Riemannian calculus in shape spaces

Abstract: Spaces of curves and surfaces or spaces of images are considered as Riemannian manifolds. The talk will develop a calculus on such spaces, which enables

• the computation of distances via minimizing a Riemannian path energy,
• interpolation of shapes along geodesic paths,
• extrapolation via the Riemannian exponential map,
• detail transfer via parallel transport,
• key pose interpolation via Riemannian splines, and
• statistical analysis via Riemannian PCA.

To this end a time discrete calculus is introduced and its convergence is discussed.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

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Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php

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