Dual/Primal mesh optimization for polygonized implicit surfaces
17 Jun 2002-pp 171-178
TL;DR: A new method for improving polygonizations of implicit surfaces with sharp features is proposed, which outperforms approaches based on the mesh evolution paradigm in speed and accuracy.
Abstract: A new method for improving polygonizations of implicit surfaces with sharp features is proposed. The method is based on the observation that, given an implicit surface with sharp features, a triangle mesh whose triangles are tangent to the implicit surface at certain inner triangle points gives a better approximation of the implicit surface than the standard marching cubes mesh Lorensen(in our experiments we use VTK marching cubes VTK). First, given an initial triangle mesh, its dual mesh composed of the triangle centroids is considered. Then the dual mesh is modified such that its vertices are placed on the implicit surface and the mesh dual to the modified dual mesh is considered. Finally the vertex positions of that "double dual" mesh are optimized by minimizing a quadratic energy measuring a deviation of the mesh normals from the implicit surface normals computed at the vertices of the modified dual mesh. In order to achieve an accurate approximation of fine surface features, these basic steps are combined with adaptive mesh subdivision and curvature-weighted vertex resampling. The proposed method outperforms approaches based on the mesh evolution paradigm in speed and accuracy.
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TL;DR: This article presents a survey of different techniques for fast visualization of implicit surfaces, focusing closely on polygonization methods, as they are the most suited to fast visualization.
Abstract: Implicit surfaces (IS) are commonly used in image creation, modeling environments, modeling objects, and scientific data visualization. In this article, we present a survey of different techniques for fast visualization of IS. The main classes of visualization algorithms are identified along with the advantages of each in the context of the different types of IS commonly used in computer graphics. We focus closely on polygonization methods, as they are the most suited to fast visualization. Classification and comparison of existing approaches are presented using criteria extracted from current research. This enables the identification of the best strategies according to the number of specific requirements, such as speed, accuracy, quality, or stylization.
52 citations
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TL;DR: A complete morphological analysis framework for 3D point clouds, starting from an unorganized point set sampling a surface, allowing to sample erosions, dilations, closings and openings of an object without any explicit mesh structure is introduced.
Abstract: We introduce a complete morphological analysis framework for 3D point clouds. Starting from an unorganized point set sampling a surface, we propose morphological operators in the form of projections, allowing to sample erosions, dilations, closings and openings of an object without any explicit mesh structure. Our framework supports structuring elements with arbitrary shape, accounts robustly for geometric and morphological sharp features, remains efficient at large scales and comes together with a specific adaptive sampler. Based on this meshless framework, we propose applications which benefit from the non-linear nature of morphological analysis and can be expressed as simple sequences of our operators, including medial axis sampling, hysteresis shape filtering and geometry-preserving topological simplification.
40 citations
TL;DR: In this paper, a reverse-engineering method for 3D computerized model from data captured by contemporary 3D scanning devices is proposed, which aggregates large-scale 3D scanned data into an extended Hierarchical Space Decomposition Model (HSDM) based on Octree data structure.
Abstract: 3D scanners developed over the past several decades have facilitated the reconstruction of complicated engineering parts. Typically the boundary representation of a part is reconstructed from its scanned cloud of points. This approach, however, is still limited and cannot be applied to a family of objects such as thin parts. Recently, new 3D scanning devices have been developed. These devices capture additional information, such as normals and texture, as well as conventional information, including clouds of sampled points.This paper describes a new and fast reverse engineering method for creating a 3D computerized model from data captured by contemporary 3D scanning devices. The proposed method aggregates large-scale 3D scanned data into an extended Hierarchical Space Decomposition Model (HSDM) based on Octree data structure. This model can represent both an object's boundary surface and its interior volume. Based on the proposed volumetric model, the surface reconstruction process becomes more robust and stable with respect to sampling noise. The hierarchical structure of the proposed volumetric model enables data reduction, while preserving sharp geometrical features and object topology. As a result of data reduction, the execution time of the reconstruction process is significantly reduced. Moreover, the proposed model naturally allows multiresolution surface reconstruction, represented by a mesh with regular properties. The proposed surface reconstruction approach is based on extracting a Connectivity Graph from the extended HSDM and reconstructing facets based on normals data. The feasibility of the method will be demonstrated on a number of complex objects, including thin parts.
40 citations
21 Jun 2005
TL;DR: This paper is to present an alternative projection operator for surface reconstruction, based on the enriched reproducing kernel particle approximation (ERKPA), which allows the reconstruction process to account for high frequency features, by letting the user explicitly tag the corresponding areas of the scanned geometry.
Abstract: There are many techniques that reconstruct continuous 3D surfaces from scattered point data coming from laser range scanners. One of the most commonly used representations are point set surfaces (PSS) defined as the set of stationary points of a moving least squares (MLS) projection operator. One interesting property of the MLS projection is to automatically filter out high frequency noise, that is usually present in raw data due to scanning errors. Unfortunately, the MLS projection also smoothes out any high frequency feature, such as creases or corners, that may be present in the scanned geometry, and does not offer any possibility to distinguish between such feature and noise. The main contribution of this paper, is to present an alternative projection operator for surface reconstruction, based on the enriched reproducing kernel particle approximation (ERKPA), which allows the reconstruction process to account for high frequency features, by letting the user explicitly tag the corresponding areas of the scanned geometry.
36 citations
TL;DR: A novel approach for accurate polygonization of implicit surfaces with sharp features based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals is presented.
Abstract: The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features. The approach is based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals. Given an initial polygonization of an implicit surface, a mesh evolution process initialized by the polygonization is used. The evolving mesh converges to a limit mesh which delivers a high quality approximation of the implicit surface. For analyzing how close the evolving mesh approachesthe implicit surface we use two error metrics. The metrics measure deviations of the mesh vertices from the implicit surface and deviations of mesh normals from the normals of the implicit surface.
32 citations
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...Our first steps in this direction [20] are very encouraging....
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References
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01 Aug 1987
TL;DR: In this paper, a divide-and-conquer approach is used to generate inter-slice connectivity, and then a case table is created to define triangle topology using linear interpolation.
Abstract: We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
13,231 citations
11,285 citations
"Dual/Primal mesh optimization for p..." refers methods in this paper
...Similar to [10] we use the singular value decomposition [17] to find a minimum-norm least squares solution to (1)....
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03 Aug 1997
TL;DR: This work has developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models, and which also supports non-manifold surface models.
Abstract: Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface and object representations
3,564 citations