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203
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 505 (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 153 (10 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 151 (12 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.
Interpolating Implicit Surfaces From Scattered Surface Data Using Compactly Supported Radial Basis Functions
, 2001
"... We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sam ..."
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Cited by 108 (4 self)
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We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sampling. These methods were first applied to implicit surfaces by Savchenko, et al. and later developed independently by Turk and O'Brien as a means of performing shape interpolation. Earlier approaches were limited as a modeling mechanism because of the order of the computational complexity involved. We explore and extend these implicit interpolating methods to make them suitable for systems of large numbers of scattered surface points by using compactly supported radial basis interpolants. The use of compactly supported elements generates a sparse solution space, reducing the computational complexity and making the technique practical for large models. The local nature of compactly supported radial basis functions permits the use of computational techniques and data structures such as kd trees for spatial subdivision, promoting fast solvers and methods to divide and conquer many of the subproblems associated with these methods. Moreover, the representation of complex models permits the exploration of diverse surface geometry. This reduction in computational complexity enables the application of these methods to the study of shape properties of large complex shapes.
Realtime raycasting and advanced shading of discrete isosurfaces
 COMPUTER GRAPHICS FORUM
, 2005
"... This paper presents a realtime rendering pipeline for implicit surfaces defined by a regular volumetric grid of samples. We use a raycasting approach on current graphics hardware to perform a direct rendering of the isosurface. A twolevel hierarchical representation of the regular grid is emplo ..."
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Cited by 82 (11 self)
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This paper presents a realtime rendering pipeline for implicit surfaces defined by a regular volumetric grid of samples. We use a raycasting approach on current graphics hardware to perform a direct rendering of the isosurface. A twolevel hierarchical representation of the regular grid is employed to allow objectorder and imageorder empty space skipping and circumvent memory limitations of graphics hardware. Adaptive sampling and iterative refinement lead to highquality ray/surface intersections. All shading operations are deferred to image space, making their computational effort independent of the size of the input data. A continuous thirdorder reconstruction filter allows onthefly evaluation of smooth normals and extrinsic curvatures at any point on the surface without interpolating data computed at grid points. With these local shape descriptors, it is possible to perform advanced shading using highquality lighting and nonphotorealistic effects in realtime.
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 74 (3 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.
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 61 (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
M.F.: Artistdirected inversekinematics using radial basis function interpolation
 Computer Graphics Forum (Proceedings of Eurographics
, 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 56 (0 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 char
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 56 (5 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.
ImageBased SpatioTemporal Modeling and View Interpolation of Dynamic Events
 TO APPEAR IN THE ACM TRANSACTIONS ON GRAPHICS
, 2005
"... We present an approach for modeling and rendering a dynamic, realworld event from an arbitrary viewpoint, and at any time, using images captured from multiple video cameras. The event is modeled as a nonrigidly varying dynamic scene, captured by many images from different viewpoints, at discrete t ..."
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Cited by 55 (1 self)
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We present an approach for modeling and rendering a dynamic, realworld event from an arbitrary viewpoint, and at any time, using images captured from multiple video cameras. The event is modeled as a nonrigidly varying dynamic scene, captured by many images from different viewpoints, at discrete times. First, the spatiotemporal geometric properties (shape and instantaneous motion) are computed. The view synthesis problem is then solved using a reverse mapping algorithm, raycasting across space and time, to compute a novel image from any viewpoint in the 4D space of position and time. Results are shown on realworld events captured in the CMU 3D Room, by creating synthetic renderings of the event from novel, arbitrary positions in space and time. Multiple such recreated renderings can be put together to create retimed flyby movies of the event, with the resulting visual experience richer than that of a regular video clip, or switching between images from multiple cameras.