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JMIV
2006

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements

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Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements
In medical image analysis and high level computer vision, there is an intensive use of geometric features like orientations, lines, and geometric transformations ranging from simple ones (orientations, lines, rigid body or affine transformations, etc.) to very complex ones like curves, surfaces, or general diffeomorphic transformations. The measurement of such geometric primitives is generally noisy in real applications and we need to use statistics either to reduce the uncertainty (estimation), to compare observations, or to test hypotheses. Unfortunately, even simple geometric primitives often belong to manifolds that are not vector spaces. In previous works [1, 2], we investigated invariance requirements to build some statistical tools on transformation groups and homogeneous manifolds that avoids paradoxes. In this paper, we consider finite dimensional manifolds with a Riemannian metric as the basic structure. Based on this metric, we develop the notions of mean value and covarian...
Xavier Pennec
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JMIV
Authors Xavier Pennec
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