Metamorphosis of images in reproducing kernel Hilbert spaces

被引：11

作者：

Richardson, Casey L. ^{[1
]}

Younes, Laurent ^{[2
,3
]}

机构：

[1] Johns Hopkins Univ, Appl Phys Lab, 11100 Johns Hopkins Rd, Laurel, MD 20723 USA

[2] Johns Hopkins Univ, Ctr Imaging Sci, 3400 North Charles St, Baltimore, MD 21218 USA

[3] Johns Hopkins Univ, Dept Appl Math & Stat, 3400 North Charles St, Baltimore, MD 21218 USA

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2016年 / 42卷 / 03期

基金：

美国国家科学基金会;

关键词：

Groups of diffeomorphisms; Shape analysis; Deformable templates; Metamorphosis; Adjoint methods; REGISTRATION; SHAPE; DEMENTIA;

D O I：

10.1007/s10444-015-9435-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this would enable the use of statistical methods based on this momentum, as well as the estimation of templates from hyper-templates using morphing. In this paper we introduce a shooting method, in the particular case of morphing images that lie in a reproducing kernel Hilbert space (RKHS). We derive the relevant shooting equations from a Lagrangian frame of reference, present the details of the numerical approach, and illustrate the method through morphing of some simple images.

引用

页码：573 / 603

页数：31

共 50 条

[1] Metamorphosis of images in reproducing kernel Hilbert spaces
Casey L. Richardson
Laurent Younes
[J]. Advances in Computational Mathematics, 2016, 42 : 573 - 603
[2] Reproducing kernel hilbert spaces
Seddighi, K.
[J]. Iranian Journal of Science & Technology, 1993, 17 (03):
[3] Noncommutative reproducing kernel Hilbert spaces
Ball, Joseph A.
Marx, Gregory
Vinnikov, Victor
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (07) : 1844 - 1920
[4] Pasting Reproducing Kernel Hilbert Spaces
Sawano, Yoshihiro
[J]. NEW TRENDS IN ANALYSIS AND INTERDISCIPLINARY APPLICATIONS, 2017, : 401 - 407
[5] A Primer on Reproducing Kernel Hilbert Spaces
Manton, Jonathan H.
Amblard, Pierre-Olivier
[J]. FOUNDATIONS AND TRENDS IN SIGNAL PROCESSING, 2014, 8 (1-2): : 1 - 126
[6] On isomorphism of reproducing kernel Hilbert spaces
V. V. Napalkov
V. V. Napalkov
[J]. Doklady Mathematics, 2017, 95 : 270 - 272
[7] On isomorphism of reproducing kernel Hilbert spaces
Napalkov, V. V.
Napalkov, V. V., Jr.
[J]. DOKLADY MATHEMATICS, 2017, 95 (03) : 270 - 272
[8] RELATIVE REPRODUCING KERNEL HILBERT SPACES
Alpay, Daniel
Jorgensen, Palle
Volok, Dan
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (11) : 3889 - 3895
[9] On reproducing kernel Hilbert spaces of polynomials
Li, XJ
[J]. MATHEMATISCHE NACHRICHTEN, 1997, 185 : 115 - 148
[10] OPERATOR INEQUALITIES IN REPRODUCING KERNEL HILBERT SPACES
Yamanci, Ulas
[J]. COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2022, 71 (01): : 204 - 211

← 1 2 3 4 5 →