A geometric flow approach for region-based image segmentation-theoretical analysis

doi:10.1007/s10255-018-0723-4

CSpace

	A geometric flow approach for region-based image segmentation-theoretical analysis
	Jing, Zhu-cui 1; Ye, Juntao 2; Xu, Guo-liang 3
	2018
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	34 期号:1 页码:65-76
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
DOI	10.1007/s10255-018-0723-4
语种	英语
资助项目	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
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29806
专题	中国科学院数学与系统科学研究院
通讯作者	Jing, Zhu-cui
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
推荐引用方式 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.