
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