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12
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 ..."
Abstract

Cited by 392 (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).
Piecewise smooth surface reconstruction
, 1994
"... We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of t ..."
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Cited by 303 (13 self)
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We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.
Largescale modeling of parametric surfaces using spherical harmonics
 In Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT
, 2006
"... We present an approach for largescale modeling of parametric surfaces using spherical harmonics (SHs). A standard least square fitting (LSF) method for SH expansion is not scalable and cannot accurately model large 3D surfaces. We propose an iterative residual fitting (IRF) algorithm, and demonstra ..."
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Cited by 18 (12 self)
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We present an approach for largescale modeling of parametric surfaces using spherical harmonics (SHs). A standard least square fitting (LSF) method for SH expansion is not scalable and cannot accurately model large 3D surfaces. We propose an iterative residual fitting (IRF) algorithm, and demonstrate its effectiveness and scalability in creating accurate SH models for large 3D surfaces. These largescale and accurate parametric models can be used in many applications in computer vision, graphics, and biomedical imaging. As a simple extension of LSF, IRF is very easy to implement and requires few machine resources. 1.
Calculating geometric properties of threedimensional objects from the spherical harmonic representation
, 2005
"... The volume, location of the centroid, and second order moments of a threedimensional starshaped object are determined in terms of the spherical harmonic coefficients of its boundary function. Bounds on the surface area of the object are derived in terms of the spherical harmonic coefficients as wel ..."
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Cited by 2 (0 self)
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The volume, location of the centroid, and second order moments of a threedimensional starshaped object are determined in terms of the spherical harmonic coefficients of its boundary function. Bounds on the surface area of the object are derived in terms of the spherical harmonic coefficients as well. Sufficient conditions under which the moments and area computed from the truncated spherical harmonic series converge to the actual moments and area are established. The proposed method is verified using a scanned head model and by recent measurements of the 433 Eros asteroid. An extension to nonstarshaped objects of genus 0 is provided. The computational complexity of our method is shown to be equal to that of the discrete spherical harmonic transform, which is O(N 2 log 2 N), where N is the maximum order of coefficients retained in the expansion. 1
Groupe de Recherche en Images et Formes de Tunisie (GRIFT),
"... Abstract—The myocardial sintigraphy is an imaging modality which provides functional informations. Whereas, coronarography modality gives useful informations about coronary arteries anatomy. In case of coronary artery disease (CAD), the coronarography can not determine precisely which moderate lesio ..."
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Abstract—The myocardial sintigraphy is an imaging modality which provides functional informations. Whereas, coronarography modality gives useful informations about coronary arteries anatomy. In case of coronary artery disease (CAD), the coronarography can not determine precisely which moderate lesions (artery reduction between 50 % and 70%), known as the “gray zone”, are haemodynamicaly significant. In this paper, we aim to define the relationship between the location and the degree of the stenosis in coronary arteries and the observed perfusion on the myocardial scintigraphy. This allows us to model the impact evolution of these stenoses in order to justify a coronarography or to avoid it for patients suspected being in the gray zone. Our approach is decomposed in two steps. The first step consists in modelling a coronary artery bed and stenoses of different location and degree. The second step consists in modelling the left ventricle at stress and at rest using the sphercical harmonics model and myocardial scintigraphic data. We use the spherical harmonics descriptors to analyse left ventricle model deformation between stress and rest which permits us to conclude if ever an ischemia exists and to quantify it. Keywords—spherical harmonics model, vascular bed, 3D reconstruction, left ventricle, myocardial scintigraphy. I.
APPROACHES DEDICATED TO THE MODELING OF COMPLEX SHAPES APPLICATION TO MEDICAL DATA
"... The way to model complex shapes has a significant influence depending on the context. Handling an object can be considerably increased if a good underlying model is used. On the contrary, preponderant problems can appear if an unsuited model is associated to the object. The main criterion to discrim ..."
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The way to model complex shapes has a significant influence depending on the context. Handling an object can be considerably increased if a good underlying model is used. On the contrary, preponderant problems can appear if an unsuited model is associated to the object. The main criterion to discriminate existing models is to determine the balance between: their ability to control global characteristics and the possibility to handle local features of the shape. The fact is very few models are adapted both to structure and to geometrical modeling. In this paper, we first describe an overview of existing approaches. They can be classified principally in two groups: skeleton based models, used to control the global aspect of the shape, and free form models, used to control local specificities of the object. Then, trying to keep the advantages of both techniques in mind, we present an original approach based on a multilayer model to represent a 3D object. We focus on the ability to take into account both global and local characteristics of a complex shape, on topological and morphological levels, as well as on the geometric level. To do that, the proposed model is composed of three layers. We call the boundary mesh the external layer, including a multiresolution feature. We enhance this representation by adding an internal structure: the inner skeleton, which is topologically equivalent to the input object. In addition to that, a third layer links the structural entity and the geometrical crust, to induce an intermediary level of representation. This approach is applied to classical and medical data through a specific algorithm. 1.
GenusZero Shape Classification Using Spherical Normal Image
"... A new method for three dimensional (3D) genuszero shape classification is proposed. It conformally maps a 3D mesh onto a unit sphere and uses normal vectors to generate a spherical normal image (SNI). Unlike extended Gaussian images which have an ambiguity problem, the SNI is unique for each shape. ..."
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A new method for three dimensional (3D) genuszero shape classification is proposed. It conformally maps a 3D mesh onto a unit sphere and uses normal vectors to generate a spherical normal image (SNI). Unlike extended Gaussian images which have an ambiguity problem, the SNI is unique for each shape. Spherical harmonics coefficients of SNIs are used as feature vectors and a selforganizing map is adopted to explore the structure of a shape model database. Since the method compares only the SNIs of different objects, it is computationally more efficient than the methods which compare multiple 2D views of 3D objects. The experimental results show that the proposed method can discriminate collected 3D shapes very well, and is robust to mesh resolution and pose difference. 1