Polynomial Regression on Riemannian Manifolds
Polynomial Regression on Riemannian Manifolds
Polynomial Regression on Riemannian Manifolds
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Kendall Shape Space Geometry<br />
(d = 2)<br />
Center point-set and scale so that ∑ N<br />
i=1 |x i| 2 = 1 (resulting<br />
object is called a preshape)<br />
Preshapes lie <strong>on</strong> sphere S 2N−1 , represented as vectors in<br />
(R 2 ) N = C N<br />
<strong>Riemannian</strong> submersi<strong>on</strong> from preshape to shape space:<br />
vertical directi<strong>on</strong> holds rotati<strong>on</strong>s of R 2<br />
Exp<strong>on</strong>ential and log map available in closed form (for d = 2)<br />
<str<strong>on</strong>g>Polynomial</str<strong>on</strong>g> <str<strong>on</strong>g>Regressi<strong>on</strong></str<strong>on</strong>g> <strong>on</strong> <strong>Riemannian</strong> <strong>Manifolds</strong> 19
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