Polynomial Regression on Riemannian Manifolds

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Nonparametric <strong>Regression</strong> Number of parameters tied to amount of data present Example: kernel regression on images using diffeomorphisms (Davis2007) <strong>Polynomial</strong> <strong>Regression</strong> on Riemannian Manifolds 2
Parametric <strong>Regression</strong> Small number of parameters can be estimated more efficiently Fletcher 2011 Geodesic regression (Niethammer2011, Fletcher2011) has recently received attention. <strong>Polynomial</strong> <strong>Regression</strong> on Riemannian Manifolds 3
Page 1: Polynomial <strong
Page 5 and 6: Riemannian Polynomial</stro
Page 15 and 16: Rolling maps Leite 2008 Unroll curv
Page 17 and 18: Polynomial <strong
Page 19 and 20: Lagrange multiplier (adjoint) vecto
Page 21 and 22: Rewrite using integration by parts
Page 23 and 24: For any smooth family of curves γ
Page 25 and 26: Now do the same with another term T
Page 27 and 28: Combine all terms to get adjoint eq
Page 29 and 30: Polynomial <strong
Page 31 and 32: Kendall Shape Space Space of N land
Page 33 and 34: Covariant derivative in shape space
Page 35 and 36: First fundamental form is (O’Neil
Page 37 and 38: Corpus Collosum Aging (www.oasis-br
Page 39 and 40: Landmark Space Space L of N points
Page 41 and 42: Have simple formula for cometric g
Page 43 and 44: For curvature, need Christoffel sym
Page 45 and 46: Landmark Regression</strong
Page 47: Thank You!

Polynomial Regression on Riemannian Manifolds

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