Marching Cubes Algorithm Research Articles

Multi-objective optimization based robotic path planning for interpolation reconstruction model of CT data

Robotic path planning plays a pivotal role in computer-aided liver tumor thermal ablation surgery. However, traditional methods face challenges in terms of low reconstruction efficiency and planning safety. To address these issues, we propose a method for robotic path planning of liver tumor thermal ablation surgery. Firstly, an interlayer interpolation algorithm based on optical flow estimation is utilized to compensate for large interlayer spacing in computed tomography (CT) images by inserting predicted images between sequence images. Secondly, the voxel traversal strategy and patch intersection calculation strategy in the standard marching cube (MC) algorithm is optimized to improve the efficiency of abdominal tissues reconstruction. Finally, comprehensive clinical constraints are summarized to ensure the surgery safety and the strength pareto evolutionary algorithm II (SPEA-II) is leveraged to optimize surgery path, which can obtain even distribution of solutions in high-dimension optimization problems. Extensive experiments conducted on the 3Dircadb and SLIVER07 datasets revealed that our proposed method reduces reconstruction time by 21.5% compared to the standard MC algorithm, while achieving an average overlap rate of 88.25% and an average Hausdorff distance of 15.25 mm between Pareto front points and surgeon's recommended puncture points.

A method framework of semi-automatic knee bone segmentation and reconstruction from computed tomography (CT) images.

Accurate delineation of knee bone boundaries is crucial for computer-aided diagnosis (CAD) and effective treatment planning in knee diseases. Current methods often struggle with precise segmentation due to the knee joint's complexity, which includes intricate bone structures and overlapping soft tissues. These challenges are further complicated by variations in patient anatomy and image quality, highlighting the need for improved techniques. This paper presents a novel semi-automatic segmentation method for extracting knee bones from sequential computed tomography (CT) images. Our approach integrates the fuzzy C-means (FCM) algorithm with an adaptive region-based active contour model (ACM). Initially, the FCM algorithm assigns membership degrees to each voxel, distinguishing bone regions from surrounding soft tissues based on their likelihood of belonging to specific bone regions. Subsequently, the adaptive region-based ACM utilizes these membership degrees to guide the contour evolution and refine segmentation boundaries. To ensure clinical applicability, we further enhance our method using the marching cubes algorithm to reconstruct a three-dimensional (3D) model. We evaluated the method on six randomly selected knee joints. We evaluated the method using quantitative metrics such as the Dice coefficient, sensitivity, specificity, and geometrical assessment. Our method achieved high Dice scores for the femur (98.95%), tibia (98.10%), and patella (97.14%), demonstrating superior accuracy. Remarkably low root mean square distance (RSD) values were obtained for the tibia and femur (0.5±0.14 mm) and patella (0.6±0.13 mm), indicating precise segmentation. The proposed method offers significant advancements in CAD systems for knee pathologies. Our approach demonstrates superior performance in achieving precise and accurate segmentation of knee bones, providing valuable insights for anatomical analysis, surgical planning, and patient-specific prostheses.

Isosurface-based marching cube algorithm for smooth geometric topology optimization within adaptive octree SBFE approach

In the era of Industry 4.0, the prominence of 3D printing as a pivotal manufacturing technology has greatly expanded, particularly within the domain of additive manufacturing (AM). Among the thriving research applications tailored for integration with AM, topology optimization (TO) has emerged as a resounding success. Given the prerequisite of TO for high-resolution meshing to ensure visual clarity in result depiction, researchers have been consistently driven to develop advanced techniques to refine optimal designs, thus elevating the challenge and popularity within this research realm. This paper presents a novel approach integrating an adaptive image-based octree mesh scaled boundary finite element (SBFE) framework with an evolutionary methodology that can effectively address the persistent challenges inherent to TO. A novel hierarchical SBFE mesh analysis not only facilitates efficient and precise TO but also substantially reduces computational resource demands. Furthermore, the pre-conditioned conjugated gradient (PCG) method is adopted to process practical-scale problems, minimizing computer memory resources. Additionally, the proposed work incorporates a post-processing technique utilizing the isosurface function based on a marching cube algorithm, thereby smoothing the boundaries of optimal results. Consequently, this research extends the horizons of design possibilities, particularly in the creation of intricate 3D structures, which can be seamlessly realized through additive manufacturing and 3D printing.

An Automatic Method for Elbow Joint Recognition, Segmentation and Reconstruction.

Elbow computerized tomography (CT) scans have been widely applied for describing elbow morphology. To enhance the objectivity and efficiency of clinical diagnosis, an automatic method to recognize, segment, and reconstruct elbow joint bones is proposed in this study. The method involves three steps: initially, the humerus, ulna, and radius are automatically recognized based on the anatomical features of the elbow joint, and the prompt boxes are generated. Subsequently, elbow MedSAM is obtained through transfer learning, which accurately segments the CT images by integrating the prompt boxes. After that, hole-filling and object reclassification steps are executed to refine the mask. Finally, three-dimensional (3D) reconstruction is conducted seamlessly using the marching cube algorithm. To validate the reliability and accuracy of the method, the images were compared to the masks labeled by senior surgeons. Quantitative evaluation of segmentation results revealed median intersection over union (IoU) values of 0.963, 0.959, and 0.950 for the humerus, ulna, and radius, respectively. Additionally, the reconstructed surface errors were measured at 1.127, 1.523, and 2.062 mm, respectively. Consequently, the automatic elbow reconstruction method demonstrates promising capabilities in clinical diagnosis, preoperative planning, and intraoperative navigation for elbow joint diseases.

A hybrid marching cubes based IsoAlpha method for interface reconstruction

SummaryIn modelling two‐phase flows, accurate representation of interfaces is crucial. A class of methods for interface reconstruction are based on isosurface extraction, which involves a non‐iterative, interpolation based approach. These approaches have been shown to be faster by an order of magnitude than the conventional PLIC schemes. In this work, we present a new isosurface extraction based interface reconstruction scheme based on the Marching Cubes algorithm (MC), which is commonly used in computer graphics for visualizing isosurfaces. The MC algorithm apriori lists and categorizes all possible interface configurations in a single grid cell into a Look Up Table (LUT), which makes this approach fast and robust. We also show that for certain interface configurations, the inverse problem of obtaining the isovalue from the cell volume fraction is not surjective, and a special treatment is required while handling these cases. We then demonstrate the capabilities of the method through benchmark cases for 2D and 3D static/dynamic interface reconstruction.

RupMC: a ray-unit parallel marching cubes algorithm on CPU/GPU heterogeneous architectures

ABSTRACT The marching cubes (MC) algorithm is widely used for extracting isosurfaces from volume data and 3D visualizations because of its effectiveness and robustness but require extensive memory and computing time for large-scale applications. Additionally, MC isosurfaces lack topologic information, making them difficult to use in some geologic applications. To overcome these limitations, this study proposes an enhanced MC using CPU/GPU heterogeneous architecture called the ray-unit parallel MC (rupMC) algorithm. First, ray units form the basic voxel to determine how the surface intersects to reduce repeated computations and enhance efficiency. Then, rupMC uses multiple computing processes and threads on a CPU/GPU heterogeneous architecture to process points concurrently. Finally, the unique surface intersection indices are preserved to compose the surface triangles, and the topological surface information is directly embedded in the triangle compositions. Experiments on five stratum datasets of varying sizes demonstrated that, rupMC achieved approximately dozens of times faster than other serial MC and 4 times faster than a parallel DMC. rupMC demonstrated high scalability and adaptability to various CPUs/GPUs and datasets of various sizes. rupMC has remarkable capabilities for efficiently and feasibly extracting precise surface intersections and triangles, making it well-suited for large-scale and high-density applications.

Модификации классических алгоритмов восстановления поверхностей для визуализации функции, заданной на прямоугольной сетке

In the paper, modifications of visualization algorithms for real-valued functions of two and three arguments given on a rectangular or parallelepipedal grid are considered. In the case of two arguments, the graph of the function is a surface embedded into the three-dimensional space. The majority of scientific visualization systems offer visualization procedures for such surfaces, but they construct them under the assumption that the functions are continuous. In the paper, for the case of a discontinuous function, a modification of this algorithm is proposed. In addition, the algorithm removes “plateaus” that occur after cutting the function at some level (in order to remove too large values). Visualization of a function of three arguments implies showing its level sets, that is, regions of the space of arguments where the magnitudes of the function do not exceed a certain value. In the case of a grid function, such sets are “voxel” sets, that is, they are composed of grid cells. With that, some smoothing of the surface of such sets is required, which is carried out by the Marching Cubes algorithm and algorithms of the Laplacian family. A modification of the Marching Cubes algorithm is proposed, which preserves the symmetry of the set surface with respect to the coordinate planes, axes, or some point, if the rendered set has such a symmetry.

Establishment and preliminary application of personalized three-dimensional reconstruction of thyroid gland with automatic detection of thyroid nodules based on ultrasound videos.

A well display of the spatial location of thyroid nodules in the thyroid is important for surgical path planning and surgeon-patient communication. The aim of this study was to establish a three-dimensional (3D) reconstruction method of the thyroid gland, thyroid nodule, and carotid artery with automatic detection based on two-dimensional (2D) ultrasound videos, and to evaluate its clinical value. Ultrasound videos, including the thyroid gland with nodule, isthmus of thyroid gland, and ipsilateral carotid artery, were recorded. BC-UNet, MTN-Net, and RDPA-U-Net network models were innovatively employed for segmentation of the thyroid glands, the thyroid nodules, and the carotid artery respectively. Marching Cubes algorithm was used for reconstruction, while Laplacian smoothing algorithm was employed to smooth the 3D model surface. Using this model, 20 patients and 15 surgeons completed surveys on the effectiveness of this model for the pre-surgery demonstration of nodule location as well as surgeon-patient communication. The thyroid gland with nodule, isthmus of gland, and carotid artery were reconstructed and displayed. With the 3D model, the understanding of the spatial location of thyroid nodules improved in all three surgeon groups, eliminating the influence of professional levels. In the patient survey, the patients' understanding of the thyroid nodule location and procedure for surgery were significantly improved. In addition, with the 3D model, the time for doctors to explain to patients was significantly reduced (16.75 vs. 8.85min, p=0.001). To our knowledge, this is the first report of constructing a 3D thyroid model using a deep learning technique for personalized thyroid segmentation based on 2D ultrasound videos. The preliminary clinical application showed that it was conducive to the comprehension of the location of thyroid nodules for surgeons and patients, with significant improvement on the efficiency of surgeon-patient communication.

Modification Rules for Improving Marching Cubes Algorithm to Represent 3D Point Cloud Curve Images

Modification Rules for Improving Marching Cubes Algorithm to Represent 3D Point Cloud Curve Images

A Comprehensive Survey of Isocontouring Methods: Applications, Limitations and Perspectives

This paper provides a comprehensive overview of approaches to the determination of isocontours and isosurfaces from given data sets. Different algorithms are reported in the literature for this purpose, which originate from various application areas, such as computer graphics or medical imaging procedures. In all these applications, the challenge is to extract surfaces with a specific isovalue from a given characteristic, so called isosurfaces. These different application areas have given rise to solution approaches that all solve the problem of isocontouring in their own way. Based on the literature, the following four dominant methods can be identified: the marching cubes algorithms, the tessellation-based algorithms, the surface nets algorithms and the ray tracing algorithms. With regard to their application, it can be seen that the methods are mainly used in the fields of medical imaging, computer graphics and the visualization of simulation results. In our work, we provide a broad and compact overview of the common methods that are currently used in terms of isocontouring with respect to certain criteria and their individual limitations. In this context, we discuss the individual methods and identify possible future research directions in the field of isocontouring.

Adaptation of Dual Contouring and Marching Cubes Algorithms for 3D Reconstruction of the Human Lumbar Spine

The article deals with the problem of three-dimensional reconstruction of the human lumbar spine using the Marching Cubes and Dual Contouring surface triangulation algorithms for subsequent planning of a surgical intervention based on the analysis of digital computed tomography images. 3D reconstructions of the human lumbar spine are presented, as well as the results of a comparative analysis of the developed methods according to the following criteria: mesh generation speed; the number of generated cells; the absence of conflict situations (intersections of the surface). The optimal algorithm for solving the problem is determined on the basis of a comparative analysis.

3D reconstruction of brain tumors from 2D MRI scans: An improved marching cube algorithm

MRI is a popular imaging technique in medicine, particularly for the diagnosis of brain malignancies. Like any other acquisition approach, it has several drawbacks in addition to its many advantages. One of these is the problem of noise, which can provide extraneous and incorrect information that can fool the human eye. Methods such as MRI and CT, produce 2D images of the body's internal organs. This research aims with the 3D reconstruction of brain tumor, as it is very crucial for surgical planning, and biological study because 2D images can never capture a tumor's true appearance. However, it is extremely difficult to visualize the tumors in MRIs due to the different complexity of tumors. This work develops an Improved Marching Cube Algorithm (IMCA) based 3D reconstruction of brain tumors under 2 phases. Phase 1 will include MF-based preprocessing, segmentation based on Modified BIRCH (M-BIRCH) and hybrid classification combining optimized CNN and optimized Bi-LSTM. The suggested Self Adaptive Chimp Optimization Algorithm (SA-CHOA) will optimize the weight of CNN and Bi-LSTM. Phase 2 involves IMC (Improved Marching Cube) based 3D reconstruction. The validation outcomes demonstrate the suggested model's superiority to other established models for 3D reconstruction.

DeepMesh: Differentiable Iso-Surface Extraction.

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

Reverse reconstruction of geometry modeling and numerical verification of 2.5D woven composites based on deep learning

This paper proposes a reverse reconstruction method to generating accurately and high-effectively the meso-scale geometry modeling of 2.5D woven composites based on the deep learning. The method first segments the yarn from the X-ray computed tomography (Micro-CT) images based on the deep convolutional neural network (DCNN). Then, reconstruct the yarn surface model from segmented yarn images by using the marching cube algorithm. Consequently, the reverse model is generated by outlining the yarn surface model. Moreover, the yarn geometric parameters are analyzed to evaluate the geometric accuracy of the reverse model. Simultaneously, for the validation of the reverse model, the parametric model, the ideal model, and the experimental tests are considered. Where the parametric model and ideal model are established based on the geometric parameters of yarns. The results show that the DCNN is capable of accurately segmenting yarns from Micro-CT images with a global accuracy of 95.08%. The stiffness prediction error of the reverse model is only 0.706%, which is less than the error of the parametric model (3.77%) and much less than the ideal model. The reverse reconstruction method improves the efficiency of geomerty modeling by focusing on actural images rather than statistical parameters.

Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering

In this paper, we propose a new method, called DoubleCoverUDF, for extracting the zero level-set from unsigned distance fields (UDFs). DoubleCoverUDF takes a learned UDF and a user-specified parameter r (a small positive real number) as input and extracts an iso-surface with an iso-value r using the conventional marching cubes algorithm. We show that the computed iso-surface is the boundary of the r -offset volume of the target zero level-set S , which is an orientable manifold, regardless of the topology of S. Next, the algorithm computes a covering map to project the boundary mesh onto S , preserving the mesh's topology and avoiding folding. If S is an orientable manifold surface, our algorithm separates the double-layered mesh into a single layer using a robust minimum-cut post-processing step. Otherwise, it keeps the double-layered mesh as the output. We validate our algorithm by reconstructing 3D surfaces of open models and demonstrate its efficacy and effectiveness on synthetic models and benchmark datasets. Our experimental results confirm that our method is robust and produces meshes with better quality in terms of both visual evaluation and quantitative measures than existing UDF-based methods. The source code is available at https://github.com/jjjkkyz/DCUDF.

Predicting 3D particles shapes based on 2D images by using convolutional neural network

In order to accurately determine the three-dimensional (3D) shape of granular particles, one laborious approach is to employ X-ray microtomography and image processing techniques. As an alternative, in this study a 3D convolutional neural network (3D-CNN) methodology is presented to generate realistic 3D models of particles from a number of distinct two-dimensional (2D) projections. Initially, 3D synthetic particles with the targeted statistical distributions of the relevant geometric parameters, such as sphericity, elongation, aspect ratio, and flatness, were randomly generated using Fourier shape descriptors (FSDs). The database based on the statistical distributions of geometric parameters of Avicel® PH 200, obtained through dynamic image analysis. Following that, projections from multiple angles of 2D particle images were extracted for model training. By using a convolutional neural network (CNN) the shape of the particles was predicted, which involves the following sequential steps: a) model training on 2D images; b) a decoder is built to generate the 3D voxel model after an encoder extracts the properties of 2D images; c) a marching cube algorithm that converts the particle 3D voxel model into a mesh model; d) the accuracy of the prediction is evaluated by comparing the geometric parameters of the prediction models that were generated by using FSDs. The methodology was validated using a database of 3D synthetic particles with targeted statistical distributions of geometric parameters, such as sphericity, elongation, aspect ratio, and flatness. The mean absolute percentage error (MAPE) of the AI model for these parameters was 2.24%, 7.01%, 10.93%, and 7.67%, respectively. The 3D-CNN methodology has the potential for broad applications in various fields, such as rock and mineral analysis, battery materials, pharmaceuticals, and space exploration, offering a practical and affordable solution for shape analysis of relevant materials. It can significantly improve the efficiency and accuracy of numerical simulations and analyses, leading to new insights and innovations in a wide range of fields.

A single-image human body reconstruction method combining normal recovery and frequency domain completion

<p><span lang="EN-US">Reconstructing a 3D human body from a single image is convenient and efficient, but it faces challenges when the face is heavily occluded or the person is wearing loose clothing. In this paper, we propose a frequency domain-based method for completing missing parts of the human body using manifold harmonics and frequency domain analysis. Our approach involves linear interpolation of the incomplete 3D human body obtained through normal integration. The interpolated points are then projected onto the appropriate dimension of the frequency domain space using manifold harmonic bases. Through Laplacian mesh editing, the interpolated points are replaced, resulting in a refined and complete 3D human body. Our method surpasses the limitations of template human bodies and marching cubes algorithms, enabling more detailed feature reconstruction. By locally completing the body in a low-dimensional frequency domain space, our method avoids over smoothing and bulging issues, effectively filling the missing regions while maintaining mesh smoothness consistency. Experimental results demonstrate the effectiveness and superiority of our frequency domain-based completion method for accurate and detailed 3D human body reconstruction from single images.</span></p>

Seedscreener: A novel integrated wheat germplasm phenotyping platform based on NIR-feature detection and 3D-reconstruction

Crop seed phenomics provides a new operational basis for breeders. However, a scarcity of seed phenotypic characterization, especially of the single seed kernels, severely restricts their use in plant breeding. In this study, we focus on designing and deploying a prototype for automatic and high throughput seed phenotyping. The novel setup, Seedscreener, allows simultaneous RGB imaging and NIR spectrum analysis pipeline to evaluate single kernel 3D morphologies and internal biochemicals. With the assistance of a data acquisition device centered on a near-infrared spectrometer and an industrial camera, as well as an automated acquisition software under the QT development framework, Seedscreener has the ability to acquire both endophenotype and exophenotype traits of single wheat kernels simultaneously. The developed biochemical endophenotype traits prediction model can forecast the protein content (PC), starch content (SC) and gluten content (GC) of wheat kernel by the full-band absorbance spectra. The developed morphological exophenotype traits extraction model based on Marching Cubes (MC) algorithm can calculate the wheat grain length (GL), grain width (GW), grain thickness (GT), grain surface area (GSA) and convex hull volume (CHV) using the three-dimensional visual hull constructed by the lateral profile information of the wheat grain. The results show that the platform could reach 94% success rate of single wheat phenotypic data collection, the average accuracy of endophenotype traits prediction is 0.85, the average accuracy of exophenotype traits extraction is 0.93, and the working flux of the platform is about 90 grains/h. Compared with existing individual wheat kernels phenotyping equipment, Seedscreener could obtain both endophenotype and exophenotype characteristics of wheat seeds with high throughput and precision.

3D Surface Reconstruction Based on Dynamic Graph Convolutional Occupancy Network

A 3D reconstruction method based on dynamic graph convolutional occupancy networks is proposed to address the issues of texture information loss, geometric information loss after voxelization, and lack of object completeness constraints in the process of 3D reconstruction using voxel representation in a block-wise manner. By constructing a dynamic graph structure for feature extraction, the method aims at restore 3D models with fewer holes and local details. In the feature extraction stage, local pooling is employed within each point cloud block to address the problem of nonsignificant texture feature loss. To tackle the issues of geometric constraint loss and insufficient scene semantic information caused by block-wise processing, a feature fusion method between adjacent blocks is proposed to learn richer scene semantic information and long-range dependencies between points. By learning features within and between blocks, each point retains as much geometric information as possible, mitigating the problem of geometric information loss due to voxelization. During the surface generation, interpolation is used to infer the occupancy value for each point, and the Marching Cubes algorithm is employed for three-dimensional surface reconstruction. Experimental validation on object-level (ShapeNet dataset) and scene-level (Synthetic Rooms dataset, MatterPort3D dataset for real-world scenes) datasets demonstrates the effectiveness and advancement of the proposed method.

Computational morphogenesis of three-dimensional free-form structures using isosurfaces based on space mapping

This paper presented a novel computational morphogenesis method based on space mapping that employed isosurfaces to generate three-dimensional free-form continuum structures from design domains of arbitrary complexity. To achieve the interaction between form and performance, a mapping was established between the parameter space and the physical space of the design domain using B-spline volume modelling. Two assumptions were introduced to ensure that the entire parameter space has mechanical properties equivalent to those of the physical space. The isosurfaces of criterion thresholds were extracted from the entire parameter space and mapped into the physical space as the boundaries of the new design. The proposed methodology effectively addresses the limitations of the non-orthogonal body-fitted meshes for structural analysis. It comprehensively reflected the redistribution of mechanical performance and yielded an optimal design at the global-structural level. Furthermore, a geometric matrix was developed for the marching cubes algorithm, which streamlines the process of extracting isosurfaces. Numerical examples were presented to validate the method, demonstrating its ability to generate free-form structures with smooth boundaries, innovative shapes, and rational topology. The unexpected architectural form can provide valuable references for conceptual design in engineering applications.