图像局部弹性变换中径向基函数紧支撑集的选取
doi: 10.3724/SP.J.1146.2007.00951
Compact Support Analysis of Radial Basis Function in Image Local Elastic Transformation
-
摘要: 弹性图像配准中常常需要采用紧支撑的径向基函数来实现局部弹性变换，径向基函数的支撑集大小决定了图像局部扭曲的范围，而如何选取基函数的支撑集大小是一个一直没有解决的问题。该文利用弹性变换模型，针对Wendland基函数，从理论上分析了双标志点空间位置与基函数支撑集的关系，并对任意标志点集合通过构造Delaunay三角剖分来确定基函数支撑集大小，文中给出了径向基函数支撑集的选取原则。人工网格图像和医学图像的局部弹性变换实验验证了该文的结论。Abstract: In image local elastic transformation, compact support radial basis functions are used to implement local elastic deformation transformation. The elastic deformation area is related to the support of radial basis function. However, how to choose the support size of the radial basis function based on space distribution of landmarks still is an unresolved doubt. In this paper, choosing the support of Wendland basis functions based on the space distribution of two landmarks is analyzed in detail. For the landmarks set, Delaunay triangle is constructed to obtain the optimal distance between landmarks, and support is chosen correspondingly. The principle of choosing the support size of radial basis functions in image local elastic transformation is given also. Experiments of the artificial images and medial images show the feasibility of this conclusion
-
[1] Bookstein F L. Principal warps: Thin-plate splines and thedecomposition of deformations[J].IEEE Trans. on. PatternAnalysis and Machine Intelligence.1989, 11(6):567-585 [2] Arad N and Reisfeld D. Image warping using few anchorpoints and radial functions[J].Computer Graphics Forum.1995,14(1):35-46 [3] Fornefett M, Rohr K, and Stiehl H S. Radial basis functionswith compact support for elastic registration of medicalimages[J].Image Vision Comput.2001, 19:87-96 [4] Fornefett M, Rohr K, and Stiehl H S. Elastic registration ofmedical images using radial basis functions with compactsupport. CVPR99, Colorada, 1999: 402-407. [5] Lie Wen-Nung and Chuang Cheng-Hung. Contour-basedimage registration with local deformations. OpticalEngineering, 2003, 42(5): 1405-1416. [6] Donato1 G and Belongie S. Approximate thin plate splinemappings. ECCV, Copenhagen, 2002: 531-542. [7] Wendland H. Piecewise polynomial, positive definite andcompactly supported radial functions of minimal degree[J].Adv.in Comp. Math.1995, 4:389-396 [8] Buhmann M D. A new class of radial basis functions withcompact support[J].Math. Comput.2000, 70:307-318 [9] Rohr K, Stiehl H S, and Sprengel R, et al.. Landmark-basedelastic registration using approximating thin-plate splines[J].IEEE Trans. on Med. Imaging.2001, 20(6):526-534 [10] Li J, Yang X, and Yu J P. Local warp algorithm in imageelastic registration. FLCI2005, Shenzhen, 2005: 693-698. -
点击查看大图
计量
- 文章访问数: 3688
- HTML全文浏览量: 87
- PDF下载量: 1350
- 被引次数: 0
下载:
