In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.
Parametric shape models for vessels learned from segmentations via differentiable voxelization
Technical University of Munich (TUM)（技术大学慕尼黑）；TUM University Hospital（慕尼黑技术大学医院）；University of Zurich（苏黎世大学）；Stanford Center for Artificial Intelligence in Medicine and Imaging（斯坦福大学人工智能医学与成像中心）；Center for Computational Health（计算健康中心）；Institute for Diagnostic and Interventional Radiology（诊断与介入放射学研究所）；German Cancer Consortium (DKTK)（德国癌症联盟（DKTK））；Department of Computing（计算部门）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
No Time to Train: Empowering Non-Parametric Networks for Few-shot 3D Scene Segmentation
Shanghai AI Lab（上海人工智能实验室）；City University of Hong Kong（香港城市大学）；Peking University（北京大学）；Tencent Youtu Lab（腾讯优图实验室）；The Chinese University of Hong Kong（香港中文大学）
TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy
Department of Applied Mathematics and Computer Science, Technical University of Denmark（技术大学丹麦应用数学和计算机科学系）；A.I. Virtanen Institute, University of Eastern Finland（东部芬兰大学A.I. Virtanen研究所）；Department of Architecture, Faculty of Engineering, Sojo University, Japan（日本早稻田大学工学系建筑系）
Topology guaranteed segmentation of the human retina from OCT using convolutional neural networks
Portland State University（波特兰州立大学）；Wilmer Eye Institute（威尔默眼科研究所）；The Johns Hopkins University（约翰斯·霍普金斯大学）；The Johns Hopkins University School of Medicine（约翰斯·霍普金斯大学医学院）
Disconnect to Connect: A Data Augmentation Method for Improving Topology Accuracy in Image Segmentation
DTU Compute, Technical University of Denmark（丹麦技术大学DTU计算学院）；A.I. Virtanen Institute, University of Eastern Finland（东芬兰大学人工智能维尔塔宁研究所）；Aarhus University（奥胡斯大学）
Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching
Department of Electrical and Computer Engineering, University of California, San Diego（电气与计算机工程系，加州大学圣地亚哥分校）；Department of Ophthalmology, University of California, San Diego（眼科学系，加州大学圣地亚哥分校）
Uncertainty-Aware Multi-Parametric Magnetic Resonance Image Information Fusion for 3D Object Segmentation
Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院保罗·C·劳特伯生物医学成像研究中心）；University of Chinese Academy of Sciences（中国科学院大学）；Peng Cheng Laboratory（鹏城实验室）；Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application（广东省医学图像分析与应用人工智能重点实验室）
TEDS-Net: Enforcing Diffeomorphisms in Spatial Transformers to Guarantee Topology Preservation in Segmentations
Institute of Biomedical Engineering（生物医学工程研究所）；University of Oxford（牛津大学）；Wellcome Centre for Integrative Neuroimaging（惠康综合神经成像中心）；FMRIB（FMRIB（功能磁共振成像与脑研究中心））；Australian Institute for Machine Learning (AIML)（澳大利亚机器学习研究所（AIML））；University of Adelaide（阿德莱德大学）；South Australian Health and Medical Research Institute (SAHMRI)（南澳大利亚健康与医学研究所（SAHMRI））
Construction of unbiased dental template and parametric dental model for precision digital dentistry
School of Biomedical Engineering, ShanghaiTech University（上海科技大学生物医学工程学院）；Faculty of Dentistry, The University of Hong Kong（香港大学牙医学院）；School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications（重庆邮电大学通信与信息工程学院）；Shanghai Ninth People’s Hospital, Shanghai Jiao Tong University（上海交通大学医学院附属第九人民医院）；Hangzhou First People’s Hospital, Zhejiang University（浙江大学附属杭州市第一人民医院）；Shanghai United Imaging Intelligence Co., Ltd.（上海联影智能医疗科技有限公司）；Shanghai Clinical Research and Trial Center（上海临床研究与试验中心）
Semi-supervised Liver Segmentation and Patch-based Fibrosis Staging with Registration-aided Multi-parametric MRI
1 Intelligent Modelling \& Analysis Group (IMA), 2 Lab for Uncertainty in Data；Decision Making (LUCID), \ of Computer Science, University of Nottingham, UK 3 Nottingham Biomedical Research Centre (BRC), \ of Medicine, University of Nottingham, UK；Intelligent Modelling \& Analysis Group (IMA), School of Computer Science, University of Nottingham, UK Lab for Uncertainty in Data；Decision Making (LUCID), School of Computer Science, University of Nottingham, UK Nottingham Biomedical Research Centre (BRC), School of Medicine, University of Nottingham, UK
Anatomically Conditioned Recurrent Refinement for Topology-Aware Circle of Willis Segmentation
Faculty of Electrical Engineering, Computer Science and Information Technology, Osijek, Croatia（奥西耶克大学电气工程、计算机科学与信息技术学院）；Clinical Medical Center Osijek, Osijek, Croatia（奥西耶克临床医学中心）；Ghent University, Dept. of Telecommunications and Information Processing, imec-TELIN-IPI, Ghent, Belgium（根特大学电信与信息处理系，imec-TELIN-IPI）；Ghent University, Dept. of Telecommunications and Information Processing, TELIN-GAIM, Ghent, Belgium（根特大学电信与信息处理系，TELIN-GAIM）
DTEA: Dynamic Topology Weaving and Instability-Driven Entropic Attenuation for Medical Image Segmentation
School of Advanced Manufacturing, Guangdong University of Technology（广东技术大学先进制造学院）；School of Electronic and Communication Engineering, Shenzhen Polytechnic University（深圳职业技术大学电子与通信工程学院）；Guangzhou City University of Technology（广州市城市技术大学）；Faculty of Science and Technology, University of Macau（澳门大学科学与技术学院）；Department of Cardiology, Guangdong Provincial People’s Hospital (Guangdong Academy of Medical Sciences), Southern Medical University（广东省人民医院心内科（广东省医学科学院））；Guangdong Cardiovascular Institute, Guangdong Provincial People’s Hospital, Guangdong Academy of Medical Sciences（广东省心血管病研究所，广东省人民医院，广东省医学科学院）
Continuous-tone Simple Points: An $\ell_0$-Norm of Cyclic Gradient for Topology-Preserving Data-Driven Image Segmentation
Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University（数学与复杂系统实验室（教育部）, 数学科学学院, 北京师范大学）；State Key Laboratory of Remote Sensing Science, Faculty of Geographical Science, Beijing Normal University（遥感科学国家重点实验室, 地理科学学院, 北京师范大学）
Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesis
Imperial College London（帝国理工学院）；University of Oxford（牛津大学）；Klinikum rechts der Isar, Technical University of Munich（慕尼黑工业大学右侧医院）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）
Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic
Department of Computing, Imperial College London（帝国理工学院计算系）；University of Oxford（牛津大学）；Weill Cornell Medicine（韦尔医学院）；Cornell Tech（康奈尔科技）；TUM University Hospital, Technical University of Munich（慕尼黑技术大学医院）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔兰根-纽伦堡弗里德里希-亚历山大大学）；King’s College London（伦敦国王学院）
Topology-aware Mamba for Crack Segmentation in Structures
School of Computer Science and Engineering, Jiangsu University of Science and Technology（江苏科技大学计算机科学与工程学院）；School of Electronic and Informatics Engineering, Jiangsu University（江苏大学电子与信息工程学院）；School of Civil and Environmental Engineering, Oklahoma State University（俄克拉荷马州立大学土木与环境工程学院）
