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175
Animating sand as a fluid
 ACM Trans. Graph. (Proc. SIGGRAPH
, 2005
"... My thesis presents a physicsbased simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulat ..."
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Cited by 128 (4 self)
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My thesis presents a physicsbased simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator within frictional regime with only a few small additions to account for intergrain and boundary friction, yet with visually acceptable result. We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame. ii Contents ii
Fast image and video colorization using chrominance blending
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2004
"... Colorization, the task of coloring a grayscale image or video, involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions, such as red, green, and blue channels. Mapping between intensity and color is therefore not unique, and colorization is a ..."
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Cited by 81 (9 self)
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Colorization, the task of coloring a grayscale image or video, involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions, such as red, green, and blue channels. Mapping between intensity and color is therefore not unique, and colorization is ambiguous in nature and requires some amount of human interaction or external information. A computationally simple yet effective approach of colorization is presented in this paper. The method is fast so it can be conveniently used “on the fly, ” permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles. Based on concepts of luminanceweighted chrominance blending and fast intrinsic distance computations, high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques. Possible extensions of the algorithm here introduced included the capability of changing colors of an existing color image or video as well as changing the underlying luminance.
3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 74 (3 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
O(N) Implementation of the Fast Marching Algorithm
 Journal of Computational Physics
, 2005
"... In this note we present an implementation of the fast marching algorithm for solving Eikonal equations that reduces the original runtime from O(N log N) to linear. This lower runtime cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm. This improv ..."
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Cited by 68 (11 self)
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In this note we present an implementation of the fast marching algorithm for solving Eikonal equations that reduces the original runtime from O(N log N) to linear. This lower runtime cost is obtained while keeping an error bound of the same order of magnitude as the original algorithm. This improvement is achieved introducing the straight forward untidy priority queue, obtained via a quantization of the priorities in the marching computation. We present the underlying framework, estimations on the error, and examples showing the usefulness of the proposed approach. Key words: Fast marching, HamiltonJacobi and Eikonal equations, distance functions, bucket sort, untidy priority queue.
Level set based shape prior segmentation
 In Proc. CVPR’05
, 2005
"... We propose a level set based variational approach that incorporates shape priors into ChanVese’s model [3] for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers’ work [5], we introduce another labelling level set function to indicate ..."
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Cited by 50 (2 self)
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We propose a level set based variational approach that incorporates shape priors into ChanVese’s model [3] for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers’ work [5], we introduce another labelling level set function to indicate the regions on which the prior shape should be compared. Our model can segment an object, whose shape is similar to the given prior shape, from a background where there are several objects. Moreover, we provide a proof for a fast solution principle, which was mentioned [7] and similar to the one proposed in [19], for minimizing ChanVese’s segmentation model without length term. We extend the principle to the minimization of our prescribed functionals. 1.
A concept for parametric surface fitting which avoids the parametrization problem
, 2003
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Integral Invariants for Robust Geometry Processing
 IN: ICCV ’95: PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON COMPUTER VISION. IEEE COMPUTER SOCIETY
, 2005
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A SURVEY ON MULTIPLE LEVEL SET METHODS WITH APPLICATIONS FOR IDENTIFYING PIECEWISE CONSTANT FUNCTIONS
, 2004
"... We try to give a brief survey about using multiple level set methods for identifying piecewise constant or piecewise smooth functions. A general framework is presented. Application using this general framework for different practical problems are shown. We try to show some details in applying the g ..."
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Cited by 30 (9 self)
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We try to give a brief survey about using multiple level set methods for identifying piecewise constant or piecewise smooth functions. A general framework is presented. Application using this general framework for different practical problems are shown. We try to show some details in applying the general approach for applications to: image segmentation, optimal shape design, elliptic inverse coefficient identification, electricall impedance tomography and positron emission tomography. Numerical experiments are also presented for some of the problems.
A volumetric approach to quantifying regiontoregion white matter connectivity in diffusion tensor MRI
 IPMI
, 2007
"... Abstract. In this paper we present a volumetric approach for quantitatively studying white matter connectivity from diffusion tensor magnetic resonance imaging (DTMRI). The proposed method is based on a minimization of path cost between two regions, defined as the integral of local costs that are d ..."
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Cited by 29 (5 self)
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Abstract. In this paper we present a volumetric approach for quantitatively studying white matter connectivity from diffusion tensor magnetic resonance imaging (DTMRI). The proposed method is based on a minimization of path cost between two regions, defined as the integral of local costs that are derived from the full tensor data along the path. We solve the minimal path problem using a HamiltonJacobi formulation of the problem and a new, fast iterative method that computes updates on the propagating front of the cost function at every point. The solutions for the fronts emanating from the two initial regions are combined, giving a voxelwise connectivity measurement of the optimal paths between the regions that pass through those voxels. The resulting highconnectivity voxels provide a volumetric representation of the white matter pathway between the terminal regions. We quantify the tensor data along these pathways using nonparametric regression of the tensors and of derived measures as a function of path length. In this way we can obtain volumetric measures on whitematter tracts between regions without any explicit integration of tracts. We demonstrate the proposed method on synthetic data and on several fiber tracts from DTMRI data of the normal human brain. 1