{"title":"ACPDNLS: Adaptive convexity preserving double nonzero level set for cardiac MR image segmentation","authors":"Ji Li , Aiwen Liu , Yan Wang","doi":"10.1016/j.apm.2025.115975","DOIUrl":null,"url":null,"abstract":"<div><div>Cardiovascular disease has become a major cause of global mortality. Clinically, quantitative assessment of cardiac MR image is usually used to determine the type and severity of cardiovascular disease, in which segmentation of cardiac MR image is a fundamental but important step. However, due to the inhomogeneity and special anatomical structures, accurate segmentation of cardiac MR images is still a challenging task. This paper proposes a double nonzero level set model for the segmentation of cardiac MR images, incorporating an adaptive convexity preserving mechanism and an improved distance regularization term. The double nonzero level set is capable of simultaneously and rapidly segmenting the left ventricle (LV) and right ventricle (RV). The adaptive convexity preserving mechanism guarantees that the segmentation of LV encompasses the cavity, papillary muscles and trabeculae while preserving convexity to meet clinical criteria. In addition, it ensures that RV retains its inherent physiological form, i.e. crescent-like shape. The improved distance regularization term effectively eliminates the need for reinitialization of double level set functions. The proposed model is evaluated on the data of ACDC MICCAI 2017. Experimental results show that in the end-diastolic (ED) and end-systolic (ES) phases, the mean Dice coefficients of LV segmentation are 0.961 (ED) and 0.936 (ES), with mean Hausdorff distances of 4.89 (ED) and 5.79 (ES), while the mean Dice coefficients of RV segmentation are 0.952 (ED) and 0.914 (ES), with mean Hausdorff distances of 8.52 (ED) and 9.60 (ES). The prominent advantage of our model is that, without the requirement of manual annotation and tedious training, it exhibits segmentation accuracy and robustness comparable to deep learning-based cardiac segmentation models. Especially, the segmentation accuracy of RV surpasses that of current state-of-the-art models.</div></div>","PeriodicalId":50980,"journal":{"name":"Applied Mathematical Modelling","volume":"142 ","pages":"Article 115975"},"PeriodicalIF":4.4000,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematical Modelling","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0307904X25000502","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Cardiovascular disease has become a major cause of global mortality. Clinically, quantitative assessment of cardiac MR image is usually used to determine the type and severity of cardiovascular disease, in which segmentation of cardiac MR image is a fundamental but important step. However, due to the inhomogeneity and special anatomical structures, accurate segmentation of cardiac MR images is still a challenging task. This paper proposes a double nonzero level set model for the segmentation of cardiac MR images, incorporating an adaptive convexity preserving mechanism and an improved distance regularization term. The double nonzero level set is capable of simultaneously and rapidly segmenting the left ventricle (LV) and right ventricle (RV). The adaptive convexity preserving mechanism guarantees that the segmentation of LV encompasses the cavity, papillary muscles and trabeculae while preserving convexity to meet clinical criteria. In addition, it ensures that RV retains its inherent physiological form, i.e. crescent-like shape. The improved distance regularization term effectively eliminates the need for reinitialization of double level set functions. The proposed model is evaluated on the data of ACDC MICCAI 2017. Experimental results show that in the end-diastolic (ED) and end-systolic (ES) phases, the mean Dice coefficients of LV segmentation are 0.961 (ED) and 0.936 (ES), with mean Hausdorff distances of 4.89 (ED) and 5.79 (ES), while the mean Dice coefficients of RV segmentation are 0.952 (ED) and 0.914 (ES), with mean Hausdorff distances of 8.52 (ED) and 9.60 (ES). The prominent advantage of our model is that, without the requirement of manual annotation and tedious training, it exhibits segmentation accuracy and robustness comparable to deep learning-based cardiac segmentation models. Especially, the segmentation accuracy of RV surpasses that of current state-of-the-art models.
期刊介绍:
Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged.
This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering.
Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.