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Mathematics
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Computer Graphics, Visualization and Medical Imaging: Theory and Applications
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Computer Graphics, Visualization and Medical Imaging: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 12725

Special Issue Editor

Prof. Dr. Shiaofen Fang

E-Mail Website
Guest Editor
Department of Computer and Information Science, Indiana University—Purdue University Indianapolis, Indianapolis, IN 46202, USA
Interests: data visualization; biomedical image analysis; visual analytic; volume graphics

Special Issue Information

Dear Colleagues,

Computer graphics and visualization play important roles in medical imaging applications including medical image processing, analysis, and diagnostics. In recent years, the rapid growth of artificial intelligence and data science has inspired a new generation of graphics and visualization techniques and applications.  Examples include interactive machine learning for medical image diagnostics, visual analytics systems, and topological analysis of big medical image datasets. This Special Issue focuses on the use of advanced computer graphics, geometric modeling, and data visualization techniques and algorithms in biomedical imaging applications. We aim to provide a special platform to promote and disseminate novel ideas, systems, and application case studies. All topics related to computer graphics, visualization and their applications in medical imaging are welcome. Such topics may include, but are not limited to: human-in-the-loop AI systems, the visualization of machine learning models, virtual and augmented reality techniques for medical applications, topological structures of medical image datasets, advanced geometric models for human anatomical structures, and visual analytics theory and applications.

Prof. Dr. Shiaofen Fang
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computer graphics
  • visualization
  • geometric modeling
  • medical image analysis

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Published Papers (6 papers)

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Research

18 pages, 12171 KiB  
Article
An Effective Method for Slicing Triangle Meshes Using a Freeform Curve
by Seung-Yong Lee, Seong-Hyeon Kweon and Seung-Hyun Yoon
Mathematics 2024, 12(10), 1432; https://doi.org/10.3390/math12101432 - 7 May 2024
Viewed by 1643
Abstract
Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces [...] Read more.
Slicing 3D polygonal meshes is a fundamental operation in various applications such as virtual surgery, garment simulation, and game development. Existing methods primarily slice meshes using either a single line or a set of line segments approximating a smooth curve. This paper introduces a novel approach to freely slice a triangle mesh using a freeform curve without discretizing it into line segments. The user draws a stroke on the screen, defining the desired cutting trajectory. Subsequently, a freeform curve approximating this stroke is generated and extended into a ruled surface in the user’s viewing direction. To efficiently compute intersections between the ruled surface and a triangle mesh, the Line–Surface Intersection (LSI) problem is broken down into two subproblems: Plane–Curve Intersection (PCI) followed by Line–Line Intersection (LLI). Intersection points are then connected to form polylines, effectively cutting the mesh into multiple submeshes. To ensure the solidity of the submeshes, cross-sections are generated by trimming the ruled surface along the polylines and merged with the corresponding submeshes. Our method empowers users to slice triangle meshes along arbitrary trajectories encompassing both straight and freely curved paths while preserving efficiency and accuracy. The effectiveness of the proposed approach is demonstrated through experimental results showing various examples of mesh slicing. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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27 pages, 21915 KiB  
Article
A Convolutional Neural Network-Based Auto-Segmentation Pipeline for Breast Cancer Imaging
by Lucas Jian Hoong Leow, Abu Bakr Azam, Hong Qi Tan, Wen Long Nei, Qi Cao, Lihui Huang, Yuan Xie and Yiyu Cai
Mathematics 2024, 12(4), 616; https://doi.org/10.3390/math12040616 - 19 Feb 2024
Cited by 2 | Viewed by 1964
Abstract
Medical imaging is crucial for the detection and diagnosis of breast cancer. Artificial intelligence and computer vision have rapidly become popular in medical image analyses thanks to technological advancements. To improve the effectiveness and efficiency of medical diagnosis and treatment, significant efforts have [...] Read more.
Medical imaging is crucial for the detection and diagnosis of breast cancer. Artificial intelligence and computer vision have rapidly become popular in medical image analyses thanks to technological advancements. To improve the effectiveness and efficiency of medical diagnosis and treatment, significant efforts have been made in the literature on medical image processing, segmentation, volumetric analysis, and prediction. This paper is interested in the development of a prediction pipeline for breast cancer studies based on 3D computed tomography (CT) scans. Several algorithms were designed and integrated to classify the suitability of the CT slices. The selected slices from patients were then further processed in the pipeline. This was followed by data generalization and volume segmentation to reduce the computation complexity. The selected input data were fed into a 3D U-Net architecture in the pipeline for analysis and volumetric predictions of cancer tumors. Three types of U-Net models were designed and compared. The experimental results show that Model 1 of U-Net obtained the highest accuracy at 91.44% with the highest memory usage; Model 2 had the lowest memory usage with the lowest accuracy at 85.18%; and Model 3 achieved a balanced performance in accuracy and memory usage, which is a more suitable configuration for the developed pipeline. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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25 pages, 4726 KiB  
Article
Homological Landscape of Human Brain Functional Sub-Circuits
by Duy Duong-Tran, Ralph Kaufmann, Jiong Chen, Xuan Wang, Sumita Garai, Frederick H. Xu, Jingxuan Bao, Enrico Amico, Alan D. Kaplan, Giovanni Petri, Joaquin Goni, Yize Zhao and Li Shen
Mathematics 2024, 12(3), 455; https://doi.org/10.3390/math12030455 - 31 Jan 2024
Cited by 4 | Viewed by 2418
Abstract
Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., a set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional [...] Read more.
Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., a set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional sub-circuits have yet to be addressed. To that end, we proposed a homological formalism that enables the quantification of higher-order characteristics of human brain functional sub-circuits. Our results indicate that each homological order uniquely unravels diverse, complementary properties of human brain functional sub-circuits. Noticeably, the H1 homological distance between rest and motor task was observed at both the whole-brain and sub-circuit consolidated levels, which suggested the self-similarity property of human brain functional connectivity unraveled by a homological kernel. Furthermore, at the whole-brain level, the rest–task differentiation was found to be most prominent between rest and different tasks at different homological orders: (i) Emotion task (H0), (ii) Motor task (H1), and (iii) Working memory task (H2). At the functional sub-circuit level, the rest–task functional dichotomy of the default mode network is found to be mostly prominent at the first and second homological scaffolds. Also at such scale, we found that the limbic network plays a significant role in homological reconfiguration across both the task and subject domains, which paves the way for subsequent investigations on the complex neuro-physiological role of such network. From a wider perspective, our formalism can be applied, beyond brain connectomics, to study the non-localized coordination patterns of localized structures stretching across complex network fibers. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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18 pages, 3156 KiB  
Article
A Method of Lung Organ Segmentation in CT Images Based on Multiple Residual Structures and an Enhanced Spatial Attention Mechanism
by Lingfei Wang, Chenghao Zhang, Yu Zhang and Jin Li
Mathematics 2023, 11(21), 4483; https://doi.org/10.3390/math11214483 - 30 Oct 2023
Cited by 1 | Viewed by 1686
Abstract
Accurate organ segmentation is a fundamental step in disease-assisting diagnostic systems, and the precise segmentation of lung is crucial for subsequent lesion detection. Prior to this, lung segmentation algorithms had typically segmented the entire lung tissue. However, the trachea is also essential for [...] Read more.
Accurate organ segmentation is a fundamental step in disease-assisting diagnostic systems, and the precise segmentation of lung is crucial for subsequent lesion detection. Prior to this, lung segmentation algorithms had typically segmented the entire lung tissue. However, the trachea is also essential for diagnosing lung diseases. Challenges in lung parenchyma segmentation include the limited robustness of U-Net in acquiring contextual information and the small size of the trachea being mixed up with lung, making it difficult to identify and reconstruct the lungs. To overcome these difficulties, this paper proposes three improvements to U-Net: multiple concatenation modules to enhance the network’s ability to capture context, multi-scale residual learning modules to improve the model’s multi-scale learning capabilities, and an enhanced gated attention mechanism to enhance the fusion of various hierarchical features. The experimental results demonstrate that our model has achieved a significant improvement in trachea segmentation compared to existing models. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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23 pages, 1996 KiB  
Article
A Comparison of the Tortuosity Phenomenon in Retinal Arteries and Veins Using Digital Image Processing and Statistical Methods
by Sufian A. Badawi, Maen Takruri, Djamel Guessoum, Isam Elbadawi, Ameera Albadawi, Ajay Nileshwar and Emad Mosalam
Mathematics 2023, 11(18), 3811; https://doi.org/10.3390/math11183811 - 5 Sep 2023
Viewed by 1668
Abstract
The tortuosity of retinal blood vessels is an important phenomenon, and it can act as a biomarker in the diagnosis of several eye diseases. The study of abnormalities in the tortuosity of retinal arteries and veins provides ophthalmologists with important information for disease [...] Read more.
The tortuosity of retinal blood vessels is an important phenomenon, and it can act as a biomarker in the diagnosis of several eye diseases. The study of abnormalities in the tortuosity of retinal arteries and veins provides ophthalmologists with important information for disease diagnosis. Our study aims to compare the tortuosity relation between retinal arteries and veins by quantifying the vessels’ tortuosity in the retina using 14 tortuosity measures applied to the AV-classification retinal dataset. Two feature sets are created, one for arteries and the other for veins. The comparison between the tortuosity of arteries and veins is based on a two-sample T-test statistical method, a regression analysis between the quantified tortuosity features, principal component analysis at the dataset level, and the introduction of the arteriovenous length ratios concept to compare the variations in these new ratios to see the tortuosity behavior in each image. The methods’ results have shown that the tortuosity of retinal arteries and veins is similar. The result of the two-sample T-test supports the research hypothesis, as the P-value obtained was greater than 0.05. Furthermore, the regression analysis between arteries and veins features showed a high correlation (r2 = 89.39% and 89.11%) for arteries and veins, respectively. The study concludes that the retinal vessel type has no statistical significance in the tortuosity calculation results. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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32 pages, 2597 KiB  
Article
Enhancing Vessel Segment Extraction in Retinal Fundus Images Using Retinal Image Analysis and Six Sigma Process Capability Index
by Sufian A. Badawi, Maen Takruri, Isam ElBadawi, Imran Ali Chaudhry, Nasr Ullah Mahar, Ajay Kamath Nileshwar and Emad Mosalam
Mathematics 2023, 11(14), 3170; https://doi.org/10.3390/math11143170 - 19 Jul 2023
Cited by 3 | Viewed by 1935
Abstract
Retinal vessel segmentation, skeletonization, and the generation of vessel segments are considered significant steps in any automated system for measuring the vessel biomarkers of several disease diagnoses. Most of the current tortuosity quantification methods rely on precise vascular segmentation and skeletonization of the [...] Read more.
Retinal vessel segmentation, skeletonization, and the generation of vessel segments are considered significant steps in any automated system for measuring the vessel biomarkers of several disease diagnoses. Most of the current tortuosity quantification methods rely on precise vascular segmentation and skeletonization of the retinal vessels. Additionally, the existence of a reference dataset for accurate vessel segment images is an essential need for implementing deep learning solutions and an automated system for measuring the vessel biomarkers of several disease diagnoses, especially for optimized quantification of vessel tortuosity or accurate measurement of AV-nicking. This study aimed to present an improved method for skeletonizing and extracting the retinal vessel segments from the 504 images in the AV classification dataset. The study utilized the Six Sigma process capability index, sigma level, and yield to measure the vessels’ tortuosity calculation improvement before and after optimizing the extracted vessels. As a result, the study showed that the sigma level for the vessel segment optimization improved from 2.7 to 4.39, the confirming yield improved from 88 percent to 99.77 percent, and the optimized vessel segments of the AV classification dataset retinal images are available in monochrome and colored formats. Full article
(This article belongs to the Special Issue Computer Graphics, Visualization and Medical Imaging: Theory and Applications)
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