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However, due to the large differences in liver shapes, low\u2010contrast to adjacent tissues, and existence of tumors or other abnormalities, liver segmentation has been very challenging. This study presents an accurate and fast liver segmentation method based on a novel probabilistic active contour (PAC) model and its fast global minimization scheme (3D\u2010FGMPAC), which is explainable as compared with deep learning\u00a0methods.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>The proposed method first constructs a slice\u2010indexed\u2010histogram to localize the volume of interest (VOI) and estimate the probability that a voxel belongs to the liver according its intensity. The probabilistic image would be used to initialize the 3D PAC model. Secondly, a new contour indicator function, which is a component of the model, is produced by combining the gradient\u2010based edge detection and Hessian\u2010matrix\u2010based surface detection. Then, a fast numerical scheme derived for the 3D PAC model is performed to evolve the initial probabilistic image into the global minimizer of the model, which is a smoothed probabilistic image showing a distinctly highlighted liver. Next, a simple region\u2010growing strategy is applied to extract the whole liver mask from the smoothed probabilistic image. Finally, a B\u2010spline surface is constructed to fit the patch of the rib cage to prevent possible leakage into adjacent intercostal\u00a0tissues.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The proposed method is evaluated on two public datasets. The average Dice score, volume overlap error, volume difference, symmetric surface distance and volume processing time are 0.96, 7.35%, 0.02%, 1.17 mm and 19.8 s for the Sliver07 dataset, and 0.95, 8.89%, , 1.45 mm and 23.08 s for the 3Dircadb dataset,\u00a0respectively.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>The proposed fully\u2010automatic approach can effectively segment the liver from low\u2010contrast and complex backgrounds. The quantitative and qualitative results demonstrate that the proposed segmentation method outperforms state\u2010of\u2010the\u2010art traditional automatic liver segmentation algorithms and achieves very competitive performance compared with recent deep leaning\u2010based\u00a0methods.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.16116","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T10:23:30Z","timestamp":1669112610000},"page":"2100-2120","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Automatic 3D CT liver segmentation based on fast global minimization of probabilistic active contour"],"prefix":"10.1002","volume":"50","author":[{"given":"Renchao","family":"Jin","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology Huazhong University of Science and Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Manyang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology Huazhong University of Science and Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lijun","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering Hubei University Wuhan China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiayi","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology Huazhong University of Science and Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enmin","family":"Song","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology Huazhong University of Science and Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangzhi","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology Huazhong University of Science and Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2022,12,13]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"crossref","unstructured":"LiS WaiteJM LennonBT StefansicJD LiR DawantBM.Development of preoperative liver and vascular system segmentation and modeling tool for image\u2010guided surgery and surgical planning. 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