Improved marching cubes using novel adjacent lookup table and random sampling for medical object-specific 3D visualization

Wang, Xuchu; Niu, Yanmin; Tan, Liwen; Zhang, Shaoxiang

doi:10.4304/jsw.9.10.2528-2537

Cited by 8 publications

(6 citation statements)

References 24 publications

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“…For example, the Krylov subspace iteration method (e.g., GMRES with preconditioners [32]) and fast algorithm (e.g., Fast Multipole Method (FMM) [33], especially kernel independent FMM [34]) are suggested for implementation. In the surface reconstruction of an implicit function, the surface-following method [35], [36] based on the Marching Cubes algorithm is implemented. The method tracks the isosurface using the voxel growing strategy.…”

Section: ) Tangent Constraintmentioning

confidence: 99%

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

Zhong

Wang

2020

IEEE Access

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In this paper, we present an extended Hermite radial basis functions interpolant for surface reconstruction of sparse contours that allows for shape control with interactive constraints. Similar to the differential operator, the difference operator is used to construct gradient constraint and tangent constraint. Based on the theory of Hermite-Birkhoff interpolation, to construct more flexible geometry constraints, we incorporate the differential operator and difference operator to construct interpolation conditions in the interpolant. We construct some constraint rules to control the local trend of shape interactively. It is useful when the method interpolates sparse data that satisfies all the constraints but exhibits an undesirable trend of shape. For example, the interactive constraints can be used to fix holes or intersections for geometrically valid meshes. Regarding the geometry domain as a signed distance field of implicit function, we implement a constraint-based approach to interpolate the contours using the interpolant. The improved method can flexibly handle both parallel and non-parallel sparse contours. The numerical results of real geological and medical data show the robustness and performance of the extended Hermite radial basis functions interpolant. INDEX TERMS Hermite radial basis functions, radial basis functions, contours interpolation, signed distance field, geometry constraints.

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Section: ) Tangent Constraintmentioning

confidence: 99%

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

Zhong

Wang

2020

IEEE Access

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“…Wang et al [15] proposed in 2014 a method to address the problem of needing to access the cubes sequentially and the inability of the algorithm to directly separate the isosurfaces. The authors propose a lookup table which tracks connected surfaces instead of searching isosurfaces cell-by-cell.…”

Section: Related Workmentioning

confidence: 99%

An extended triangulation to the Marching Cubes 33 algorithm

2019

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The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with "+," "−," and "=," according to the relationship between its scalar field value and the isovalue. The inclusion of the "=" grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

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“…To ensure fast dynamic update of the implicit model, in addition to fast solution of interpolation equations for the implicit model, fast evaluation of interpolation points for the implicit model should also be realized. By constructing the initial voxel seed points and using certain voxel growth rules [31] to track the surface reconstruction process, we can avoid the radial basis functions from evaluating the function values on all voxel grid points and thus speed up the process of surface reconstruction.…”

Section: Fast Reconstructionmentioning

confidence: 99%

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

et al. 2019

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In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.

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Improved marching cubes using novel adjacent lookup table and random sampling for medical object-specific 3D visualization

Cited by 8 publications

References 24 publications

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

Extended Hermite Radial Basis Functions for Sparse Contours Interpolation

An extended triangulation to the Marching Cubes 33 algorithm

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

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