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Marching Cubes: A High Resolution 3d Surface Construction Algorithm

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... In order to visualize the in-process workpiece or machined part, a boundary representation, such as a triangle mesh, can be built by implementing the marching cubes algorithm [28] based on the voxel model. Triangle mesh has been widely used by many CAM systems due to its strong capability to represent free-form surfaces with simple triangles. ...
... The use of this function aims to identify every intersecting voxel as well as all voxel edges crossed by the cutter surface, as shown in Figure 2. The edge intersection point is then determined by calculating the real intersection between the voxel edge and the cutter surface. In order to visualize the in-process workpiece or machined part, a boundary representation, such as a triangle mesh, can be built by implementing the marching cubes algorithm [28] based on the voxel model. Triangle mesh has been widely used by many CAM systems due to its strong capability to represent free-form surfaces with simple triangles. ...
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Virtual simulation of high-resolution multi-axis machining processes nowadays plays an important role in the production of complex parts in various industries. In order to improve the surface quality and productivity, process parameters, such as spindle speed, feedrate, and depth of cut, need to be optimized by using an accurate process model of milling, which requires both the fast virtual prototyping of machined part geometry for tool path verification and accurate determination of cutter–workpiece engagement for cutting force predictions. Under these circumstances, this paper presents an effective volumetric method that can accurately provide the required geometric information with high and stable computational efficiency under the condition of high grid resolution. The proposed method is built on a tri-level grid, which applies two levels of adaptive refinement in space decomposition to abolish the adverse effect of a large fine-level branching factor on its efficiency. Since hierarchical space decomposition is used, this multi-level representation enables the batch processing of affected voxels and minimal intersection calculations, achieving fast and accurate modeling results. To calculate the instantaneous engagement region, the immersion angles are obtained by fusing the intersection points between the bottom-level voxel edges and the cutter surface, which are then trimmed by feasible contact arcs determined using envelope theory. In a series of test cases, the proposed method shows higher efficiency than the tri-dexel model and stronger applicability in high-precision machining than the two-level grid.
... The trained PIFu network was sampled on this grid to predict the scalar occupancy field of the phase distribution. Subsequently, the isosurface extraction algorithm marching cubes [54,55] was employed to reconstruct the surface mesh from the occupancy field. All calculations were performed on a single Nvidia RTX A5000 graphics processing unit. ...
... The prediction of the scalar occupancy field for the phase distribution by the PIFu neural network serves as an accurate basis for the surface reconstruction. In this study, the efficient implementation [54] of the marching cubes algorithm [55] is employed to reconstruct the surface meshes. However, alternative isosurface extraction algorithms, including extensions of the marching cubes algorithm [57,58], methods based on Delaunay triangulation [59], or methods used in the numerical simulation of two-phase flows, such as the Piecewise-Linear Interface Calculation (PLIC) scheme [60], may offer improved reconstruction performance. ...
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The flow within adhering droplets subjected to external shear flows has a significant influence on the stability and eventual detachment of the droplets from the surface. Most commonly, the velocity field inside adhering droplets is measured by means of particle image velocimetry (PIV), which requires a correction step for distortion caused by refraction of light at the gas-liquid interface. Current methods for distortion correction based on ray tracing are limited to low external flow velocities. However, the ray-tracing method can be extended to arbitrarily deformed droplet shapes if the instantaneous three-dimensional droplet interface is availble. In the present work, a previously introduced method for the image-based reconstruction of gas-liquid interfaces by means of deep learning is adapted to determine the instantaneous interface of adhering droplets in external shear flows. In this regard, a purposefully developed optical measurement technique based on the shadowgraphy method is employed that encodes additional three-dimensional (3D) information of the interface in the images via glare points from lateral light sources. On the basis of the images recorded in the experiments, the volumetric shape of the droplet is reconstructed by a neural network that was trained on the spatio-temporal dynamics of the gas-liquid interface from a synthetic dataset obtained by numerical simulation. The results for experiments with adhering droplets at different velocities of external flow demonstrate that the combination of the learned droplet geometry with the depth encoding through the glare points facilitates a robust and flexible reconstruction. The proposed method reconstructs the instantaneous three-dimensional interface of adhering droplets at both high resolution and spatial accuracy and thereby enables the distortion correction of PIV measurements at high external flow velocities.
... Following the machine learning segmentation methods, the delineated abdominal aorta was further evaluated via surface geometry modeling. In this regard, the marching cubes algorithm [40] was employed to generate the reconstructed surface geometries, ...
... Following the machine learning segmentation methods, the delineated abdominal aorta was further evaluated via surface geometry modeling. In this regard, the marching cubes algorithm [40] was employed to generate the reconstructed surface geometries, serving as a 3D surface model for both visualization and mesh processing tasks. Briefly, the marching cubes algorithm is a widely used technique for extracting a polygonal mesh from a three-dimensional scalar field (utilized in this study to create a surface mesh from volumetric data from the extracted segmentation mask). ...
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Abdominal aortic aneurysm (AAA) is a complex vascular condition associated with high mortality rates. Accurate abdominal aorta segmentation is essential in medical imaging, facilitating diagnosis and treatment for a range of cardiovascular diseases. In this regard, deep learning-based automated segmentation has shown significant promise in the precise delineation of the aorta. However, comparisons across different models remain limited, with most studies performing algorithmic training and testing on the same dataset. Furthermore, due to the variability in AAA presentation, using healthy controls for deep learning AAA segmentation poses a significant challenge. This study provides a detailed comparative analysis of four deep learning architectures—UNet, SegResNet, UNet Transformers (UNETR), and Shifted-Windows UNet Transformers (SwinUNETR)—for full abdominal aorta segmentation. The models were evaluated both qualitatively and quantitatively using private and public 3D (Computed Tomography) CT datasets. Moreover, they were successful in attaining high performance in delineating AAA aorta, while being trained on healthy aortic imaging data. Our findings indicate that the UNet architecture achieved the highest segmentation accuracy among the models tested.
... While most methods suffice for CT images as the information is mostly of hard tissue structure and outlines, MRI have a lacuna with preservation of the internal tissue structure. The Marching cubes [24] algorithm is widely accepted for reconstructing a 3D surface from a given 3D image. For approximating contours, it uses patterned cubes or iso-surfaces. ...
... (a) Input Sequence of slices with slice gap of 3mm (b) Reconstructed 3D image The Marching Cubes method [24,37] is a simple iterative algorithm for creating a mesh of triangles to represent the surfaces of a given 3D object specified as a 3D array of pixels. The algorithm works by marching over the entire image of the 3D object, which has been equally sub-divided into cubes. ...
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Magnetic Resonance Imaging (MRI) is a technology for non-invasive imaging of anatomical features in detail. It can help in functional analysis of organs of a specimen but it is very costly. In this work, methods for (1) virtual three-dimensional (3D) reconstruction from a single sequence of two-dimensional (2D) slices of MR images of a human spine and brain taken at a certain gap along a single axis, and (2) generation of missing inter-slice data are proposed. Our approach helps in preserving the edges, shape, and size, as well as the internal tissue structures of the object being captured. The sequence of original 2D slices along a single axis is divided into smaller equal sub-parts which are then reconstructed using edge-preserved kriging interpolation to predict the missing slice information. In order to speed up the process of interpolation, we have used parallel processing by carrying out the initial interpolation on parallel cores. From the 3D matrix thus formed, shearlet transform is applied to estimate the edges considering the 2D blocks along the Z axis, and to minimize the blurring effect using a proposed mean-median logic. Finally, for visualization, the sub-matrices are merged into a final 3D matrix. Next, the newly formed 3D matrix is split up into voxels, and the marching cubes method is applied to get the approximate 3D image for viewing. To the best of our knowledge it is a first of its kind approach based on kriging interpolation and parallel processing for 3D reconstruction from 2D slices, and approximately 98.89% accuracy is achieved with respect to similarity metrics for image comparison. The time required for reconstruction has also been reduced by approximately 70% with parallel processing even for a large input data set compared to that with single core processing.
... Since the observed defects are linear or planar, it was possible to remove this noise without degrading the observed defect features. The processed data is then binned by 5 × 5 to reduce computational costs and plotted with the marching cubes algorithm (Lorensen et al., 1987) with scaling relevant to the 3D spatial axes from the scan. ...
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Dark field x-ray microscopy (DXFM) can visualize microstructural distortions in bulk crystals. Using the femtosecond x-ray pulses generated by x-ray free-electron lasers (XFELs), DFXM can achieve sub-μm spatial resolution and <100 fs time resolution simultaneously. In this paper, we demonstrate ultrafast DFXM measurements at the European XFEL to visualize an optically driven longitudinal strain wave propagating through a diamond single crystal. We also present two DFXM scanning modalities that are new to the XFEL sources: spatial 3D and 2D axial-strain scans with sub-μm spatial resolution. With this progress in XFEL-based DFXM, we discuss new opportunities to study multi-timescale spatiotemporal dynamics of microstructures.
... Using Avizo 7.0 software (Thermo Fisher Scientific), a semiautomatic threshold-based segmentation of bony and dental tissues was carried out, followed by manual corrections. Surface rendering was then performed using triangulation and constrained smoothing (marching cube algorithm; Lorensen & Cline, 1987). To reduce time processing during analyses, bone 3D meshes (cortical bone and medullary cavity) and dental 3D meshes (enamel, dentine, and pulp tissues) were simplified to 800,000 and 200,000 triangles, respectively. ...
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Cortical bone and dentine are two mineralized tissues sharing a common embryological origin, developmental, and genetic background, distinct from those of enamel. Understanding their relationship is crucial to decipher the factors acting on their postnatal development, and shedding light on the evolutionary patterns of tissue proportions. Here, we investigate the coordinated variation between cortical bone and dentine volumes measured from arm and forearm bones (humeri, ulnae, radii) and upper anterior teeth (central incisors, lateral incisors, canines) of modern humans. Given the shared characteristics of cortical bone and dentine, we expect similarities in their postnatal development, which may lead to covariation between their volumes. The degree of bone-dentine covariation may be influenced by the physiological response of upper limb bones to mechanical loading. No such covariation is expected with enamel volumes, due to the greater developmental independence of bone and enamel. Our sample includes 55 adults of African and European ancestries from South African osteological collections. Principal component analysis of cortical thickness variation along the shafts of paired humeri, ulnae, and radii is used to assess asymmetry. Bone regions with bilateral asymmetry in cortical bone thickness are considered sensitive to functional loads, while regions with minimal bilateral variation likely reflect genetic influences during bone postnatal development. Statistical analyses reveal strong positive correlations between cortical bone and dentine volumes across all bones and teeth, and weaker correlations between cortical bone and enamel. We outline a complex pattern of bone-dentine covariation that varies by skeletal location and tooth type. Contrary to our expectations, the presumed functional sensitivity of bone regions does not influence the covariation signal. Additionally, the strength of the covariation appears to align with the developmental sequence of the anterior teeth, with the upper canines showing the strongest correlation with cortical bone volumes, followed by lateral and central incisors. These results provide insights into the functional and biological factors influencing the coordinated variation of cortical bone and dentine volumes during postnatal development. Further research on the cortical bone-dentine covariation across different skeletal parts, including lower limb elements, would enhance our understanding of the effects of both endogenous and exogenous factors on the development of the mineralized tissues.
... The 3D bone model of the distal radius was analyzed using BoneSimulator software (Orthree, Osaka, Japan, https://www.e-radfan.com/product/7255/). Image data were imported into the software, where 3D surface models of the distal radius were generated using a surface construction algorithm [14,15]. ...
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Objectives: This study aims to define three-dimensional (3D) parameters for the inclination of the distal radius joint surface. The goal is to develop standardized parameters for fracture reduction through comprehensive 3D evaluations of the joint surfaces. Methods: We analyzed 112 CT scans of unaffected wrists (56 males and 56 females) to construct 3D models of the distal radius. Using 3D coordinates, the normal vectors and angles were calculated based on three reference points on the distal radius joint surface. These normal vector components were then converted into unit vector components A, B, and C for the x, y, and z axes, respectively. Additionally, the angles of these unit vectors were assessed in the xy, yz, and xz planes. The 3D measurements were compared between males and females and against traditional two-dimensional (2D) parameters such as palmar tilt and radial inclination. Results: For males, the unit vector components were as follows: A: −0.14 ± 0.09, B: −0.92 ± 0.02, and C: −0.36 ± 0.07; for females, A: −0.21 ± 0.08, B: −0.90 ± 0.03, and C: −0.36 ± 0.05. Significant differences were found between males and females for the A and B vector components (representing the palmar–dorsal and proximal–distal axes, p < 0.01). The angles of the unit vectors in the xy, yz, and xz planes were 8.9 ± 5.4°/12.9 ± 5.0°, 21.3 ± 4.1°/22.1 ± 3.2°, and 22.2 ± 14.8°/28.8 ± 10.1° for males and females, respectively. There were significant differences between males and females in the angles of the xy and xz planes (sagittal and axial planes, p < 0.01). Strong correlations were observed between the xy-plane vectors and palmar tilt (r = 0.96), as well as between the yz-plane vectors and radial inclination (r = 0.88). Conclusions: This study evaluated the 3D inclination of the distal radius joint surface, revealing significant gender differences. This method, which also allows for the assessment of rotational alignment—difficult with conventional techniques—is expected to be a key 3D parameter in treating distal radius fractures.
... It then applies Otsu's thresholding [50] to binarize the filtered image, enabling the detection of relevant structures. Next, the marching squares algorithm [36], from the scikit-image library [65], identifies contours, as shown in Figure 1 panel A-iii. These contours are then classified as z-discs based solely on their length (contours with lengths less than 15 or above 200 pixels are filtered out) -a simplistic approach similar to the length-based filtering used to differentiate z-bodies from z-discs in related work [47]. ...
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In cardiac cells, structural organization is an important indicator of cell maturity and healthy function. Healthy cardiomyocytes exhibit well-aligned morphology with densely packed and organized sarcomeres. Immature or diseased cardiomyocytes typically lack this organized structure. Critically, human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) offer a valuable model for studying human cardiac cells in a controlled environment. However, these cells often exhibit a disorganized structure. In this work, we extend the SarcGraph computational framework -- designed to assess the structural and functional behavior of hiPSC-CMs -- to better accommodate the structural features of immature cells. There are two key enhancements: (1) incorporating a deep learning-based z-disc classifier, and (2) introducing a novel ensemble graph-scoring approach. These modification significantly reduced false positive sarcomere detections in immature cells, and resulted in the detection of longer myofibrils in mature samples. With this enhanced framework, we analyze an open-source dataset published by the Allen Institute for Cell Science, where, for the first time, we are able to extract key structural features from these data using information from each individually detected sarcomere. Not only are we able to use these structural features to predict expert scores, but we are also able to use these structural features to identify bias in expert scoring and offer an alternative unsupervised learning approach based on explainable clustering. These results demonstrate the efficacy of our modified SarcGraph in extracting biologically meaningful features, enabling a deeper understanding of hiPSC-CM structural integrity. By making our code and tools open-source, we aim to empower the broader cardiac research community and foster further development of computational tools for cardiac tissue analysis.
... Furthermore, the octree algorithm [47] can be used in refining the voxels, and the ONet evaluates the newly added vertices of the refined voxels until the required resolution is achieved. At last, the marching cubes algorithm [48] can extract a smooth 3-D surface mesh. ...
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Driven by deep learning, three-dimensional (3-D) target reconstruction from two-dimensional (2-D) synthetic aperture radar (SAR) images has been developed. However, there is still room for improvement in the reconstruction quality. In this paper, we propose a structurally flexible occupancy network (SFONet) to achieve high-quality reconstruction of a 3-D target using one or more 2-D SAR images. The SFONet consists of a basic network and a pluggable module that allows it to switch between two input modes: one azimuthal image and multiple azimuthal images. Furthermore, the pluggable module is designed to include a complex-valued (CV) long short-term memory (LSTM) submodule and a CV attention submodule, where the former extracts structural features of the target from multiple azimuthal SAR images, and the latter fuses these features. When two input modes coexist, we also propose a two-stage training strategy. The basic network is trained in the first stage using one azimuthal SAR image as the input. In the second stage, the basic network trained in the first stage is fixed, and only the pluggable module is trained using multiple azimuthal SAR images as the input. Finally, we construct an experimental dataset containing 2-D SAR images and 3-D ground truth by utilizing the publicly available Gotcha echo dataset. Experimental results show that once the SFONet is trained, a 3-D target can be reconstructed using one or more azimuthal images, exhibiting higher quality than other deep learning-based 3-D reconstruction methods. Moreover, when the composition of a training sample is reasonable, the number of samples required for the SFONet training can be reduced.
... These limitations do not apply to the filling approach, in which surface meshes are derived directly from segmentations in an initial step, which is often done by applying the marching cubes algorithm (Lorensen and Cline, 1987). Acquiring MRI scans involves capturing multiple slices of one to 3 mm thickness from various perspectives, partly leading to limited spatial resolution and voxels with heterogeneous properties. ...
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Introduction Biomechanical simulations can enhance our understanding of spinal disorders. Applied to large cohorts, they can reveal complex mechanisms beyond conventional imaging. Therefore, automating the patient-specific modeling process is essential. Methods We developed an automated and robust pipeline that generates and simulates biofidelic vertebrae and intervertebral disc finite element method (FEM) models based on automated magnetic resonance imaging (MRI) segmentations. In a first step, anatomically-constrained smoothing approaches were implemented to ensure seamless contact surfaces between vertebrae and discs with shared nodes. Subsequently, surface meshes were filled isotropically with tetrahedral elements. Lastly, simulations were executed. The performance of our pipeline was evaluated using a set of 30 patients from an in-house dataset that comprised an overall of 637 vertebrae and 600 intervertebral discs. We rated mesh quality metrics and processing times. Results With an average number of 21 vertebrae and 20 IVDs per subject, the average processing time was 4.4 min for a vertebra and 31 s for an IVD. The average percentage of poor quality elements stayed below 2% in all generated FEM models, measured by their aspect ratio. Ten vertebra and seven IVD FE simulations failed to converge. Discussion The main goal of our work was to automate the modeling and FEM simulation of both patient-specific vertebrae and intervertebral discs with shared-node surfaces directly from MRI segmentations. The biofidelity, robustness and time-efficacy of our pipeline marks an important step towards investigating large patient cohorts for statistically relevant, biomechanical insight.
... Um ein 3D-Modell zu generieren, werden die schichtweisen Konturen gestapelt und über VerfahrenwieMarching Cubes [9] zu einer polygonalen Oberfläche zusammengesetzt. Diese Modelloberfläche kann volumenerhaltend (!) geglättet und weiter optimiert werden, um ein möglichst realistisches 3D-Modell des Organs oder der darzustellenden Struktur zu erzeugen. ...
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Augmented and virtual reality (AR and VR, respectively) are already being used or evaluated in some medical fields: however, the widespread application is still hampered by inconsistent and often confusing terminology, in particular for people who are not familiar with current developments. Additionally, the technical principles and requirements for its use are often insufficiently well known. This overview article therefore aims to clarify the most important terminology and presents the current technical state of the art, spanning from the requirements of medical imaging, through 3D models and the various forms of visualization to the interaction possibilities within VR and AR. This should help to facilitate a common language among developers and users and to ensure that the potentials offered by digital assistive technologies can be fully exploited in the future.
... After segmentation, parcels are vectorized using the marching cubes algorithm [35]. A corner cutting algorithm [36] is used to perform polygon simplification on circular parcels, identified by their circularity score (ratio of perimeter:area). ...
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Satellite remote sensing enables monitoring of regenerative agriculture practices, such as crop rotation, cover cropping, and conservation tillage to allow tracking and quantification at unprecedented scales. The Monitor system presented here capitalizes on the scope and scale of these data by integrating crop identification, cover cropping, and tillage intensity estimations annually at field scales across the contiguous United States (CONUS) from 2014 to 2023. The results provide the first ever mapping of these practices at this temporal fidelity and spatial scale, unlocking valuable insights for sustainable agricultural management. Monitor incorporates three datasets: CropID, a deep learning transformer model using Sentinel-2 and USDA Cropland Data Layer (CDL) data from 2018 to 2023 to predict annual crop types; the living root data, which use Normalized Difference Vegetation Index (NDVI) data to determine cover crop presence through regional parameterization; and residue cover (RC) data, which uses the Normalized Difference Tillage Index (NDTI) and crop residue cover (CRC) index to assess tillage intensity. The system calculates field-scale statistics and integrates these components to compile a comprehensive field management history. Results are validated with 35,184 ground-truth data points from 19 U.S. states, showing an overall accuracy of 80% for crop identification, 78% for cover crop detection, and 63% for tillage intensity. Also, comparisons with USDA NASS Ag Census data indicate that cover crop adoption rates were within 20% of estimates for 90% of states in 2017 and 81% in 2022, while for conventional tillage, 52% and 25% of states were within 20% of estimates, increasing to 75% and 67% for conservation tillage. Monitor provides a comprehensive view of regenerative practices by crop season for all of CONUS across a decade, supporting decision-making for sustainable agricultural management including associated outcomes such as reductions in emissions, long term yield resiliency, and supply chain stability.
... The marching cubes algorithm is a fundamental technique for converting implicit functions into surface meshes. Introduced by Lorensen and Cline in 1987 [39], it has become a cornerstone in the field of 3D surface reconstruction [40]. The algorithm efficiently transforms volumetric data into polygonal surfaces, enabling the visualization and analysis of complex 3D structures. ...
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This paper proposes a method for 3D reconstruction from Freehand Design Sketching (FDS) in architecture and industrial design. The implementation begins by extracting features from the FDS using the self-supervised learning model DINO, followed by the continuous Signed Distance Function (SDF) regression as an implicit representation through a Multi-Layer Perceptron network. Taking eyeglass frames as an example, the 2D contour and freehand sketch optimize the alignment by their geometrical similarity while exploiting symmetry to improve reconstruction accuracy. Experiments demonstrate that this method can effectively reconstruct high-quality 3D models of eyeglass frames from 2D freehand sketches, outperforming existing deep learning-based 3D reconstruction methods. This research offers practical information for understanding 3D modeling methodology for FDS, triggering multiple modes of design creativity and efficient scheme adjustments in industrial or architectural conceptual design. In conclusion, this novel approach integrates self-supervised learning and geometric optimization to achieve unprecedented fidelity in 3D reconstruction from FDS, setting a new benchmark for AI-driven design processes in industrial and architectural applications.
... To compare the porosity of different regions within the GDL, two virtual boxes were defined in these regions of the cropped sample and the "rolling ball" method was used to define the surface. Within the boxes, the surface-area-to-volume ratio was calculated with the Dragonfly software using the marching cubes algorithm (Lorensen and Cline, 1987). ...
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Polytetrafluoroethylene (PTFE) is used as commercial hydrophobic treatment for gas diffusion layers (GDL) in polymer electrolyte fuel cells. This commercial hydrophobic treatment can reduce the electrical conductivity of GDLs and is facing an uncertain future due to the pending restriction of perfluoroalkyl substances (PFAS). Previously, we proposed surfactant doped polyaniline (PANI) coatings as a fluorine-free alternative hydrophobic treatment. Due to their anti-corrosion properties as well as the electrical conductivity, these coatings offer additional benefits for the GDL compared to PTFE. Prior work demonstrated improved maximum power of a low temperature polymer electrolyte fuel cell (LT-PEFC) using the PANI coated GDL compared to the commercial PTFE treated reference. Based on these findings, additional investigations are needed to optimize the coating and assess possible areas of applications. With this study, we propose the use of the coating in high temperature PEFCs due to its thermal stability determined via thermogravimetric analysis of polyaniline doped with different types of surfactants. A main focus of this work is the investigation of the uniformity and overall porosity of the polyaniline coatings on GDLs via µCT supported by deep learning. This analysis is complemented with fluid dynamics simulations to determine the tortuosity and the gas flow through the GDL. In the future, this approach could enable the optimization of the fluorine-free hydrophobic coatings in combination with the different layers of the membrane electrode assembly (MEA) such as the GDL and the catalyst layer to prevent mass transport limitations.
... dataarts/dat.gui), marching cube [28], marching tetrahedra [29] and surface net [30] [31]. And, Mikola Lysenko transformed the codes to Javascript version and connected with Three.js to show isosurface images in a web browser [32]. ...
Preprint
The OpenMX Viewer (Open source package for Material eXplorer Viewer) is a web-based graphical user interface (GUI) program for visualization and analysis of crystalline and molecular structures and 3D grid data in the Gaussian cube format such as electron density and molecular orbitals. The web-based GUI program enables us to quickly visualize crystalline and molecular structures by dragging and dropping XYZ, CIF, or OpenMX input/output files, and analyze static/dynamic structural properties conveniently in a web browser. Several basic functionalities such as analysis of Mulliken charges, molecular dynamics, geometry optimization and band structure are included. In addition, based on marching cubes, marching tetrahedra and surface nets algorithms with Affine transformation, 3D isosurface techniques are supported to visualize electron density and molecular/crystalline orbitals in the cube format with superposition of a crystalline or molecular structure. Furthermore, the Band Structure Viewer is implemented for showing a band structure in a web browser. By accessing the website of the OpenMX Viewer, the latest OpenMX Viewer is always available for users to visualize various structures and analyze their properties without installations, upgrades, updates, registration, sign-in and terminal commands.
... One example of indirect rendering is to render the isosurface of a volume [26]. First, the generation of an intermediate representation of the dataset is required (e.g., a polygonal representation of an isosurface generated by Marching Cubes [27]). The second step is the rendering of this representation. ...
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Traditional tools, such as 3D Slicer, Fiji, and MATLAB®, often encounter limitations in rendering performance and data management as the dataset sizes increase. This work presents a GPU-enabled volume renderer with a MATLAB® interface that addresses these issues. The proposed renderer uses flexible memory management and leverages the GPU texture-mapping features of NVIDIA devices. It transfers data between the CPU and the GPU only in the case of a data change between renderings, and uses texture memory to make use of specific hardware benefits of the GPU and improve the quality. A case study using the ViBE-Z zebrafish larval dataset demonstrated the renderer’s ability to produce visualizations while managing extensive data effectively within the MATLAB® environment. The renderer is available as open-source software.
... An implicit assumption for this type of meshing approach is that an approximate surface representation of the bones is available a priori. Such a preliminary surface mesh could be acquired by using a contouring algorithm such as marching cubes (Lorensen and Cline, 1987), which had been applied to a segmented voxel dataset such as a computed tomography (CT), magnetic resonance imaging (MRI), or reflection-based ultrasound reconstruction. ...
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This work explores techniques for accurately modeling the propagation of ultrasound waves in lossy fluid-solid media, such as within transcranial ultrasound, using the spectral-element method. The objectives of this work are twofold, namely, (1) to present a formulation of the coupled viscoacoustic-viscoelastic wave equation for the spectral-element method in order to incorporate attenuation in both fluid and solid regions and (2) to provide an end-to-end workflow for performing spectral-element simulations in transcranial ultrasound. The matrix-free implementation of this high-order finite-element method is very well-suited for performing waveform-based ultrasound simulations for both transcranial imaging and focused ultrasound treatment thanks to its excellent accuracy, flexibility for dealing with complex geometries, and computational efficiency. The ability to explicitly mesh distinct interfaces between regions with high impedance contrasts eliminates staircasing artifacts, which are otherwise non-trivial to mitigate within discretization approaches based on regular grids. This work demonstrates the efficacy of this modeling technique for transcranial ultrasound through a number of numerical examples. While the examples in this work primarily focus on transcranial applications, this type of modeling is equally relevant within other soft tissue-bone systems such as in limb or spine imaging.
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Electroanatomical mapping is a technique used in cardiology to create a detailed 3D map of the electrical activity in the heart. It is useful for diagnosis, treatment planning and real time guidance in cardiac ablation procedures to treat arrhythmias like atrial fibrillation. A probabilistic machine learning model trained on a library of CT/MRI scans of the heart can be used during electroanatomical mapping to generate a patient-specific 3D model of the chamber being mapped. The use of probabilistic machine learning models under a Bayesian framework provides a way to quantify uncertainty in results and provide a natural framework of interpretability of the model. Here we introduce a Bayesian approach to surface reconstruction of cardiac chamber models from a sparse 3D point cloud data acquired during electroanatomical mapping. We show how probabilistic graphical models trained on segmented CT/MRI data can be used to generate cardiac chamber models from few acquired locations thereby reducing procedure time and x-ray exposure. We show how they provide insight into what the neural network learns from the segmented CT/MRI images used to train the network, which provides explainability to the resulting cardiac chamber models generated by the model.
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The National Cancer Institute (NCI) supports numerous research consortia that rely on imaging technologies to study cancerous tissues. To foster collaboration and innovation in this field, the Image Analysis Working Group (IAWG) was created in 2019. As multiplexed imaging techniques grow in scale and complexity, more advanced computational methods are required beyond traditional approaches like segmentation and pixel intensity quantification. In 2022, the IAWG held a virtual hackathon focused on addressing challenges in analyzing complex, high‐dimensional datasets from fixed cancer tissues. The hackathon addressed key challenges in three areas: (1) cell type classification and assessment, (2) spatial data visualization and translation, and (3) scaling image analysis for large, multi‐terabyte datasets. Participants explored the limitations of current automated analysis tools, developed potential solutions, and made significant progress during the hackathon. Here we provide a summary of the efforts and resultant resources and highlight remaining challenges facing the research community as emerging technologies are integrated into diverse imaging modalities and data analysis platforms.
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This article introduces a robust numerical strategy for tracking the arbitrarily large motion of a region G(t) embedded in a surface S of R3{{\mathbb {R}}}^3 under the effect of a complex velocity field V(t, x). Following our earlier work about evolving domains in the two- or three-dimensional Euclidean space, two complementary representations of the region G(t)SG(t) \subset S are combined at each stage of the iterative process. On the one hand, G(t) is equipped with a mesh, which allows for precise geometric and finite element computations, such as those required by the evaluation of V(t, x). On the other hand, G(t) is represented implicity, via the level set method—a format under which dramatic deformations of this region can be captured, including changes in its topology. Efficient numerical algorithms make it possible to switch consistently from one of these representations to the other, depending on its relevance with respect to the ongoing operation. After numerical validation, this strategy is applied to address two concrete physical problems, namely the simulation of the evolution of a fire front within a complex landscape, and the optimization of the shape of regions supporting the boundary conditions of a mechanical boundary value problem.
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Accurate reconstruction of the right heart geometry and motion from time‐resolved medical images is crucial for diagnostic enhancement and computational analysis of cardiac blood dynamics. Commonly used segmentation and/or reconstruction techniques, exclusively relying on short‐axis cine‐MRI, lack precision in critical regions of the right heart, such as the ventricular base and the outflow tract, due to its unique morphology and motion. Furthermore, the reconstruction procedure is time‐consuming and necessitates significant manual intervention for generating computational domains. This study introduces an end‐to‐end hybrid reconstruction method specifically designed for computational simulations. Integrating information from various cine‐MRI series (short/long‐axis and 2/3/4 chambers views) with minimal user contribution, our method leverages registration‐ and morphing‐based algorithms to accurately reconstruct crucial cardiac features and complete cardiac motion. The reconstructed data enable the creation of patient‐specific computational fluid dynamics models, facilitating the analysis of the hemodynamics in healthy and clinically relevant scenarios. We assessed the accuracy of our reconstruction method against ground truth and a standard method. We also evaluated volumetric clinical parameters and compared them with the literature values. The method's adaptability was investigated by reducing the number of cine‐MRI views, highlighting its robustness with varying imaging data. Numerical findings supported the reliability of the approach for simulating hemodynamics. Combining registration‐ and morphing‐based algorithms, our method offers accurate reconstructions of the right heart chambers' morphology and motion. These reconstructions can serve as valuable tools as domain and boundary conditions for computational fluid dynamics simulations, ensuring seamless and effective analysis.
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W medycynie i implantologii ważną rolę odgrywa znajomość własności mechanicznych kości. W typowej kości wyróżnić można dwie tkanki: kość zbitą i kość gąbczastą. Kość gąbczasta ma niezwykle złożoną strukturę przestrzenną, w której przeplatają się obszary ściśle do siebie przylegających beleczek kostnych z obszarami porów, wypełnionych w organizmie przez tłuszcz, szpik oraz inne tkanki miękkie. Bardzo ważny jest rozwój modeli komputerowych pozwalających przewidywać własności mechaniczne kości na podstawie precyzyjnych pomiarów nieniszczących tak, aby mogły zostać zaadaptowane i wykorzystane w przyszłości w praktyce klinicznej. Celem niniejszej pracy było przeprowadzenie symulacji komputerowych własności mechanicznych tkanki kostnej. Dane wejściowe do modelowania uzyskano w oparciu o wysokorozdzielcze pomiary mikrotomograficzne. Ponieważ głównym celem było opracowanie metodologii modelowania własności mechanicznych tkanki kostnej, w badaniach zdecydowano się wykorzystać kości zwierzęce. Opracowana metodologia pozostanie taka sama dla kości ludzkich, natomiast wykorzystanie w badaniach zwierząt rzeźnych zagwarantowało łatwy dostęp do dużej liczby zróżnicowanych próbek, nie wymagało również zgody komisji etycznej. Metodologia ta oparta została na metodzie elementów skończonych z wykorzystaniem opracowanego dedykowanego biomechanicznego modelu układu kostno-mięśniowego.
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Given only a set of images, neural implicit surface representation has shown its capability in 3D surface reconstruction. However, as the nature of per-scene optimization is based on the volumetric rendering of color, previous neural implicit surface reconstruction methods usually fail in the low-textured regions, including floors, walls, etc., which commonly exist for indoor scenes. Being aware of the fact that these low-textured regions usually correspond to planes, without introducing additional ground-truth supervisory signals or making additional assumptions about the room layout, we propose to leverage a novel Pseudo-plane regularized Signed Distance Field (PPlaneSDF) for indoor scene reconstruction. Specifically, we consider adjacent pixels with similar colors to be on the same pseudo-planes. The plane parameters are then estimated on the fly during training by an efficient and effective two-step scheme. Then the signed distances of the points on the planes are regularized by the estimated plane parameters in the training phase. As the unsupervised plane segments are usually noisy and inaccurate, we propose to assign different weights to the sampled points on the plane in plane estimation as well as the regularization loss. The weights come by fusing the plane segments from different views. As the sampled rays in the planar regions are redundant, leading to inefficient training, we further propose a keypoint-guided rays sampling strategy that attends to the informative textured regions with large color variations, and the implicit network gets a better reconstruction, compared with the original uniform ray sampling strategy. Experiments show that our PPlaneSDF achieves competitive reconstruction performance in Manhattan scenes. Further, as we do not introduce any additional room layout assumption, our PPlaneSDF generalizes well to the reconstruction of non-Manhattan scenes.
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Objectives The shape is commonly used to describe the objects. State-of-the-art algorithms in medical imaging are predominantly diverging from computer vision, where voxel grids, meshes, point clouds, and implicit surface models are used. This is seen from the growing popularity of ShapeNet (51,300 models) and Princeton ModelNet (127,915 models). However, a large collection of anatomical shapes (e.g., bones, organs, vessels) and 3D models of surgical instruments is missing. Methods We present MedShapeNet to translate data-driven vision algorithms to medical applications and to adapt state-of-the-art vision algorithms to medical problems. As a unique feature, we directly model the majority of shapes on the imaging data of real patients. We present use cases in classifying brain tumors, skull reconstructions, multi-class anatomy completion, education, and 3D printing. Results By now, MedShapeNet includes 23 datasets with more than 100,000 shapes that are paired with annotations (ground truth). Our data is freely accessible via a web interface and a Python application programming interface and can be used for discriminative, reconstructive, and variational benchmarks as well as various applications in virtual, augmented, or mixed reality, and 3D printing. Conclusions MedShapeNet contains medical shapes from anatomy and surgical instruments and will continue to collect data for benchmarks and applications. The project page is: https://medshapenet.ikim.nrw/ .
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The complex geological architecture, complicated dynamics processes and nonlinear association in mineral systems are the major intrinsic hindrances to predictive mineral exploration. For effectively overcoming such difficulties to achieve credible prediction, 3D geological modeling, numerical dynamics simulation (NDS) and machine learning (ML) were applied to characterize the complex geological architecture, to replay the complicated dynamics processes and to predict mineralization-favor spaces by extracting nonlinear association of multi-features with mineralization in the Dongguashan orefield. The method of SHapley Additive exPlanations (SHAP) was used to explain the correlations between different features and mineralization in the predictive model. The results of the 3D geological modeling revealed that the orebodies are unevenly distributed around the intrusion and closely related to the features of the intrusion’s contact zone and wall rocks. The 3D distribution of resistivity can provide some evidence to infer underground geological architecture rather than a threshold to separate orebodies from wall rocks. The NDS results showed that dilation zones developed around the intrusion and within some beds, being closely associated with the known orebodies. By applying the most popular ML algorithm, random forest, and combining different geological, geophysical and dynamics features as evidence variables, eight ML models were run to predict potential orebodies. The predictive model performance on the test samples indicates that the integration of dynamics evidence with geological evidence significantly improves the predictive capacity of the ML model. The SHAP values demonstrate that volumetric strain is the most important feature, while the inclination of the contact zone has the greatest positive contribution to the predictions. The SHAP values of variable interactions indicate that complex intrusion contact zones and low-pressure, high-dilation areas are closely related to mineralization. The 3D ML prediction evidenced synthetically by geological, geophysical and geodynamical features demonstrates that there are substantial potential ores at depth of the northern east and southern east parts of the orefield.
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Reconstructing three-dimensional (3D) granular microstructures through X-ray micro-computed tomography (μCT) imaging is significant for elucidating micromechanical behaviors of granular media and optimizing geotechnical designs. However, due to the irregular morphology and dense packing of granular media, traditional image-processing techniques often lack the precision required for accurate reconstructions. This paper presents a novel framework for accurate 3D reconstruction of arbitrary granular media using vision foundation models (VFMs). Two-dimensional (2D) mask maps representing the granular media are extracted from μCT images along the x, y, and z-axes using VFMs and then processed by a two-step strategy to repair textures and remove noises. An optimal transport (OT)-based method is employed to reconstruct a complete 3D mask map based on 2D mask maps. The proposed method is applied to reconstruct two carbonate sand samples with irregular grain shapes and four lentil samples composed of nearly 10,000 grains captured in triaxial loading, utilizing various VFMs and prompt configurations. The framework demonstrated a 50 % improvement in reconstruction accuracy over the state-of-the-art method for carbonate sands and achieved a 95 % accuracy for lentil samples. This advancement offers a more effective alternative for investigating the micromechanics of granular media.
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In surgical stabilization of rib fractures (SSRF), the current standard relies on preoperative CT imaging and often incorporates ultrasound (US) imaging. As an alternative, mixed reality (MR) technology holds promise for improving rib fracture localization. This study presents an MR-based visualization system designed for SSRF in a clinical setting. We developed RibMR – a visualization system using an MR head-mounted display that projects a patient-specific 3D hologram onto the patient. RibMR enables the localization of rib fractures in relation to the patient’s anatomy. We conducted phantom study using a human mannequin, a preclinical study with two healthy patients, and clinical study with two patients to evaluate RibMR and compared it to US practice. RibMR localized rib fractures with an average accuracy of 0.38 ± 0.21 cm in phantom, 3.75 ± 2.45 cm in preclinical, and 1.47 ± 1.33 cm in clinical studies. RibMR took an average time (minutes) of 4.42 ± 0.98 for the phantom, 8.03 ± 3.67 for the preclinical, and 8.76 ± 0.65 for the clinical studies. Compared to US, RibMR located more fractures, including fractures occluded by other structures, with higher accuracy, faster speed, and improved localization rate. All participating surgeons provided positive feedback regarding accuracy, visualization quality, and usability. RibMR enabled accurate and time-efficient localization of rib fractures and showed better performance compared to US. RibMR is a promising alternative to US for localizing rib fractures in SSRF.
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Reconstruction of surfaces from point clouds is essential in numerous practical applications. An approach in which neural fields are trained as surface representations from point clouds has garnered significant interest in recent years. However, these techniques present scalability issues to large scenes since they are limited in the size of point clouds that can be processed. This work proposes a learnable point cloud sampling designed to address the scalability issues. We introduce a sampling network that considers a seed point acting as the origin to sample points from a part of the scene. The seed point is one of the input points that is selected in a spatially uniform manner. This prompts a surface reconstruction network to learn the detailed geometry on partial regions of the scene. We also propose a training pipeline based on point cloud splitting and merging to avoid an increase in the memory footprint. We jointly train the sampling network and surface reconstruction network using a task loss to optimize the sampling network for the surface reconstruction task. Experimental results on scene-level datasets captured from real-world environments demonstrate that our method performs better than state-of-the-art methods in surface reconstruction.
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We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors such as noise, outliers, non-uniform sampling, and missing data. Traditional approaches often simplify the problem by imposing handcrafted priors on either the input point clouds or the resulting surface, a process that can require tedious hyperparameter tuning. In contrast, deep learning models have the capability to directly learn the properties of input point clouds and desired surfaces from data. We study the influence of handcrafted and learned priors on the precision and robustness of surface reconstruction techniques. We evaluate various time-tested and contemporary methods in a standardized manner. When both trained and evaluated on point clouds with identical characteristics, the learning-based models consistently produce higher-quality surfaces compared to their traditional counterparts—even in scenarios involving novel shape categories. However, traditional methods demonstrate greater resilience to the diverse anomalies commonly found in real-world 3D acquisitions. For the benefit of the research community, we make our code and datasets available, inviting further enhancements to learning-based surface reconstruction. This can be accessed at https://github.com/raphaelsulzer/dsr-benchmark .
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The reliable computation of microstructure metrics such as specific surface area and tortuosity factors is key to bridge the gap between the battery microscale and fast, homogenized cell models. In this work, we present an approach to compute the surface area of phases based on pixelated image data which is both easy-to-implement and computationally efficient. The concept is inspired from the diffuse surface representation in phase-field methods. Subsequently, the approach is validated and compared with common python libraries on two benchmark cases and actual battery microstructure data. The results underline the reliability and fast computational performance of the approach. Furthermore, the concept of through-feature connectivity in pixelated image data is introduced and explored to quantify the reliability of tortuosity factor computations. Overall, this work enhances the computational tools to bridge the scale from battery microstructures to cell models and gives an overview of state-of-the-art methodology. The developed code is published to further accelerate the scientific progress in this field.
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A geometric modeling technique called Octree Encoding is presented. Arbitrary 3-D objects can be represented to any specified resolution in a hierarchical 8-ary tree structure or “octree” Objects may be concave or convex, have holes (including interior holes), consist of disjoint parts, and possess sculptured (i.e., “free-form”) surfaces. The memory required for representation and manipulation is on the order of the surface area of the object. A complexity metric is proposed based on the number of nodes in an object's tree representation. Efficient (linear time) algorithms have been developed for the Boolean operations (union, intersection and difference), geometric operations (translation, scaling and rotation), N-dimensional interference detection, and display from any point in space with hidden surfaces removed. The algorithms require neither floating-point operations, integer multiplications, nor integer divisions. In addition, many independent sets of very simple calculations are typically generated, allowing implementation over many inexpensive high-bandwidth processors operating in parallel. Real time analysis and manipulation of highly complex situations thus becomes possible.
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Two-dimensional images of 3D objects require realistic shading to create the illusion of depth. Traditional (object space) shading methods require extra data (normal vectors) to be stored with the object description. When object representations are obtained directly from measured data, these normal vectors may be expensive to compute; if the object is modified interactively, they must be recomputed frequently. To avoid these problems a simple shading method is devised which uses only information available in image space, after coordinates have been transformed, hidden surfaces removed, and a complete pre-image of all objects has been assembled. The method uses both the distance from the light source and the surface orientation as the basis for shading. The theory and its implementation are discussed and shaded images of a number of objects are presented.
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For the 3D-reconstruction of organ surfaces from tomograms, a shading method based on the partial volume effect is presented. In contrast to methods based on the depth and/or the angle of the voxel surface, here the gray-level gradient along the surface is used for shading. It is shown, that at least for bone and soft tissue surfaces, the results are superior to conventional shading. This is due to the high dynamic range of the gray levels within a small spatial neighborhood.
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Most X-ray CT scanners require a few seconds to produce a single two-dimensional (2-D) image of a cross section of the body. The accuracy of full three-dimensional (3-D) images of the body synthesized from a contiguous set of 2-D images produced by sequential CT scanning of adjacent body slices is limited by 1) slice-to-slice registration (positioning of patient); 2) slice thickness; and 3) motion, both voluntary and involuntary, which occurs during the total time required to scan all slices. Therefore, this method is inadequate for true dynamic 3-D imaging of moving organs like the heart, lungs, and circulation. To circumvent these problems, the Dynamic Spatial Reconstructor (DSR) was designed by the Biodynamics Research Unit at the Mayo Clinic to provide synchronous volume imaging, that is stop-action (1/100 s), high-repetition rate (up to 60/s), simultaneous scanning of many parallel thin cross sections (up to 240, each 0.45 mm thick, 0.9 mm apart) spanning the entire anatomic extent of the bodily organ(s)of interest. These capabilities are achieved by using multiple X-ray sources and multiple 2-D fluoroscopic video camera assemblies on a continually rotating gantry. Desired tradeoffs between temporal, spatial, and density resolution can be achieved by retrospective selection and processing of appropriate subsets of the total data recorded during a continuous DSR scan sequence.
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A simple algorithm is presented for processing complex contour arrangements to produce polygonal element mosaics which are suitable for line drawing and continuous tone display. The program proceeds by mapping adjacent contours onto the same unit square and, subject to ordering limitations, connecting nodes of one contour to their nearest neighbors in the other contour. While the mapping procedure provides a basis for branching decisions, highly ambiguous situations are resolved by user interaction. The program was designed to interface a contour definition of the components of a human brain. These brain data are a most complex definition and, as such, serve to illustrate both the capabilities and limitations of the procedures.
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Three-dimensional results from engineering and scientific computations often involve the display and interpretation of a large volume of complex data. A method is developed for color display of 3D data with several interactive options to facilitate interpretation. The method is based on representing points whose values fall within a specified range as a single hue. An image is formed by overlaying successive 2D frames with increasing hue lightness towards the front. Interactive options to aid interpretations are viewpoint, contour lines, multiple range display, slicing, veiled surfaces, and stereo image pairs. The display method is successfully applied to several types of data. The overall structure and variations of the 3D data are observable, as well as transients which may be overlooked in a large input data set.
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A new family of clipping algorithms is described. These algorithms are able to clip polygons against irregular convex plane-faced volumes in three dimensions, removing the parts of the polygon which lie outside the volume. In two dimensions the algorithms permit clipping against irregular convex windows. Polygons to be clipped are represented as an ordered sequence of vertices without repetition of first and last, in marked contrast to representation as a collection of edges as was heretofore the common procedure. Output polygons have an identical format, with new vertices introduced in sequence to describe any newly-cut edge or edges. The algorithms easily handle the particularly difficult problem of detecting that a new vertex may be required at a corner of the clipping window. The algorithms described achieve considerable simplicity by clipping separately against each clipping plane or window boundary. Code capable of clipping the polygon against a single boundary is reentered to clip against subsequent boundaries. Each such reentrant stage of clipping need store only two vertex values and may begin its processing as soon as the first output vertex from the preceeding stage is ready. Because the same code is reentered for clipping against subsequent boundaries, clipping against very complex window shapes is practical. For perspective applications in three dimensions, a six-plane truncated pyramid is chosen as the clipping volume. The two additional planes parallel to the projection screen serve to limit the range of depth preserved through the projection. A perspective projection method which provides for arbitrary view angles and depth of field in spite of simple fixed clipping planes is described. This method is ideal for subsequent hidden-surface computations.
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We present high resolution three dimensional (3D) connectivity, surface construction and display algorithms that detect, extract, and display the surface of a brain from contiguous magnetic resonance (MR) images. The algorithms identify the external brain surface and create a 3D image, showing the fissures and surface convolutions of the cerebral hemispheres, cerebellum, and brain stem. Images produced by these algorithms also show the morphology of other soft tissue boundaries such as the cerebral ventricular system and the skin of the patient. For the purposes of 3D reconstruction, our experiments show that T1 weighted images give better contrast between the surface of the brain and the cerebral spinal fluid than T2 weighted images. 3D reconstruction of MR data provides a non-invasive procedure for examination of the brain surface and other anatomical features.
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Dry skulls from patients with Crouzon syndrome or orbital neurofibromatosis were studied using three-dimensional reconstruction of computed tomography data. The images were compared with one another and with the actual skulls. It was concluded that the use of dry skulls is helpful in pointing out errors of inclusion or exclusion. Thinner sections permit more accurate representation. Since reconstructed data do not appear to be significantly enhanced by using overlapping sections, radiation can be reduced by using abutting sections.
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Computer programs that produce 3D surface reformations from sets of contiguous axial CT scans were used in evaluating a variety of acetabular fractures in 20 patients. The 3D images were easily correlated with plain radiographs, and new views were produced that provided a unique perspective not obtainable by conventional radiography. The 3D images were useful in complex displaced fractures in cases in which the interpretation of plain radiographs was difficult. Plain radiographs and conventional CT scans were more sensitive than the 3D images in detecting undisplaced fractures.
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Three-dimensional (3D) computed tomography (CT) scan data were used to quantitate the geometry of all heart chambers. The Dynamic Spatial Reconstructor (DSR) was used to scan dogs with in situ casts of the cardiac chambers. Chamber volumes estimated from DSR images were accurate within 5% of water displacement volume measurements of the actual casts for chambers greater than 11 ml and within 10% of water displacement volumes for chambers less than 11 ml. Anatomic features of the actual cast correlated closely with anatomy visible in computer-generated surface images of the 3D DSR image data. The important effect of reconstructed section thickness and orientation on the fidelity of 3D cardiac geometry is demonstrated.
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Multisection, dual-echo magnetic resonance (MR) transaxial images of blood vessels contain both anatomic and qualitative information about flow. Even so, the images are produced as a series of two-dimensional tomographic sections from which full visualization of connected structures is difficult. A computer algorithm was developed that automatically detects flowing blood based on pixel intensity and calculated T2 and provides reconstructed views of vessels while analyzing and displaying flow characteristics. Images of abdominal vessels, aortic aneurysms, and the heart were encoded by flow and color to demonstrate depth. In addition, these data were reconstructed to derive a more accurate assessment of patency. With this technique, transaxial images can be used to analyze flow patterns, determine patent areas, and visualize all levels of vessels in a single image.
Article
The computed tomographic studies obtained routinely in the examination of patients with congenital or acquired defects of the skull and facial bones can be utilized as a substrate to provide an accurate three-dimensional representation of osseous abnormalities. The total dose of x-irradiation is reduced as other means of radiological examination are eliminated. Osseous structures are faithfully reproduced. Complete inspection of the reproduced structure can be made from any viewpoint, including internal inspection.
Article
Three dimensional reconstruction images of bony and soft tissue surfaces have improved understanding of complex facial deformities. Applied to CT studies of complex craniofacial abnormalities, this method has delineated abnormal facial soft tissue and bony morphology, facilitated surgical planning, and improved quantitative postoperative evaluation. Advanced computer-aided aircraft design techniques were adapted and applied to craniofacial surgical procedure-planning and evaluation using surface contours obtained from CT scans.
Article
Consider a three-dimensional "scene" in which a density f(x, y, z) is assigned to every point (x, y, z). In a discretized version of the scene the density D(i, j, k) assigned to the (i, j, k) th volume element (voxel) is the average value of f(x, y, z) over the voxel. Suppose that the points in the original scene can be meaningfully segmented into classes 1, 2, and 3 separated by two threshold values l and u. Partial volume artifact is the phenomenon that a voxel (i, j, k) which is at the interface of class 1 and class 3 (and thus contains only points with low and high densities) usually has a density D(i, j, k) between l and u, and so cannot be distinguished by density alone from a voxel which contains only points in class 2. We describe how a two-dimensional (gradient, density) feature space can be used for the segmentation of such discrete scenes into three classes in a meaningful way. We illustrate the method using examples from medical imaging.
Article
The overall feasibility of 3-D color imaging is determined, taking into account display method, display options, and image processing system. The method is based on the display of 3-D colored ranges of data values and allows very complex convoluted structures with disjoint parts to be imaged. This approach results in a very fast, interactive method for interpreting the position, size, and shape of 3-D structures. Display options are needed to clarify the perception of the three-dimensional relationships; a single presentation mode is not sufficient. Seven options are used: multiple structures, point of view, projection angle, cutout, transparency, contours, and stereo. The options are selected by interacting visually with the image of the 3-D structures on a high-resolution color monitor 1024×1024. The image processing system consists of a host computer IBM 370/168 and an image processing workstation IBM 7350. The host performs data file management, selection of subimages, initial data smoothing, and 3-D data rotation. The workstation provides interactive 3-D imaging with oblique projection, data cutout, transparency, smoothing, and color selection. Since all of the scan data are resident in the 7350 storage buffers, 3-D images can be formed in 10 to 20 seconds. These techniques are illustrated using computer tomography (CT) scans from a group of patients with various structural abnormalities of the brain. Examples of the enhanced diagnostic capability of CT with 3-D imaging as well as its application in the surgical approach to tumors of the central nervous system (CNS) are presented.
Article
Digital formatted imaging examinations are considered and their advantages over conventional methods emphasized. One display technique, the three-dimensional rendering of solid surfaces of multiple objects, is examined, and a large number of Computerized Tomography (CT) data applications is completed, where the heuristic reconstruction algorithm performs on a visual par with the optimal algorithm of Fuchs et al. The optimal algorithm, however, is much slower than the heuristic algorithm; furthermore, it requires much greater storage. The quantitative aspects of these algorithms, namely the polyhedral surface area and volume, show virtually no difference in the many cases in which comparisons are made.
Article
These new approaches to 3-D medical imaging promise better and more cost-effective object identification, representation, and manipulation in space and time.
Article
The emerging technology of NMR imaging is introduced here as a problem in system identification. We show how selected families of signals may be input into the system ("system," in this case, is almost synonymous with "patient") in order that the system's responses to these inputs may be directly interpreted in terms of the system parameters. Once identified, a raster display of the system parameters provides an internal image of the patient. Inputs to the system age four-component functions of time. One component describes the strength of an RF signal, and the other three components govern the strength of three spatially varying, independently controlled magnetic fields (the gradient fields) in which the patient is immersed. In response to these inputs some of the protons in the patient, acting in concordance with the Bloch equation, give rise to local fluctuations in the magnetization which are detected with a tuned antenna and a sensitive receiver. The relationship between this output signal and the system parameters is summarized in the imaging equation.
Article
Computerized tomography (CT) which permits imaging the internal anatomy in axial cross section, has had a major impact in medicine, primarily in the diagnostic area. The CT scans are also useful in determining the extent of disease which is important in selecting the appropriate therapy. For therapy, the CT scan is becoming important in planning a course of radiation therapy for a cancer patient and to a lesser extent, in planning a surgical reconstruction for some patients. For both of these treatment modalities it would be desirable to have a three-dimensional reconstruction of the internal anatomy. This paper discusses the use of a three-dimensional perspective of the internal anatomy, obtained from multiple CT scans, as a guide to these two therapeutic modalities.
Article
The applications of computer-assisted, or comput(eriz)ed, tomography (CT) are reviewed. The major emphasis is on medical applications, but all relevant technical sciences are covered. A unified descriptive account of the underlying principles is presented (detailed reviews of algorithms and their mathematical backgrounds can be found elsewhere in this special issue). Deficiencies in existing hardware and software are identified and the possible means of remedying the more urgent of these are outlined. Promising approaches for future research and development into CT are suggested.
Article
The subject of singl-photon emission computed tomography (SPECT) is generally reviewed. The basic interaction processes of gamma rays in matter are outlined, and the formation of conventional gamma-ray images is described. We then outline the extension of these concepts to the formation of three-dimensional or tomographic images. Of particular concern in emission tomography, the effects of gamma-ray attenuation and scattering are outlined. Several examples are given of practical SPECT systems, and representative results are given.
3D Reconstruction of Cerebral Blood Vessels. IEEE Comlmwr Graphk's attd Applk'ations
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Interactive Surgical Planning
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3D Reconstruction of the Brain from Magnetic Resonance Images
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Color 3 D Imaging of Normal and Pathologic Intracranial Structures
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