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57
Geometric Skinning with Approximate Dual Quaternion Blending
, 2008
"... Skinning of skeletally deformable models is extensively used for realtime animation of characters, creatures and similar objects. The standard solution, linear blend skinning, has some serious drawbacks that require artist intervention. Therefore, a number of alternatives have been proposed in re ..."
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Cited by 56 (3 self)
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Skinning of skeletally deformable models is extensively used for realtime animation of characters, creatures and similar objects. The standard solution, linear blend skinning, has some serious drawbacks that require artist intervention. Therefore, a number of alternatives have been proposed in recent years. All of them successfully combat some of the artifacts, but none challenge the simplicity and efficiency of linear blend skinning. As a result, linear blend skinning is still the number one choice for the majority of developers. In this paper, we present a novel skinning algorithm based on linear combination of dual quaternions. Even though our proposed method is approximate, it does not exhibit any of the artifacts inherent in previous methods and still permits an efficient GPU implementation. Upgrading an existing animation system from linear to dual quaternion skinning is very easy and has a relatively minor impact on runtime performance.
Reconstruction of Deforming Geometry from TimeVarying Point Clouds
, 2007
"... In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent realtime range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondenc ..."
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Cited by 46 (12 self)
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In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent realtime range scanning devices. Our technique reconstructs both the geometry and dense correspondences over time. Using the correspondences, holes due to occlusion are filled in from other frames. Our reconstruction technique is based on a statistical framework: The reconstruction should both match the measured data points and maximize prior probability densities that prefer smoothness, rigid deformation and smooth movements over time. The optimization procedure consists of an inner loop that optimizes the 4D shape using continuous numerical optimization and an outer loop that infers the discrete 4D topology of the data set using an iterative model assembly algorithm. We apply the technique to a variety of data sets, demonstrating that the new approach is capable of robustly retrieving animated models with correspondences from data sets suffering from significant noise, outliers and acquisition holes.
Skinning with dual quaternions
 IN PROCEEDINGS OF THE 2007 SYMPOSIUM ON INTERACTIVE 3D GRAPHICS AND GAMES
, 2007
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Fourth order partial differential equations on general geometries
 UNIVERSITY OF CALIFORNIA LOS ANGELES
, 2005
"... We extend a recently introduced method for numerically solving partial differential equations on implicit surfaces (Bertalmío, Cheng, Osher, and Sapiro 2001) to fourth order PDEs including the CahnHilliard equation and a lubrication model for curved surfaces. By representing a surface in ¡ N as the ..."
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Cited by 26 (4 self)
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We extend a recently introduced method for numerically solving partial differential equations on implicit surfaces (Bertalmío, Cheng, Osher, and Sapiro 2001) to fourth order PDEs including the CahnHilliard equation and a lubrication model for curved surfaces. By representing a surface in ¡ N as the level set of a smooth function, φ ¢ we compute the PDE using only finite differences on a standard Cartesian mesh in ¡ N. The higher order equations introduce a number of challenges that are of small concern when applying this method to first and second order PDEs. Many of these problems, such as timestepping restrictions and large stencil sizes, are shared by standard fourth order equations in Euclidean domains, but others are caused by the extreme degeneracy of the PDEs that result from this method and the general geometry. We approach these difficulties by applying convexity splitting methods, ADI schemes, and iterative solvers. We discuss in detail the differences between computing these fourth order equations and computing the first and second order PDEs considered in earlier work. We explicitly derive schemes for the linear fourth order diffusion, the CahnHilliard equation for phase transition in a binary alloy, and surface tension driven flows on complex geometries. Numerical examples validating our methods are presented for these flows for data on general surfaces.
A geometric method for automatic extraction of sulcal fundi
 IEEE Intl. Symp. Biomedical Imaging, From Nano to Macro
, 2006
"... Sulcal fundi are 3D curves that lie in the depths of the cerebral cortex and are often used as landmarks for downstream computations in brain imaging. We present a sequence of geometric algorithms which automatically extract the sulcal fundi from magnetic resonance images and represent them as smoot ..."
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Cited by 17 (5 self)
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Sulcal fundi are 3D curves that lie in the depths of the cerebral cortex and are often used as landmarks for downstream computations in brain imaging. We present a sequence of geometric algorithms which automatically extract the sulcal fundi from magnetic resonance images and represent them as smooth polylines lying on the cortical surface. First we compute a geometric depth measure for each point on the cortical surface, and based on this information we extract sulcal regions by checking the connectivity above a depth threshold. We then extract the endpoints of each fundus and delineate the fundus by thinning each connected region keeping the endpoints fixed. The curves thus defined are smoothed using weighted splines on the graymatter surface to yield highquality representations of the sulcal fundi 1.
Implicit brain imaging
 NeuroImage
, 2004
"... We describe how implicit surface representations can be used to solve fundamental problems in brain imaging. This kind of representation is not only natural following the stateoftheart segmentation algorithms reported in the literature to extract the different brain tissues, but it is also, as sh ..."
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Cited by 16 (7 self)
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We describe how implicit surface representations can be used to solve fundamental problems in brain imaging. This kind of representation is not only natural following the stateoftheart segmentation algorithms reported in the literature to extract the different brain tissues, but it is also, as shown in this paper, the most appropriate one from the computational point of view. Examples are provided for finding constrained special curves on the cortex, such as sulcal beds, regularizing surface based measures, such as cortical thickness, and for computing warping fields between surfaces such as the brain cortex. All these result from efficiently solving partial differential equations and variational problems on surfaces represented in implicit form. The implicit framework avoids the need to construct intermediate mappings between 3D anatomical surfaces and parametric objects such planes or spheres, a complex step that introduces errors and is required by many other cortical processing approaches. 1
A Robust TwoStep Procedure for QuadDominant Remeshing
 Computer Graphics Forum
, 2006
"... We propose a new technique for quaddominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches w ..."
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Cited by 15 (2 self)
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We propose a new technique for quaddominant remeshing which separates the local regularity requirements from the global alignment requirements by working in two steps. In the first step, we apply a slight variant of variational shape approximation in order to segment the input mesh into patches which capture the global structure of the processed object. Then we compute an optimized quadmesh for every patch by generating a finite set of candidate curves and applying a combinatorial optimization procedure. Since the optimization is performed independently for each patch, we can afford more complex operations while keeping the overall computation times at a reasonable level. Our quadmeshing technique is robust even for noisy meshes and meshes with isotropic or flat regions since it does not rely on the generation of curves by integration along estimated principal curvature directions.
Constrained curve fitting on manifolds
 COMPUTERAIDED DESIGN
, 2008
"... When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a Bspline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to ..."
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Cited by 7 (1 self)
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When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a Bspline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to lie on a smooth manifold. The onmanifold constraint is included by using the first fundamental form of the surface for squared distance computations between the point cloud and the fitting curve. For the solution we employ a constrained optimization algorithm that allows us to include further constraints such as onesided fitting or surface regions that have to be avoided by the fitting curve. We illustrate the effectiveness of our algorithm at hand of several examples showing different applications.
A Fast and Practical Algorithm for Generalized Penetration Depth Computation
 Robotics: Science and Systems Conference (RSS07
, 2007
"... Abstract — We present an efficient algorithm to compute the generalized penetration depth (PD g) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PD g computation ba ..."
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Cited by 6 (2 self)
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Abstract — We present an efficient algorithm to compute the generalized penetration depth (PD g) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PD g computation based on modeldependent distance metrics using displacement vectors. As a result, our formulation is independent of the choice of inertial and bodyfixed reference frames, as well as specific representation of the configuration space. Furthermore, we show that the optimum answer lies on the boundary of the contact space and pose the computation as a constrained optimization problem. We use global approaches to find an initial guess and present efficient techniques to compute a local approximation of the contact space for iterative refinement. We highlight the performance of our algorithm on many complex models. I.