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26
SemiRegular Mesh Extraction from Volumes
, 2000
"... We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale f ..."
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Cited by 91 (10 self)
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We present a novel method to extract isosurfaces from distance volumes. It generates high quality semiregular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multiscale forcebased solver refines the initial mesh into a semiregular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete isodistance ribbons are rapidly built and connected while respecting the topology of the isosurface implied by the data. Subsequent multiscale refinement is driven by a simple forcebased solver designed to combine good isosurface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the isosurface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.
Interactive Multiresolution Surface Viewing
, 1996
"... Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and levelofdetail control of complex meshes in a unified and theoretically sound way. ..."
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Cited by 79 (6 self)
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Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and levelofdetail control of complex meshes in a unified and theoretically sound way.
Global Illumination of Glossy Environments using Wavelets and Importance
 ACM Transactions on Graphics
, 1996
"... We show how importancedriven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wa ..."
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Cited by 47 (6 self)
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We show how importancedriven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wavelets are used to provide an efficient representation of radiance, importance, and the transport operator. We discuss a number of choices that must be made when constructing a finite element algorithm for glossy global illumination. Our algorithm is based on the standard wavelet decomposition of the transport operator and makes use of a fourdimensional wavelet representation for spatially and angularlyvarying radiance distributions. We use a final gathering step to improve the visual quality of the solution. Features of our implementation include support for curved surfaces as well as texturemapped anisotropic emission and reflection functions. 1 Introduction Radiosity algorithms assum...
Framework for the statistical shape analysis of brain structures using spharmpdm
 In Insight Journal, Special Edition on the Open Science Workshop at MICCAI
, 2006
"... Abstract — Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical ..."
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Cited by 32 (4 self)
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Abstract — Shape analysis has become of increasing interest to the neuroimaging community due to its potential to precisely locate morphological changes between healthy and pathological structures. This manuscript presents a comprehensive set of tools for the computation of 3D structural statistical shape analysis. It has been applied in several studies on brain morphometry, but can potentially be employed in other 3D shape problems. Its main limitations is the necessity of spherical topology. The input of the proposed shape analysis is a set of binary segmentation of a single brain structure, such as the hippocampus or caudate. These segmentations are converted into a corresponding spherical harmonic description (SPHARM), which is then sampled into a triangulated surfaces (SPHARMPDM). After alignment, differences between groups of surfaces are computed using the Hotelling T 2 two sample metric. Statistical pvalues, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information. The correction for multiple comparisons is performed via two separate methods that each have a distinct view of the problem. The first one aims to control the familywise error rate (FWER) or falsepositives via the extrema histogram of nonparametric permutations. The second method controls the false discovery rate and results in a less conservative estimate of the falsenegatives. I.
Multiresolution Curve and Surface Representation: Reversing Subdivision Rules by LeastSquares Data Fitting
, 1998
"... This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, leastsquares data fitting, and wavelets. We show how leastsquares data fitting can be used to "reverse" a subdivision rule, how this reversal is rela ..."
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Cited by 25 (13 self)
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This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, leastsquares data fitting, and wavelets. We show how leastsquares data fitting can be used to "reverse" a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decomposition/reconstruction process can be carried out in linear time and space through the use of a matrix factorization. Some insights that this work brings forth are that the inner product used in a multiresolution analysis influences the support of a wavelet, that wavelets can be constructed by straightforward matrix observations, and that matrix partitioning and factorization can provide alternatives to inverses or duals for building efficient decomposition and reconstruction processes. We illustrate our findings using an example curve, greyscale image, and tensorproduct surface. Keywords: Su...
A Novel Hemispherical Basis for Accurate and Efficient Rendering
, 2004
"... This paper presents a new set of hemispherical basis functions dedicated to hemispherical data representation. These functions are derived from associated Legendre polynomials. We demonstrate the usefulness of this basis for representation of surface reectance functions, rendering using environment ..."
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Cited by 22 (6 self)
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This paper presents a new set of hemispherical basis functions dedicated to hemispherical data representation. These functions are derived from associated Legendre polynomials. We demonstrate the usefulness of this basis for representation of surface reectance functions, rendering using environment maps and for efficient global illumination computation using radiance caching. We show that our basis is more appropriate for hemispherical functions than spherical harmonics. This basis can be efficiently combined with spherical harmonics in applications involving both hemispherical and spherical data.
Multiresolution Analysis on Irregular Surface Meshes
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... Waveletbased methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to b ..."
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Cited by 20 (3 self)
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Waveletbased methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4to1 split triangular meshes. In particular, the necessity of subdivisionconnectivity prevents the application of waveletbased methods on irregular triangular meshes. In this paper a "waveletlike" decomposition is introduced, that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelettheory allowing hierarchical meshes without subdivisionconnectivity property. Among others, this approach has the following features: ffl it allows exact reconstr...
Interactive Rendering of Wavelet Projected Light Fields
, 1999
"... Light field techniques allow the rendering of objects in time complexity unrelated to their geometric complexity. The technique discretely samples the space of light rays exiting the boundary around an object and then reconstructs a requested view from these data. In order to generate high quality i ..."
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Cited by 17 (0 self)
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Light field techniques allow the rendering of objects in time complexity unrelated to their geometric complexity. The technique discretely samples the space of light rays exiting the boundary around an object and then reconstructs a requested view from these data. In order to generate high quality images a dense sampling of the space is required which leads to large data sets. These data sets exhibit a high degree of coherence and should be compressed in order to make their size manageable. We present
Surface modeling and parameterization with manifolds
 In ACM SIGGRAPH 2006 Courses, 1–81
"... What do the configuration space of an animation skeleton, a subdivision surface and a panorama have in common? All of these are examples of manifolds. The goal of this course is to present an overview of manifold constructions which are useful for graphics applications, with a focus on twodimension ..."
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Cited by 10 (1 self)
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What do the configuration space of an animation skeleton, a subdivision surface and a panorama have in common? All of these are examples of manifolds. The goal of this course is to present an overview of manifold constructions which are useful for graphics applications, with a focus on twodimensional manifolds (surfaces). Description Many diverse applications in different areas of computer graphics, including geometric modeling, rendering and animation, require dealing with sets which cannot be easily represented with a single function on a simple domain in a Euclidean space: Examples include surfaces of nontrivial topology, environment maps, reflection/transmission functions, light fields, configuration spaces of animation skeletons, and others. In most cases these objects are described as collections of functions defined on multiple simple domains, with the functions satisfying various constraints (e.g., join smoothly). The unified mathematical view of many such structures is provided by the theory of smooth manifolds. While the concept is standard in mathematics, it is not broadly known in the graphics community and is often perceived as an impractical and complex abstraction. The goal of this halfday course is to present the basic concepts and definitions of manifold theory,
Radiance Caching for Efficient Global Illumination
 IEEE Transactions on Visualization and Computer Graphics
, 2005
"... In this paper we present a ray tracing based method for accelerated global illumination computation in scenes with lowfrequency glossy BRDFs. The method is based on sparse sampling, caching, and interpolating radiance on glossy surfaces. In particular we extend the irradiance caching scheme propose ..."
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Cited by 9 (0 self)
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In this paper we present a ray tracing based method for accelerated global illumination computation in scenes with lowfrequency glossy BRDFs. The method is based on sparse sampling, caching, and interpolating radiance on glossy surfaces. In particular we extend the irradiance caching scheme proposed by Ward et al. [1] to cache and interpolate directional incoming radiance instead of irradiance. The incoming radiance at a point is represented by a vector of coefficients with respect to a spherical or hemispherical basis. The surfaces suitable for interpolation are selected automatically according to the roughness of their BRDF. We also propose a novel method for computing translational radiance gradient at a point.