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68
Gaussian kdtrees for fast highdimensional filtering
 ACM Trans. Graph
, 2009
"... Figure 1: The Gaussian kdtree accelerates a broad class of nonlinear filters, including the bilateral (left), nonlocal means (middle), and a novel nonlocal means for geometry (right). We propose a method for accelerating a broad class of nonlinear filters that includes the bilateral, nonlocal ..."
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Cited by 69 (5 self)
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Figure 1: The Gaussian kdtree accelerates a broad class of nonlinear filters, including the bilateral (left), nonlocal means (middle), and a novel nonlocal means for geometry (right). We propose a method for accelerating a broad class of nonlinear filters that includes the bilateral, nonlocal means, and other related filters. These filters can all be expressed in a similar way: First, assign each value to be filtered a position in some vector space. Then, replace every value with a weighted linear combination of all values, with weights determined by a Gaussian function of distance between the positions. If the values are pixel colors and the positions are (x, y) coordinates, this describes a Gaussian blur. If the positions are instead (x, y, r, g, b) coordinates in a fivedimensional spacecolor volume, this describes a bilateral filter. If we instead set the positions to local patches of color around the associated pixel, this describes nonlocal means. We describe a MonteCarlo kdtree sampling algorithm that efficiently computes any filter that can be expressed in this way, along with a GPU implementation of this technique. We use this algorithm to implement an accelerated bilateral filter that respects full 3D color distance; accelerated nonlocal means on single images, volumes, and unaligned bursts of images for denoising; and a fast adaptation of nonlocal means to geometry. If we have n values to filter, and each is assigned a position in a ddimensional space, then our space complexity is O(dn) and our time complexity is O(dn log n), whereas existing methods are typically either exponential in d or quadratic in n.
Conformal Flattening by Curvature Prescription and Metric Scaling
, 2008
"... We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topo ..."
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Cited by 52 (2 self)
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We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasiconformal distortion.
Dense Nonrigid Surface Registration Using HighOrder Graph Matching
"... In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper incl ..."
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Cited by 49 (11 self)
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In this paper, we propose a highorder graph matching formulation to address nonrigid surface matching. The singleton terms capture the geometric and appearance similarities (e.g., curvature and texture) while the highorder terms model the intrinsic embedding energy. The novelty of this paper includes: 1) casting 3D surface registration into a graph matching problem that combines both geometric and appearance similarities and intrinsic embedding information, 2) the first implementation of highorder graph matching algorithm that solves a nonconvex optimization problem, and 3) an efficient twostage optimization approach to constrain the search space for dense surface registration. Our method is validated through a series of experiments demonstrating its accuracy and efficiency, notably in challenging cases of large and/or nonisometric deformations, or meshes that are partially occluded. 1.
Volumetric Parameterization and Trivariate Bspline Fitting using Harmonic Functions
"... We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate Bspline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric anal ..."
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Cited by 45 (3 self)
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We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate Bspline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric analysis [Hughes T.J. 2005]. Input data consists of both a closed triangle mesh representing the exterior geometric shape of the object and interior triangle meshes that can represent material attributes or other interior features. The trivariate Bspline geometric and attribute representations are generated from the resulting parameterization, creating trivariate Bspline material property representations over the same parameterization in a way that is related to [Martin and Cohen 2001] but is suitable for application to a much larger family of shapes and attributes. The technique constructs a Bspline representation with guaranteed quality of approximation to the original data. Then we focus attention on a model of simulation interest, a femur, consisting of hard outer cortical bone and inner trabecular bone. The femur is a reasonably complex object to model with a single trivariate Bspline since the shape overhangs make it impossible to model by sweeping planar slices. The representation is used in an elastostatic isogeometric analysis, demonstrating its ability to suitably represent objects for isogeometric analysis.
Discrete Surface Ricci Flow
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
"... This work introduces a unified framework for discrete surface Ricci flow algorithms, including spherical, Euclidean, and hyperbolic Ricci flows, which can design Riemannian metrics on surfaces with arbitrary topologies by userdefined Gaussian curvatures. Furthermore, the target metrics are conform ..."
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Cited by 42 (22 self)
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This work introduces a unified framework for discrete surface Ricci flow algorithms, including spherical, Euclidean, and hyperbolic Ricci flows, which can design Riemannian metrics on surfaces with arbitrary topologies by userdefined Gaussian curvatures. Furthermore, the target metrics are conformal (anglepreserving) to the original metrics. Ricci flow conformally deforms the Riemannian metric on a surface according to its induced curvature, such that the curvature evolves like a heat diffusion process. Eventually, the curvature becomes the user defined curvature. Discrete Ricci flow algorithms are based on a variational framework. Given a mesh, all possible metrics form a linear space, and all possible curvatures form a convex polytope. The Ricci energy is defined on the metric space, which reaches its minimum at the desired metric. The Ricci flow is the negative gradient flow of the Ricci energy. Furthermore, the Ricci energy can be optimized using Newton’s method more efficiently. Discrete Ricci flow algorithms are rigorous and efficient. Our experimental results demonstrate the efficiency, accuracy and flexibility of the algorithms. They have the potential for a wide range of applications in graphics, geometric modeling, and medical imaging. We demonstrate their practical values by global surface parameterizations.
Masked photo blending: mapping dense photographic dataset on highresolution sampled 3D models
 COMPUTER & GRAPHICS
, 2008
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Almost isometric mesh parameterization through abstract domains
 621–635, July/August 2010. [Online]. Available: http://vcg.isti.cnr.it/Publications/ 2010/PTC10
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SketchBased Procedural Surface Modeling and Compositing Using Surface Trees
 EUROGRAPHICS
, 2008
"... We present a system for creating and manipulating layered procedural surface editing operations, which is motivated by the limited support for iterative design in freeform modeling. A combination of sketchbased and traditional modeling tools are used to design soft displacements, sharp creases, ex ..."
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Cited by 18 (4 self)
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We present a system for creating and manipulating layered procedural surface editing operations, which is motivated by the limited support for iterative design in freeform modeling. A combination of sketchbased and traditional modeling tools are used to design soft displacements, sharp creases, extrusions along 3D paths, and topological holes and handles. Using local parameterizations, these edits are combined in a dynamic hierarchy, enabling procedural operations like linked copyandpaste and draganddrop layerbased editing. Such dynamic, layered "surface compositing" is formalized as a Surface Tree, an analog of CSG trees which generalizes previous hierarchical surface modeling techniques. By "anchoring" tree nodes in the parameter space of lower layers, our surface tree implementation can better preserve the semantics of an edit as the underlying surface changes. Details of our implementation are described, including an efficient procedural mesh data structure.
A framework for the objective evaluation of segmentation algorithms using a groundtruth of human segmented 3Dmodels
 SMI ’09: Proceedings of the IEEE International Conference on Shape Modeling and Applications
, 2009
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Mesh Colors
"... Figure 1: A head model textured using mesh colors. The image in the middle shows color samples on the low resolution mesh and the image on the right shows the result after final filtering operations. (Modelled and painted by Murat Afsar) The coloring of three dimensional models using two or three di ..."
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Cited by 14 (0 self)
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Figure 1: A head model textured using mesh colors. The image in the middle shows color samples on the low resolution mesh and the image on the right shows the result after final filtering operations. (Modelled and painted by Murat Afsar) The coloring of three dimensional models using two or three dimensional texture mapping has well known intrinsic problems, such as mapping discontinuities and limitations to model editing after coloring. Workarounds for these problems often require adopting very complex approaches. Here we propose a new technique, called mesh colors, for associating color data directly with a polygonal mesh. The approach eliminates all problems deriving from using a map from texture space to model space. Mesh colors is an extension of vertex colors where, in addition to keeping color values on each vertex, color values are also kept on edges and faces. Like texture mapping, the approach allows higher texture resolution than model resolution, but at the same time it guarantees onetoone correspondence between the model surface and the color data, and eliminates discontinuities. We show that mesh colors integrate well with the current graphics pipeline and can be used to generate very high quality textures.