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159
Reconstruction and Representation of 3D Objects with Radial Basis Functions
 Computer Graphics (SIGGRAPH ’01 Conf. Proc.), pages 67–76. ACM SIGGRAPH
, 2001
"... We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs al ..."
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Cited by 385 (1 self)
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We use polyharmonic Radial Basis Functions (RBFs) to reconstruct smooth, manifold surfaces from pointcloud data and to repair incomplete meshes. An object's surface is defined implicitly as the zero set of an RBF fitted to the given surface data. Fast methods for fitting and evaluating RBFs allow us to model large data sets, consisting of millions of surface points, by a single RBFpreviously an impossible task. A greedy algorithm in the fitting process reduces the number of RBF centers required to represent a surface and results in significant compression and further computational advantages. The energyminimisation characterisation of polyharmonic splines result in a "smoothest" interpolant. This scaleindependent characterisation is wellsuited to reconstructing surfaces from nonuniformly sampled data. Holes are smoothly filled and surfaces smoothly extrapolated. We use a noninterpolating approximation when the data is noisy. The functional representation is in effect a solid model, which means that gradients and surface normals can be determined analytically. This helps generate uniform meshes and we show that the RBF representation has advantages for mesh simplification and remeshing applications. Results are presented for realworld rangefinder data.
Feature Sensitive Surface Extraction from Volume Data
"... The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) ..."
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Cited by 123 (8 self)
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The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) or freeform modeling often need a topological manifold representation where neighborhood information within the surface is explicitly available. Consequently, it is necessary to find effective conversion algorithms to generate explicit surface descriptions for the geometry which is implicitly defined by a volumetric data set. Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces. In this paper we present a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm. We demonstrate the effectiveness of the new technique with a number of application examples ranging from CSG modeling and simulation to surface reconstruction and remeshing of polygonal models. 1
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 118 (11 self)
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In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
Feature matching and deformation for texture synthesis
 SIGGRAPH ’04, Computer Graphics Proceedings
"... One significant problem in patchbased texture synthesis is the presence of broken features at the boundary of adjacent patches. The reason is that optimization schemes for patch merging may fail when neighborhood search cannot find satisfactory candidates in the sample texture because of an inaccur ..."
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Cited by 50 (2 self)
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One significant problem in patchbased texture synthesis is the presence of broken features at the boundary of adjacent patches. The reason is that optimization schemes for patch merging may fail when neighborhood search cannot find satisfactory candidates in the sample texture because of an inaccurate similarity measure. In this paper, we consider both curvilinear features and their deformation. We develop a novel algorithm to perform feature matching and alignment by measuring structural similarity. Our technique extracts a feature map from the sample texture, and produces both a new feature map and texture map. Texture synthesis guided by feature maps can significantly reduce the number of feature discontinuities and related artifacts, and gives rise to satisfactory results.
Reconstructing surfaces using anisotropic basis functions
 In International Conference on Computer Vision (ICCV) 2001
, 2001
"... Point sets obtained from computer vision techniques are often noisy and nonuniform. We present a new method of surface reconstruction that can handle such data sets using anisotropic basis functions. Our reconstruction algorithm draws upon the work in variational implicit surfaces for constructing ..."
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Cited by 49 (4 self)
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Point sets obtained from computer vision techniques are often noisy and nonuniform. We present a new method of surface reconstruction that can handle such data sets using anisotropic basis functions. Our reconstruction algorithm draws upon the work in variational implicit surfaces for constructing smooth and seamless 3D surfaces. Implicit functions are often formulated as a sum of weighted basis functions that are radially symmetric. Using radially symmetric basis functions inherently assumes, however, that the surface to be reconstructed is, everywhere, locally symmetric. Such an assumption is true only at planar regions, and hence, reconstruction using isotropic basis is insufficient to recover objects that exhibit sharp features. We preserve sharp features using anisotropic basis that allow the surface to vary locally. The reconstructed surface is sharper along edges and at corner points. We determine the direction of anisotropy at a point by performing principal component analysis of the data points in a small neighborhood. The resulting field of principle directions across the surface is smoothed through tensor filtering. We have applied the anisotropic basis functions to reconstruct surfaces from noisy synthetic 3D data and from real range data obtained from space carving. I.
Spatiotemporal view interpolation
 In Proceedings of the 13th ACM Eurographics Workshop on Rendering
, 2002
"... We propose an algorithm for creating novel views of a nonrigidly varying dynamic event by combining images captured from different positions, at different times. The algorithm operates by combining images captured across space and time to compute voxel models of the scene shape at each time instant ..."
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Cited by 48 (5 self)
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We propose an algorithm for creating novel views of a nonrigidly varying dynamic event by combining images captured from different positions, at different times. The algorithm operates by combining images captured across space and time to compute voxel models of the scene shape at each time instant, and dense 3D scene flow between the voxel models (the nonrigid motion of every point in the scene). To interpolate in time the voxel models are “flowed ” using the appropriate scene flow and a smooth surface fit to the result. The novel image is then computed by raycasting to the surface at the intermediate time, following the scene flow to the neighboring time instants, projecting into the input images at those times, and finally blending the results. We use the algorithm to create retimed slowmotion flyby
A Multiscale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
, 2003
"... In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing loca ..."
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Cited by 48 (3 self)
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In this paper, we propose a hierarchical approach to 3D scattered data interpolation with compactly supported basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarsetofine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point
Artistdirected inversekinematics using radial basis function interpolation
 Computer Graphics Forum
, 2001
"... One of the most common tasks in computer animation is inversekinematics, or determining a joint configuration required to place a particular part of an articulated character at a particular location in global space. Inversekinematics is required at designtime to assist artists using commercial 3D ..."
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Cited by 39 (1 self)
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One of the most common tasks in computer animation is inversekinematics, or determining a joint configuration required to place a particular part of an articulated character at a particular location in global space. Inversekinematics is required at designtime to assist artists using commercial 3D animation packages, for motion capture analysis, and for runtime applications such as games. We present an efficient inversekinematics methodology based on the interpolation of example motions and positions. The technique is demonstrated on a number of inversekinematics positioning tasks for a human figure. In addition to simple positioning tasks, the method provides complete motion sequences that satisfy an inversekinematic goal. The interpolation at the heart of the algorithm allows an artist’s influence to play a major role in ensuring that the system always generates plausible results. Due to the lightweight nature of the algorithm, we can position a character at extremely high frame rates, making the technique useful for timecritical runtime applications such as games. 1. Overview A talented animator can create believable characters that spark a desired response in an audience. Believable characters,
Controllable smoke animation with guiding objects
 ACM Transactions on Graphics
, 2005
"... This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target im ..."
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Cited by 35 (3 self)
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This article addresses the problem of controlling the density and dynamics of smoke (a gas phenomenon) so that the synthetic appearance of the smoke (gas) resembles a still or moving object. Both the smoke region and the target object are represented as implicit functions. As a part of the target implicit function, a shape transformation is generated between an initial smoke region and the target object. In order to match the smoke surface with the target surface, we impose carefully designed velocity constraints on the smoke boundary during a dynamic fluid simulation. The velocity constraints are derived from an iterative functional minimization procedure for shape matching. The dynamics of the smoke is formulated using a novel compressible fluid model which can effectively absorb the discontinuities in the velocity field caused by imposed velocity constraints while reproducing realistic smoke appearances. As a result, a smoke region can evolve into a regular object and follow the motion of the object, while maintaining its smoke appearance.
Reconstructing Surfaces By Volumetric Regularization Using Radial Basis Functions
"... We present a new method of surface reconstruction that generates smooth and seamless models from sparse, noisy, nonuniform, and low resolution range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce 3D point sets that are imprecise and no ..."
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Cited by 35 (3 self)
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We present a new method of surface reconstruction that generates smooth and seamless models from sparse, noisy, nonuniform, and low resolution range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce 3D point sets that are imprecise and nonuniform when compared to laser or optical range scanners. Traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to visionbased data sets. Our method constructs a 3D implicit surface, formulated as a sum of weighted radial basis functions. We achieve three primary advantages over existing algorithms: (1) the implicit functions we construct estimate the surface well in regions where there is little data; (2) the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate, rather than exactly interpolate, the data; and (3) the reconstructed surface is locally detailed, yet globally smooth, because we use radial basis functions that achieve multiple orders of smoothness.