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A geometric flow approach for region-based image segmentation-theoretical analysis
Jing, Zhu-cui1; Ye, Juntao2; Xu, Guo-liang3
2018
Source PublicationACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN0168-9673
Volume34Issue:1Pages:65-76
AbstractIn this paper, we analyze the well-posedness of an image segmentation model. The main idea of that segmentation model is to minimize one energy functional by evolving a given piecewise constant image towards the image to be segmented. The evolution is controlled by a serial of mappings, which can be represented by B-spline basis functions. The evolution terminates when the energy is below a given threshold. We prove that the correspondence between two images in the segmentation model is an injective and surjective mapping under appropriate conditions. We further prove that the solution of the segmentation model exists using the direct method in the calculus of variations. These results provide the theoretical support for that segmentation model.
KeywordL-2-gradient flow Bi-cubic B-spline direct method image segmentation
DOI10.1007/s10255-018-0723-4
Language英语
Funding ProjectNSFC[61379096] ; Chinese- Guangdong's S T project[2014A050503004]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000427057400006
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29806
Collection中国科学院数学与系统科学研究院
Affiliation1.Beijing Jiaotong Univ, Sch Econ & Management, Beijing 100044, Peoples R China
2.Chinese Acad Sci, Inst Automat, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Jing, Zhu-cui,Ye, Juntao,Xu, Guo-liang. A geometric flow approach for region-based image segmentation-theoretical analysis[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2018,34(1):65-76.
APA Jing, Zhu-cui,Ye, Juntao,&Xu, Guo-liang.(2018).A geometric flow approach for region-based image segmentation-theoretical analysis.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,34(1),65-76.
MLA Jing, Zhu-cui,et al."A geometric flow approach for region-based image segmentation-theoretical analysis".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 34.1(2018):65-76.
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