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Interpolation of Manifold-Valued Functions via the Polar Decomposition

Evan Gawlik


Manifold-valued data and manifold-valued functions play an important role in a wide variety of applications, including mechanics, computer vision and graphics, medical imaging, and numerical relativity. This talk will discuss techniques for interpolating manifold-valued functions, approximating the Riemannian exponential map on matrix manifolds, and computing means on matrix manifolds. Emphasis will be placed on techniques that involve the polar decomposition -- the well-known factorization of a real nonsingular matrix into the product of a symmetric positive-definite matrix times an orthogonal matrix -- and its generalization to Lie groups.

Tuesday, February 6, 2018
11:00AM AP&M 2402