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2013


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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.

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pdf Project Page [BibTex]


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Class-Specific Hough Forests for Object Detection

Gall, J., Lempitsky, V.

In Decision Forests for Computer Vision and Medical Image Analysis, pages: 143-157, 11, (Editors: Criminisi, A. and Shotton, J.), Springer, 2013 (incollection)

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code Project Page [BibTex]

code Project Page [BibTex]

2012


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Virtual Human Bodies with Clothing and Hair: From Images to Animation

Guan, P.

Brown University, Department of Computer Science, December 2012 (phdthesis)

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pdf [BibTex]

2012


pdf [BibTex]


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From Pixels to Layers: Joint Motion Estimation and Segmentation

Sun, D.

Brown University, Department of Computer Science, July 2012 (phdthesis)

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pdf [BibTex]

pdf [BibTex]


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An Introduction to Random Forests for Multi-class Object Detection

Gall, J., Razavi, N., van Gool, L.

In Outdoor and Large-Scale Real-World Scene Analysis, 7474, pages: 243-263, LNCS, (Editors: Dellaert, Frank and Frahm, Jan-Michael and Pollefeys, Marc and Rosenhahn, Bodo and Leal-Taix’e, Laura), Springer, 2012 (incollection)

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code code for Hough forest publisher's site pdf Project Page [BibTex]

code code for Hough forest publisher's site pdf Project Page [BibTex]


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Home 3D body scans from noisy image and range data

Weiss, A., Hirshberg, D., Black, M. J.

In Consumer Depth Cameras for Computer Vision: Research Topics and Applications, pages: 99-118, 6, (Editors: Andrea Fossati and Juergen Gall and Helmut Grabner and Xiaofeng Ren and Kurt Konolige), Springer-Verlag, 2012 (incollection)

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Project Page [BibTex]

Project Page [BibTex]