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Accurate geometry modeling of vasculatures using implicit fitting with 2D radial basis functions

Hong, Qingqi; Li, Qingde; Wang, Beizhan; Liu, Kunhong; Lin, Fan; Lin, Juncong; Cheng, Xuan; Zhang, Zhihong; Zeng, Ming


Qingqi Hong

Beizhan Wang

Kunhong Liu

Fan Lin

Juncong Lin

Xuan Cheng

Zhihong Zhang

Ming Zeng


Accurate vascular geometry modeling is an essential task in computer assisted vascular surgery and therapy. This paper presents a vessel cross-section based implicit vascular modeling technique, which represents a vascular surface as a set of locally fitted implicit surfaces. In the proposed method, a cross-section based technique is employed to extract from each cross-section of the vascular surface a set of points, which are then fitted with an implicit curve represented as 2D radial basis functions. All these implicitly represented cross-section curves are then being considered as 3D cylindrical objects and combined together using a certain partial shape-preserving spline to build a complete vessel branch; different vessel branches are then blended using a extended smooth maximum function to construct the complete vascular tree. Experimental results show that the proposed method can correctly represent the morphology and topology of vascular structures with high level of smoothness. Both qualitative comparison with other methods and quantitative validations to the proposed method have been performed to verify the accuracy and smoothness of the generated vascular geometric models.


Hong, Q., Li, Q., Wang, B., Liu, K., Lin, F., Lin, J., …Zeng, M. (2018). Accurate geometry modeling of vasculatures using implicit fitting with 2D radial basis functions. Computer aided geometric design, 62, 206-216.

Journal Article Type Article
Acceptance Date Feb 8, 2018
Online Publication Date Mar 22, 2018
Publication Date May 1, 2018
Deposit Date Jun 14, 2019
Publicly Available Date Jun 14, 2019
Journal Computer Aided Geometric Design
Print ISSN 0167-8396
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 62
Pages 206-216
Keywords Geometry modeling; Vasculature; Implicit fitting
Public URL
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