Marching Cubes Method Research Articles

Segmentation and Vascular Vectorization for Coronary Artery by Geometry-based Cascaded Neural Network.

Segmentation of the coronary artery is an important task for the quantitative analysis of coronary computed tomography angiography (CCTA) images and is being stimulated by the field of deep learning. However, the complex structures with tiny and narrow branches of the coronary artery bring it a great challenge. Coupled with the medical image limitations of low resolution and poor contrast, fragmentations of segmented vessels frequently occur in the prediction. Therefore, a geometry-based cascaded segmentation method is proposed for the coronary artery, which has the following innovations: 1) Integrating geometric deformation networks, we design a cascaded network for segmenting the coronary artery and vectorizing results. The generated meshes of the coronary artery are continuous and accurate for twisted and sophisticated coronary artery structures, without fragmentations. 2) Different from mesh annotations generated by the traditional marching cube method from voxel-based labels, a finer vectorized mesh of the coronary artery is reconstructed with the regularized morphology. The novel mesh annotation benefits the geometry-based segmentation network, avoiding bifurcation adhesion and point cloud dispersion in intricate branches. 3) A dataset named CCA-200 is collected, consisting of 200 CCTA images with coronary artery disease. The ground truths of 200 cases are coronary internal diameter annotations by professional radiologists. Extensive experiments verify our method on our collected dataset CCA-200 and public ASOCA dataset, with a Dice of 0.778 on CCA-200 and 0.895 on ASOCA, showing superior results. Especially, our geometry-based model generates an accurate, intact and smooth coronary artery, devoid of any fragmentations of segmented vessels.

A Two-Step Surface Reconstruction Method Using Signed Marching Cubes

In this paper, we explore a new approach, a two-step surface reconstruction method to extract the target isosurface from a given implicit function efficiently. Our main contribution is that we improve the surface reconstruction process by accelerating the speed of evaluation using signed marching cubes. The basic strategy is to filter the invalid voxels that do not intersect with the target isosurface in a low-cost manner, and to evaluate the valid voxels that intersect with the target isosurface accurately. The improved signed marching cubes method consists of a rough evaluation step and an exact evaluation step. The coarse evaluation step evaluates the points of all voxels using the fast multipole method with a lower order. After the rough evaluation step, the voxels that intersect with the target isosurface are screened out. Then, the exact evaluation step evaluates the points of filtered voxels using the fast multipole method with a higher order. The experimental results show that, compared with the traditional marching cubes method, the improved reconstruction method reduces the amounts of calculation for invalid voxels that do not intersect with the target isosurfaces, which is useful to improve the efficiency of surface reconstruction.

Improved Algorithm to Trace Boundary Curves on Two-Dimensional Square Meshes

In the contoured cutter path computation of a mold part, the Minkowski sum shape of the mold part CAD model and an inverted cutter model is sliced by a horizontal plane at a specific height. The cutter path can be obtained by tracing the boundary curve of the cross-sectional figure in the two-dimensional (2D) square mesh model. In the boundary curve tracing of the square mesh, the 2D marching cubes method based on the classification of the cell pattern of the mesh is typically used. We extended the classification pattern so that the existence of very small shapes in the cell, which is ignored by the conventional 2D marching cubes method, is evaluated in tracing the boundary curve. By using this technology, a robust and accurate contoured cutter path can be obtained without any increase in the computation time.

Marching Cubes and Histogram Pyramids for 3D Medical Visualization.

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.

Assessment of the talar deformity and alignment in congenital clubfoot using three-dimensional MRI after Ponseti method

BackgroundPonseti method have been widely accepted as the initial treatment of congenital idiopathic clubfoot because its excellent primary result. On the other hand, relapses after Ponseti method are not uncommon and the cause of relapses have not been fully elucidated. We investigated detailed morphology and alignment of tarsal bones in clubfoot after Ponseti method using three-dimensional MRI analysis. MethodsWe performed MRI with 10 patients of unilateral clubfoot at three months after Achilles tenotomy. Based on the MRI volume data, we reconstructed three-dimensional bone surface model using the marching cubes method. We evaluated the volume of the talus and navicular bone, medial and planter deviation of the talar head and neck, medial deviation of the navicular bone, and internal rotation angle of the distal tibiofibular joint. ResultsIn clubfoot, the volume of talus and navicular bone were significantly smaller compared with the contralateral side. Deviation of the talar head and neck varied from medially to almost the same as that on the contralateral side. The degree of deformity of the talus and alignment of the navicular bone and distal tibiofibular joint showed correlations. ConclusionsPatients with the medial deviated talar neck might have the alignment change of navicular bone and distal tibiofibular joint. Deformity of talar neck might to be compensated by talonavicular joint and distal tibiofibular joint through the manipulation of Ponseti method.

3D modelling strategy for weather radar data analysis

Weather radar data, which have obvious spatial characteristics, represent an important and essential data source for weather identification and prediction, and the multi-dimensional visualization and analysis of such data in a three-dimensional (3D) environment are important strategies for meteorological assessments of potentially disastrous weather. The previous studies have generally used regular 3D raster grids as a basic structure to represent radar data and reconstruct convective clouds. However, conducting weather radar data analyses based on regular 3D raster grids is time-consuming and inefficient, because such analyses involve considerable amounts of tedious data interpolation, and they cannot be used to address real-time situations or provide rapid-response solutions. Therefore, a new 3D modelling strategy that can be used to efficiently represent and analyse radar data is proposed in this article. According to the mode by which the radar data are obtained, the proposed 3D modelling strategy organizes the radar data using logical objects entitled radar-point, radar-line, radar-sector, and radar-cluster objects. In these logical objects, the radar point is the basic object that carries the real radar data unit detected from the radar scan, and the radar-line, radar-sector, and radar-cluster objects organize the radar-point collection in different spatial levels that are consistent with the intrinsic spatial structure of the radar scan. Radar points can be regarded as spatial points, and their spatial structure can support logical objects; thus, the radar points can be flexibly connected to construct continuous surface data with quads and volume data with hexahedron cells without additional tedious data interpolation. This model can be used to conduct corresponding operations, such as extracting an isosurface with the marching cube method and a radar profile with a designed sectioning algorithm to represent the outer and inner structure of a convective cloud. Finally, a case study is provided to verify that the proposed 3D modelling strategy has a better performance in radar data analysis and can intuitively and effectively represent the 3D structure of convective clouds.

Three-dimensional visualization of soil pore structure using computed tomography

The geometric and spatial characteristics of pore structures determine the permeability and water retention of soils, which have important effects on soil functional diversity and ecological restoration. Until recently, there have not been tools and methods to visually and quantitatively describe the characteristics of soil pores. To solve this problem, this research reconstructs the geometry and spatial distribution of soil pores by the marching cubes method, texture mapping method and the ray casting method widely used in literature. The objectives were to explore an optimal method for three-dimensional visualization of soil pore structure by comparing the robustness of the three methods on soil CT images with single pore structure and porosity ranging from low (2–5%) to high (12–18%), and to evaluate the reconstruction performance of the three methods with different geometric features. The results demonstrate that there are aliases (jagged edges) and deficiency at the boundaries of the model reconstructed by the marching cubes method and pore volumes are smaller than the ground truth, whereas the results of the texture mapping method lack the details of pore structures. For all the soil images, the ray casting method is preferable since it better preserves the pore characteristics of the ground truth. Furthermore, the ray casting method produced the best soil pore model with higher rendering speed and lower memory consumption. Therefore, the ray casting method provides a more advanced method for visualization of pore structures and provides an optional technique for the study of the transport of moisture and the exchange of air in soil.

Nonrigid registration of cardiac DSCT images by integrating intensity and point features

Abstract In order to obtain accurate anatomical information for the whole heart, we propose a nonrigid registration method combining mutual information with the marching cubes method. Certain points are regarded as prior knowledge of the shape landmarks of cardiac structures. The registration process for the heart image can be divided into two steps: coarse alignment and accurate registration. The coarse alignment uses affine transformations to localize and center the image of the heart, and the accurate registration uses a B-spline method to constrain the deformation field. Mutual information combined with feature point pairs are used as the similarity measure function. All 15-dimensional feature descriptors are used to identify matched point pairs between marching cubes points in atlas intensity images and other points in the neighborhood of target images needing segmentation. Adaptive stochastic gradient descent optimization is used to obtain optimal registration parameters. Two groups of experiments show that the proposed method achieves higher registration accuracy than traditional ones based only on mutual information. They indicate that accurate anatomical information of the whole cardiac structure can be obtained.

Three dimensional electrochemical simulation of solid oxide fuel cell cathode based on microstructure reconstructed by marching cubes method

In the present study, a model is introduced to correlate the electrochemical performance of solid oxide fuel cell (SOFC) with the 3D microstructure reconstructed by focused ion beam scanning electron microscopy (FIB-SEM) in which the solid surface is modeled by the marching cubes (MC) method. Lattice Boltzmann method (LBM) is used to solve the governing equations. In order to maintain the geometries reconstructed by the MC method, local effective diffusivities and conductivities computed based on the MC geometries are applied in each grid, and partial bounce-back scheme is applied according to the boundary predicted by the MC method. From the tortuosity factor and overpotential calculation results, it is concluded that the MC geometry drastically improves the computational accuracy by giving more precise topology information.

Real-time bone sawing interaction in orthopedic surgical simulation based on the volumetric object

Bone sawing is widely used for mandibular angle reduction. In this paper, we develop a surgical simulator for mandibular angle reduction with real-time collision detection, bone reconstruction and force haptic. A volume-based model was organized following the CT or MRI image sequence arrangement. The surgical instrument was simplified into two triangles in geometric model. Then, a new volume-based collision detection method was used to meet the real-time requirements of the simulator. Currently, most of the bone sawing operations regarded the swept surface as the real cut surface of bone. Due to the high-speed reciprocating of the bone saw operation, we innovatively used Marching Cubes Method for the real-time reconstruction of the bone internal sawing part and provided the users with a fine cutting surface. In addition, to obtain a well virtual effect, a simplified bone removal and reconstruction method is carried out to implement the real-time topological changing of the mandibular surface. This paper presents a mechanistic model for prediction of the force during bone sawing, and the simulated force is similar to the measured force in real surgery. Eventually, we realized the high quality visual rendering and tactile rendering, the refresh rate of the force reaches 1000 Hz, and visual refresh frequency up to 30 Hz. To validate the effectiveness of the system, some experiments of simulator evaluation based on the patient-specific data was constructed. Results shown that the virtual orthopedic surgical simulation system can provide inexperienced interns and students with a low-cost, repeatable surgical training platform.

A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods

This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid (VOF) method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.

Heterogeneous model integration of complex mechanical parts based on semantic feature fusion

Due to the rapid development of computer, sensor, and automatic control technologies, the amount of data generated during product design and manufacturing is increasing significantly. The product data bank is large, complex, heterogeneous, and often fast-changing; it is difficult to integrate heterogeneous models using the conventional method. Therefore, a semantic feature fusion-based heterogeneous model integration method is proposed. First, the error in the geometric dimensions and position are extracted using model registration. Second, the basic geometric feature is obtained using slippage analysis. Third, the extracted data, such as the basic geometric feature and the error in the geometric dimensions and position, are fused into the design model using the level set method. Finally, the marching cubes method is introduced to reconstruct the surface of the fused model. The empirical results demonstrate that the proposed algorithm can integrate all types of semantic features and geometric features into a basic product model effectively and efficiently.

Fast and accurate triangular model generation for the shape-from-silhouette technique

ABSTRACTIn this study, we propose a method for generating triangular meshes of objects based on the shape-from-silhouette (SFS) technique. The proposed algorithm uses the direct intersection of multiple sets of infinite polygons from the silhouettes of two-dimensional (2D) images to acquire the surface points of an object. The surface points are then triangulated according to the topological relationship of the obtained points and the polygons corresponding to each of the points. In addition, a comprehensive study between the proposed method and the marching-cubes method was conducted. The main advantages of the proposed method are that all 3D points are precisely located on the silhouettes of 2D images, and that the number of vertices on the triangular model is very efficient compared to that for the results from the marching-cubes method. In contrast, the marching-cubes method faces noise and resolution problems, where the former is because the vertices are interpolated, and the latter is because the ma...

Octree-based Multiple-material Parallel Unstructured Mesh Generation Method for Seismic Response Analysis of Soil-Structure Systems

We developed an unstructured finite element mesh generation method capable of modeling multiple-material complex geometry problems for large-scale seismic analysis of soil-structure systems. We used an octree structure to decompose the target domain into small subdomains and use the multiple material marching cubes method for robust and parallel tetrahedralization of each subdomain. By using the developed method on a 32 core shared memory machine, we could generate a 594,168,792 tetrahedral element soil-structure model of a power plant in 13h 01min. The validity of the generated model was confirmed by conducting a seismic response analysis on 2,304 compute nodes of the K computer at RIKEN. Although the model contains a small approximation in geometry (half of the minimum octree size) at present, we can expect fast and high quality meshing of large-scale models by making geometry correction in the future, which is expected to help improve the seismic safety of important structures and complex urban systems.

Segmentation of Liver from Abdomen CT images and 3D Visualization

Segmentation of liver is the initial and fundamental step for the diagnosis of liver disease, 3-D volume construction and volume measurement. However, segmentation of liver is a challenging task due to it’s inter and intra intensity and texture similarities among other organs present in CT abdominal images. A semiautomatic method has been proposed to segment the liver portion from CT abdominal images and their three dimensional volume construction by (i)Noise removal using median filter,(ii)Segmentation of liver portion based on active contour method using sparse field method and(iii)liver volume construction using marching cube method. Evaluation of proposed method is carried out on clinically acquired CT images and effectiveness of algorithm is evaluated by comparing manually segmented liver portion marked by radiologist with proposed method

An adaptive octree finite element method for PDEs posed on surfaces

Abstract The paper develops a finite element method for partial differential equations posed on hypersurfaces in R N , N = 2 , 3 . The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk finite element space is defined on an octree grid which is locally refined or coarsened depending on error indicators and estimated values of the surface curvatures. The cartesian structure of the bulk mesh leads to easy and efficient adaptation process, while the trace finite element method makes fitting the mesh to the surface unnecessary. The number of degrees of freedom involved in computations is consistent with the two-dimension nature of surface PDEs. No parametrization of the surface is required; it can be given implicitly by a level set function. In practice, a variant of the marching cubes method is used to recover the surface with the second order accuracy. We prove the optimal order of accuracy for the trace finite element method in H 1 and L 2 surface norms for a problem with smooth solution and quasi-uniform mesh refinement. Experiments with less regular problems demonstrate optimal convergence with respect to the number of degrees of freedom, if grid adaptation is based on an appropriate error indicator. The paper shows results of numerical experiments for a variety of geometries and problems, including advection–diffusion equations on surfaces. Analysis and numerical results of the paper suggest that combination of cartesian adaptive meshes and the unfitted (trace) finite elements provide simple, efficient, and reliable tool for numerical treatment of PDEs posed on surfaces.

Virtual Reality Haptic Simulation of Root Canal Therapy

Here we report a haptic virtual reality simulator for root canal treatment (endodontic procedures). A virtual jaw model was extracted from CT data of a live patient and the volumetric data obtained were visualized using a Marching Cubes algorithm. Collision detection and collision response algorithms were developed using a voxel-based approach. Removal of bone was visualized using a modified real-time Marching Cubes method and deformation of the K-files in the internal surface of tooth canal was simulated haptically and graphically using OpenGL and HDAPI of OpenHaptics Libraries. Using a haptic robot (Omni Phantom) the user can burr the enamel and dentin until reaching the pulp chamber and then the internal surface of a root canal can be cleaned using a simulated K-file.

水面の品質と計算速度のための流体シミュレーションと可視化

A mesh-free method MPS is implemented for fluid simulation. A Marching Cubes method is applied to obtain the free surface of the fluid which is represented by particles. We used a cubic spline instead of the weight function to map particle data into the scalar field in 3D space. The method shows smoothness in surface representation. Then we give a CUDA implementation of both the simulation part and the rendering part, and for performance consideration, a novel method for neighbor particle searching is given. We finally get a near real-time outcome running at a frame rate of 30fps.

SU‐C‐WAB‐01: Computerized Production of Statistical Clinical Target Volume Models in Prostate Cancer Radiation Treatment Planning

Purpose: Inter‐and intra‐observer variability of clinical target volume (CTV) contours for prostate cancer is a critical issue in radiation treatment planning. Automated contouring based on statistical CTV models could be one of possible approaches for reducing the variability. Therefore, the purpose of our study is to develop a computerized method for producing the statistical CTV models to be used as CTV templates for automated contouring in prostate cancer radiation treatment planning. Methods: Eighteen, seventeen and sixteen radiation oncologists belonging to different facilities delineated CTV contours for low‐, intermediate‐and high‐risk prostate cancers, respectively. The low‐risk, intermediate‐risk, and high‐risk CTVs include only a prostate, a prostate plus a 1‐cm seminal vesicle base, and a prostate plus 2‐cm seminal vesicle, respectively. The statistical CTV models for the three risk types were derived based on a principal component analysis (PCA), which statistically took into account the inter‐observer variability. CTV regions were triangulated by using a marching cubes method. For matching the number of points on the surfaces of all CTV regions, the number of vertices on each CTV region was reduced to 1,000 with a quadric error metrics. All CTV regions were registered with a reference CTV by using an iterative closest point algorithm for calculation of a covariance matrix to be employed for the PCA‐based CTV modeling. Results: CTV models of three risk types were produced, which consisted of a mean CTV and PCA coefficients multiplied by eigenvectors, i.e., eigen‐CTV image. Average Euclidean distances between corresponding points of a mean CTV and the other CTVs for three risk types were 2.05 mm, 3.64 mm, 2.55 mm, respectively. Conclusion: The proposed method could provide probabilistic CTV models to be used as CTV templates in delineating CTV contours.

Further study of grain boundary fracture in the breakage of single multiphase particles using X-ray microtomography procedures

The present work aims to verify the 3D quantitative analysis of grain boundary fracture in the breakage of single multiphase particles using X-ray microtomography. The breakage of single multiphase copper ore particles (6mm cubic particles) by slow compression was examined. From XMT reconstructed images using the Marching Cube method, interfacial areas between copper mineral grains and host rock were determined for both parent particles and progeny particles. In this way, the specific interfacial area ratio was calculated as a metric for grain boundary fracture. Preferential grain boundary fracture only occurs at low energy dissipation rates and the current results confirm initial results for 3mm cubes published previously by Garcia et al. (2009).