A geometric flow approach for region-based image segmentation-theoretical analysis
Jing, Zhu-cui1; Ye, Juntao2; Xu, Guo-liang3
2018
发表期刊ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
卷号34期号:1页码:65-76
文章类型Article
摘要In 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.
关键词L-2-gradient Flow Bi-cubic B-spline Direct Method Image Segmentation
WOS标题词Science & Technology ; Physical Sciences
DOI10.1007/s10255-018-0723-4
关键词[WOS]ACTIVE CONTOURS ; MUMFORD ; MODEL ; EDGES
收录类别SCI
语种英语
项目资助者NSFC(61379096) ; Chinese- Guangdong's S T project(2014A050503004)
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000427057400006
引用统计
文献类型期刊论文
条目标识符http://ir.ia.ac.cn/handle/173211/21979
专题模式识别国家重点实验室_多媒体计算与图形学
作者单位1.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
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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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