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Actions as spacetime shapes
 IN ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 651 (4 self)
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Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes
Shape space
, 2010
"... Abstract This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L2metric. We first show how to solve differenti ..."
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Abstract This paper deals with restricting curve evolution to a finite and not necessarily flat space of curves, obtained as a subspace of the infinite dimensional space of planar curves endowed with the usual but weak parametrization invariant curve L2metric. We first show how to solve
Geometric modeling in shape space
 In Proc. SIGGRAPH
, 2007
"... Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an asisometricaspossible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, ..."
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Cited by 74 (8 self)
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, segmentation, or knowledge of articulated components is used. We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes – triangular meshes or more generally straight line graphs in Euclidean space – are treated as points in a shape space. We introduce useful Riemannian metrics
A theory of shape by space carving
 In Proceedings of the 7th IEEE International Conference on Computer Vision (ICCV99), volume I, pages 307– 314, Los Alamitos, CA
, 1999
"... In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarilyshaped scene from multiple photographs taken at known but arbitrarilydistributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a ..."
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Cited by 566 (14 self)
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of a special member of this class, the photo hull, that (1) can be computed directly from photographs of the scene, and (2) subsumes all other members of this class. We then give a provablycorrect algorithm, called Space Carving, for computing this shape and present experimental results on complex
Shape space from deformation
 Computational Geometry: Theory and Applications 19
, 2001
"... The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. ..."
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Cited by 20 (10 self)
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The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes
Keywords: Shape space
"... a no els. A at eac ing two shapes on the shape space manifold. The geodesic distance illustrates the similarity ies, s missi Therefore, physically based approaches, such as deformable models, are employed to approximate the object e shape [2], consuch as m. Then, an r is minim classify the shapes. ..."
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a no els. A at eac ing two shapes on the shape space manifold. The geodesic distance illustrates the similarity ies, s missi Therefore, physically based approaches, such as deformable models, are employed to approximate the object e shape [2], consuch as m. Then, an r is minim classify the shapes
Directional Statistics and Shape Analysis
, 1995
"... There have been various developments in shape analysis in the last decade. We describe here some relationships of shape analysis with directional statistics. For shape, rotations are to be integrated out or to be optimized over whilst they are the basis for directional statistics. However, various c ..."
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Cited by 794 (33 self)
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to shape analysis. Note that the idea of using tangent space for analysis is common to both manifold as well. 1 Introduction Consider shapes of configurations of points in Euclidean space. There are various contexts in which k labelled points (or "landmarks") x 1 ; :::; x k in IR m are given
RNA Shape Space Topology
, 1999
"... The distinction between continuous and discontinuous transitions is a longstanding problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the probabi ..."
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Cited by 18 (8 self)
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the probabilities with which of one phenotype is accessible from another through changes at the genotypic level. The shape space of RNA secondary structures is used to illustrate this approach. We show that evolutionary trajectories are continuous if and only if they follow connected paths in phenotype space.
Shape Space Exploration of . . .
"... We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of nonlinear constraints. We computationally access such manifolds, typically of high dimension and codimension, through first and second order approximants, namel ..."
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We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of nonlinear constraints. We computationally access such manifolds, typically of high dimension and codimension, through first and second order approximants
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2004
"... For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths of ge ..."
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Cited by 170 (37 self)
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For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinitedimensional spaces and their pairwise di#erences are quantified using the lengths
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