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Progressive Meshes
"... Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new s ..."
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Cited by 1120 (11 self)
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Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuousresolution representation addresses several practical problems in graphics: smooth geomorphing of levelofdetail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.
Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
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Cited by 443 (7 self)
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ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We present here a selfcontained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers. 1.
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 385 (16 self)
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. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, inplace calculation of the wavelet transform. Several examples are included. Key words. wavelet, multiresolution, second generation wavelet, lifting scheme AMS subject classifications. 42C15 1. Introduction. Wavelets form a versatile tool for representing general functions or data sets. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients. This is based on the fact that most data sets have correlation both in time (or space) and frequenc...
MAPS: Multiresolution Adaptive Parameterization of Surfaces
, 1998
"... We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial param ..."
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Cited by 229 (12 self)
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We construct smooth parameterizations of irregular connectivity triangulations of arbitrary genus 2manifolds. Our algorithm uses hierarchical simplification to efficiently induce a parameterization of the original mesh over a base domain consisting of a small number of triangles. This initial parameterization is further improved through a hierarchical smoothing procedure based on Loop subdivision applied in the parameter domain. Our method supports both fully automatic and user constrained operations. In the latter, we accommodate point and edge constraints to force the align # wailee@cs.princeton.edu + wim@belllabs.com # ps@cs.caltech.edu cowsar@belllabs.com dpd@cs.princeton.edu ment of isoparameter lines with desired features. We show how to use the parameterization for fast, hierarchical subdivision connectivity remeshing with guaranteed error bounds. The remeshing algorithm constructs an adaptively subdivided mesh directly without first resorting to uniform subdivision followed by subsequent sparsification. It thus avoids the exponential cost of the latter. Our parameterizations are also useful for texture mapping and morphing applications, among others.
NonLinear Approximation of Reflectance Functions
, 1997
"... We introduce a new class of primitive functions with nonlinear parameters for representing light reflectance functions. The functions are reciprocal, energyconserving and expressive. They can capture important phenomena such as offspecular reflection, increasing reflectance and retroreflection. ..."
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Cited by 218 (10 self)
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We introduce a new class of primitive functions with nonlinear parameters for representing light reflectance functions. The functions are reciprocal, energyconserving and expressive. They can capture important phenomena such as offspecular reflection, increasing reflectance and retroreflection. We demonstrate this by fitting sums of primitive functions to a physicallybased model and to actual measurements. The resulting representation is simple, compact and uniform. It can be applied efficiently in analytical and Monte Carlo computations. CR Categories: I.3.7 [Computer Graphics]: ThreeDimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation Keywords: Reflectance function, BRDF representation 1 INTRODUCTION The bidirectional reflectance distribution function (BRDF) of a material describes how light is scattered at its surface. It determines the appearance of objects in a scene, through direct illumination and global interreflection effects. Local r...
Progressive Geometry Compression
, 2000
"... We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the r ..."
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Cited by 189 (13 self)
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We propose a new progressive compression scheme for arbitrary topology, highly detailed and densely sampled meshes arising from geometry scanning. We observe that meshes consist of three distinct components: geometry, parameter, and connectivity information. The latter two do not contribute to the reduction of error in a compression setting. Using semiregular meshes, parameter and connectivity information can be virtually eliminated. Coupled with semiregular wavelet transforms, zerotree coding, and subdivision based reconstruction we see improvements in error by a factor four (12dB) compared to other progressive coding schemes. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  hierarchy and geometric transformations; G.1.2 [Numerical Analysis]: Approximation  approximation of surfaces and contours, wavelets and fractals; I.4.2 [Image Processing and Computer Vision]: Compression (Coding)  Approximate methods Additional K...
Wavelet and Multiscale Methods for Operator Equations
 Acta Numerica
, 1997
"... this paper is to highlight some of the underlying driving analytical mechanisms. The price of a powerful tool is the effort to construct and understand it. Its successful application hinges on the realization of a number of requirements. Some space has to be reserved for a clear identification of th ..."
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Cited by 173 (40 self)
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this paper is to highlight some of the underlying driving analytical mechanisms. The price of a powerful tool is the effort to construct and understand it. Its successful application hinges on the realization of a number of requirements. Some space has to be reserved for a clear identification of these requirements as well as for their realization. This is also particularly important for understanding the severe obstructions, that keep us at present from readily materializing all the principally promising perspectives.
Allfrequency shadows using nonlinear wavelet lighting approximation
 ACM Transactions on Graphics
, 2003
"... We present a method, based on precomputed light transport, for realtime rendering of objects under allfrequency, timevarying illumination represented as a highresolution environment map. Current techniques are limited to small area lights, with sharp shadows, or large lowfrequency lights, with ..."
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Cited by 159 (24 self)
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We present a method, based on precomputed light transport, for realtime rendering of objects under allfrequency, timevarying illumination represented as a highresolution environment map. Current techniques are limited to small area lights, with sharp shadows, or large lowfrequency lights, with very soft shadows. Our main contribution is to approximate the environment map in a wavelet basis, keeping only the largest terms (this is known as a nonlinear approximation). We obtain further compression by encoding the light transport matrix sparsely but accurately in the same basis. Rendering is performed by multiplying a sparse light vector by a sparse transport matrix, which is very fast. For accurate rendering, using nonlinear wavelets is an order of magnitude faster than using linear spherical harmonics, the current best technique.
The Lifting Scheme: A New Philosophy in Biorthogonal Wavelet Constructions
 in Wavelet Applications in Signal and Image Processing III
, 1995
"... In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in ..."
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Cited by 154 (0 self)
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In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in a later stage. We show how lifting leads to a faster, fully inplace implementation of the wavelet transform. Moreover, it can be used in the construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one function. A typical example of the latter are wavelets on the sphere. Keywords: wavelet, biorthogonal, inplace calculation, lifting 1 Introduction At the present day it has become virtually impossible to give the definition of a "wavelet". The research field is growing so fast and novel contributions are made at such a rate that even if one manages to give a definition today, it might be obsolete tomorrow. One, very vague, way of thinking about...