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113
Decimation of triangle meshes
 Computer Graphics (SIGGRAPH '92 Proceedings
, 1992
"... The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software. ..."
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Cited by 645 (2 self)
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The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.
Deformable models in medical image analysis: A survey
 Medical Image Analysis
, 1996
"... This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They hav ..."
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Cited by 591 (7 self)
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This article surveys deformable models, a promising and vigorously researched computerassisted medical image analysis technique. Among modelbased techniques, deformable models offer a unique and powerful approach to image analysis that combines geometry, physics, and approximation theory. They have proven to be effective in segmenting, matching, and tracking anatomic structures by exploiting (bottomup) constraints derived from the image data together with (topdown) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the significant variability of biological structures over time and across different individuals. Furthermore, they support highly intuitive interaction mechanisms that, when necessary, allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task. This article reviews the rapidly expanding body of work on the development and application of deformable models to problems of fundamental importance in medical image analysis, includingsegmentation, shape representation, matching, and motion tracking.
Mesh Optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
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Cited by 398 (8 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
A levelset approach to 3d reconstruction from range data
 International Journal of Computer Vision
, 1998
"... This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application d ..."
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Cited by 195 (24 self)
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This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of 3 dimensions, i.e. a volume. Such levelset models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxelbased modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper builds on previous work in both 3D reconstruction and levelset modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for levelset modeling, called the sparsefield algorithm, which combines the advantages of a levelset approach with the computational efficiency and accuracy of a parametric representation. The sparsefield algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the levelset model more accurately than the grid itself. These properties, computational efficiency and subcell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.
A Review of Vessel Extraction Techniques and Algorithms
 ACM Computing Surveys
, 2000
"... Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing r ..."
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Cited by 183 (0 self)
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Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing research. While we have mainly targeted the extraction of blood vessels, neurosvascular structure in particular, we have also reviewed some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We have divided vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) modelbased approaches, (3) trackingbased approaches, (4) artificial intelligencebased approaches, (5) neural networkbased approaches, and (6) miscellaneous tubelike object detection approaches. Some of these categories are further divided into sub categories. We have also created tables to compare the papers in each category against such criteria as dimensionality, input type, preprocessing, user interaction, and result type.
Predicting the Drape of Woven Cloth Using Interacting Particles
, 1994
"... We demonstrate a physicallybased technique for predicting the drape of a wide variety of woven fabrics. The approach exploits a theoretical model that explicitly represents the microstructure of woven cloth with interacting particles, rather than utilizing a continuum approximation. By testing a cl ..."
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Cited by 143 (5 self)
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We demonstrate a physicallybased technique for predicting the drape of a wide variety of woven fabrics. The approach exploits a theoretical model that explicitly represents the microstructure of woven cloth with interacting particles, rather than utilizing a continuum approximation. By testing a cloth sample in a Kawabata fabric testing device, we obtain data that is used to tune the model's energy functions, so that it reproduces the draping behavior of the original material. Photographs, comparing the drape of actual cloth with visualizations of simulation results, show that we are able to reliably model the unique largescale draping characteristics of distinctly different fabric types. iii Figure 1.1: Draping cloth objects 1 Introduction The vast number of uses for cloth are mirrored in the extraordinary variety of types of woven fabrics. These range from the most exquisite fine silks, to the coarsest of burlaps, and are woven from such diverse fibers as natural wool and synth...
A topology preserving level set method for geometric deformable models
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2003
"... Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implement ..."
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Cited by 121 (7 self)
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Active contour and surface models, also known as deformable models, are powerful image segmentation techniques. Geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior, parameterization independence, and ease of implementation. However, a long claimed advantage of geometric deformable models—the ability to automatically handle topology changes—turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved. In this paper, we present a new class of geometric deformable models designed using a novel topologypreserving level set method, which achieves topology preservation by applying the simple point concept from digital topology. These new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces. Moreover, since the topologypreserving constraint is enforced efficiently through local computations, the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models. Several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm.
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 105 (13 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.
Function Representation of Solids Reconstructed from Scattered Surface Points and Contours
 Computer Graphics Forum
, 1995
"... This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation o ..."
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Cited by 93 (13 self)
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This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from crosssections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD for bodies with complex surfaces. 1. Introduction There are a number of applied problems that require interpolation or smoothing of large arrays of randomly measured points of a surface. The main sources of such data are physical measurements taken by scanning an object from different viewing directions. Scattered points arise also in mathematical simulation, for examp...
Topology Adaptive Deformable Surfaces for Medical Image Volume Segmentation
 IEEE Transactions on Medical Imaging
, 1999
"... Deformable models, which include deformable contours (the popular "snakes") and deformable surfaces, are a powerful modelbased medical image analysis technique. We develop a new class of deformable models by formulating deformable surfaces in terms of an Affine Cell Image Decomposition (A ..."
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Cited by 85 (1 self)
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Deformable models, which include deformable contours (the popular "snakes") and deformable surfaces, are a powerful modelbased medical image analysis technique. We develop a new class of deformable models by formulating deformable surfaces in terms of an Affine Cell Image Decomposition (ACID). Our approach significantly extends standard deformable surfaces while retaining their interactivity and other desirable properties. In particular, the ACID induces an efficient reparameterization mechanism that enables parametric deformable surfaces to evolve into complex geometries, even modifying their topology as necessary. We demonstrate that our new ACIDbased deformable surfaces, dubbed "Tsurfaces", can effectively segment complex anatomic structures from medical volume images. KeywordsSegmentation, deformable models, deformable surfaces. I. Introduction The imperfections typical of medical images, such as partial volume averaging, intensity inhomogeneities, limited resolution, and i...