Header logo is


2013


Statistics on Manifolds with Applications to Modeling Shape Deformations
Statistics on Manifolds with Applications to Modeling Shape Deformations

Freifeld, O.

Brown University, August 2013 (phdthesis)

Abstract
Statistical models of non-rigid deformable shape have wide application in many fi elds, including computer vision, computer graphics, and biometry. We show that shape deformations are well represented through nonlinear manifolds that are also matrix Lie groups. These pattern-theoretic representations lead to several advantages over other alternatives, including a principled measure of shape dissimilarity and a natural way to compose deformations. Moreover, they enable building models using statistics on manifolds. Consequently, such models are superior to those based on Euclidean representations. We demonstrate this by modeling 2D and 3D human body shape. Shape deformations are only one example of manifold-valued data. More generally, in many computer-vision and machine-learning problems, nonlinear manifold representations arise naturally and provide a powerful alternative to Euclidean representations. Statistics is traditionally concerned with data in a Euclidean space, relying on the linear structure and the distances associated with such a space; this renders it inappropriate for nonlinear spaces. Statistics can, however, be generalized to nonlinear manifolds. Moreover, by respecting the underlying geometry, the statistical models result in not only more e ffective analysis but also consistent synthesis. We go beyond previous work on statistics on manifolds by showing how, even on these curved spaces, problems related to modeling a class from scarce data can be dealt with by leveraging information from related classes residing in di fferent regions of the space. We show the usefulness of our approach with 3D shape deformations. To summarize our main contributions: 1) We de fine a new 2D articulated model -- more expressive than traditional ones -- of deformable human shape that factors body-shape, pose, and camera variations. Its high realism is obtained from training data generated from a detailed 3D model. 2) We defi ne a new manifold-based representation of 3D shape deformations that yields statistical deformable-template models that are better than the current state-of-the- art. 3) We generalize a transfer learning idea from Euclidean spaces to Riemannian manifolds. This work demonstrates the value of modeling manifold-valued data and their statistics explicitly on the manifold. Specifi cally, the methods here provide new tools for shape analysis.

ps

pdf Project Page [BibTex]


no image
Brownian motion of optically trapped ellipsoids

Dibak, Manuel

Universität Stuttgart, Stuttgart, 2013 (mastersthesis)

icm

[BibTex]

[BibTex]


no image
Phase behavior of colloidal suspensions with critical solvents

Mohry, T. F.

Universität Stuttgart, Stuttgart, 2013 (phdthesis)

icm

link (url) [BibTex]

link (url) [BibTex]


no image
Zweidimensionale Monte-Carlo-Gittersimulationen im muVT- und NpT-Ensemble

Kirn, Kai Ludwig

Universität Stuttgart, Stuttgart, 2013 (mastersthesis)

icm

[BibTex]

[BibTex]


no image
Permittivity of an inhomogeneous dipolar lattice fluid

Schütz, Christian

Universität Stuttgart, Stuttgart, 2013 (mastersthesis)

icm

[BibTex]

[BibTex]

2009


no image
From colloids to biophysics: applications of classical density functional theory

Roth, R.

Universität Stuttgart, Stuttgart, 2009 (phdthesis)

icm

[BibTex]

2009


[BibTex]


no image
Stäbchensuspensionen in Kontakt mit geometrisch strukturierten Substraten

Günther, F.

Universität Stuttgart, Stuttgart, 2009 (mastersthesis)

icm

[BibTex]

[BibTex]


no image
Bayesian Methods for Autonomous Learning Systems (Phd Thesis)

Ting, J.

Department of Computer Science, University of Southern California, Los Angeles, CA, 2009, clmc (phdthesis)

am

PDF [BibTex]

PDF [BibTex]

2008


no image
Entropic Forces on Bio-Molecules

Hansen-Goos, H.

Universität Stuttgart, Stuttgart, 2008 (phdthesis)

icm

link (url) [BibTex]

2008


link (url) [BibTex]


no image
Wetting of geometrically structured substrates

Marinescu, M.

Universität Stuttgart, Stuttgart, Germany, 2008 (mastersthesis)

icm

[BibTex]

[BibTex]


no image
Fluktuations- und Kapillarkräfte zwischen Kolloiden an fluiden Grenzflächen

Lehle, H.

Universität Stuttgart, Stuttgart, 2008 (phdthesis)

icm

link (url) [BibTex]

link (url) [BibTex]


no image
Microscopic calculation of line tensions

Merath, R.-J.

Universität Stuttgart, Stuttgart, 2008 (phdthesis)

icm

link (url) [BibTex]

link (url) [BibTex]


no image
Lattice model for fluid flow in narrow channels

Dotti, C.

Universität Stuttgart, Stuttgart, 2008 (phdthesis)

icm

[BibTex]

[BibTex]


no image
Critical Casimir forces

Mohry, T. F.

Universität Stuttgart, Stuttgart, 2008 (mastersthesis)

icm

[BibTex]

[BibTex]

2001


no image
Einflußvon Teilchenbestrahlung auf die Selbst- und Interdiffusion in amorphen Fe-Zr-Legierungen

Schuler, T.

Universität Stuttgart, Stuttgart, 2001 (phdthesis)

icm

[BibTex]

2001


[BibTex]


no image
Diffusion im unterkühlten flüssigen und amorphen Zustand von Zr65Cu175,Ni10Al17,5

Schaaff, P.

Universität Stuttgart, Stuttgart, 2001 (phdthesis)

icm

[BibTex]

[BibTex]