Fast Implicit Surface Reconstruction for the Radial Basis Functions Interpolant

Zhong, Deyun; Zhang, Ju; Wang, Liguan

doi:10.3390/app9245335

Cited by 17 publications

(9 citation statements)

References 33 publications

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“…On the other hand, the number of voxel points involved in the calculation can be reduced through the surface tracking method. For example, the MC algorithm based on the voxel growing method [38] can improve the efficiency of the surface reconstruction.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Repair of Geological Models Based on Multiple Material Marching Cubes

Zhong

Wang

2021

Mathematics

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In this paper, we present a multi-domain implicit surface reconstruction algorithm for geological modeling based on the labeling of voxel points. The improved algorithm sets a label for each voxel point to represent the type of its geological domain and then obtains all the voxel points in the void areas. After that, the improved algorithm modifies the labels of the voxel points in the void areas and finally reconstructs the geological models through the Multiple Material Marching Cubes (M3C) algorithm. The improved algorithm solves the problems of some unexpected overlaps and voids in geological modeling by setting and modifying the labels of the voxel points. Our key contribution is proposing a labeling processing method to repair the overlap and void defects generated in the geological modeling and realizing the improved M3C algorithm. The experimental results of some geological models show the performance of the improved method. Compared with the original method, the improved method can repair the overlap and void defects in geological modeling to ensure the raw structural adjacency relationships of the geological bodies.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Repair of Geological Models Based on Multiple Material Marching Cubes

Zhong

Wang

2021

Mathematics

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“…In Table 2, (1 − r) + means the control function of the compactly supported domain, which satisfies Equation (10). Othake [22] suggests using σ s = 0.75 times the diagonal of the bounding box of the sample points as the r cs , as shown in Equation (11). In practice, the selection of σ s should depend on specific problems.…”

Section: Order Of Continuity Definitionmentioning

confidence: 99%

“…RBF is one of the most stable and accurate implicit method to solve scatter approximation and interpolation problems [7,[9][10][11]. It has been used for a wide range of applications, such as computer graphics, neural network, medical imaging and geological modeling, and intelligent mining [6,[11][12][13]. The RBF has a simple structure and easy to be implemented.…”

Section: Introductionmentioning

confidence: 99%

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An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

2020

Symmetry

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Complex single/multi-body structures are generally found in ship and ocean engineering. They have the smooth, sharp, concave, and convex surface features in common. Precise modeling of the structures is the basis of numerical simulation. However, the most widely used explicit modeling method requires considerable manual operations. The result is also difficult to reproduce. Therefore, this paper presents a Radial basis function (RBF) based hierarchical (h-) adaptive Cartesian grid method. The RBF is introduced for arbitrary implicit modeling over the Cartesian framework. Thanks to its natural properties, the RBF is easy to use, highly automated, and only needs a set of scatter points for modeling. The block-based h-adaptive mesh refinement (AMR) combined with the RBF aims to enhance the local grid resolution. It accelerates the calculation of intersecting points compared with the uniform Cartesian grid. The accuracy, efficiency, and robustness of the proposed method are validated by the simulation of the 3D analytical ellipsoidal surface and the unclosed conic surface. To select suitable parameters, we thoroughly investigated the uncertainty factors including sample points, RBF functions, and h-AMR grids. The simulation results of the single/multi-body Wigley hull and KCS hull forms verified the proper selection of the factors and the feasibility of our method to solve practical problems.

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“… 3D human head model, constructed by marching cubes method (the original source file of this figure is [ 12 ]). …”

Section: Figurementioning

confidence: 99%

Marching Cubes and Histogram Pyramids for 3D Medical Visualization

Visutsak

2020

J. Imaging

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This paper aims to implement histogram pyramids with marching cubes method for 3D medical volumetric rendering. The histogram pyramids are used for feature extraction by segmenting the image into the hierarchical order like the pyramid shape. The histogram pyramids can decrease the number of sparse matrixes that will occur during voxel manipulation. The important feature of the histogram pyramids is the direction of segments in the image. Then this feature will be used for connecting pixels (2D) to form up voxel (3D) during marching cubes implementation. The proposed method is fast and easy to implement and it also produces a smooth result (compared to the traditional marching cubes technique). The experimental results show the time consuming for generating 3D model can be reduced by 15.59% in average. The paper also shows the comparison between the surface rendering using the traditional marching cubes and the marching cubes with histogram pyramids. Therefore, for the volumetric rendering such as 3D medical models and terrains where a large number of lookups in 3D grids are performed, this method is a particularly good choice for generating the smooth surface of 3D object.

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Fast Implicit Surface Reconstruction for the Radial Basis Functions Interpolant

Cited by 17 publications

References 33 publications

Repair of Geological Models Based on Multiple Material Marching Cubes

Repair of Geological Models Based on Multiple Material Marching Cubes

An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

Marching Cubes and Histogram Pyramids for 3D Medical Visualization

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