基于粘滞流体B样条模型的快速非刚体配准方法

荣成城; 周  健; 曹国刚; 罗立民

doi:10.11834/jig.20090423

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基于粘滞流体B样条模型的快速非刚体配准方法
Fast Non-rigid Image Registration Using Viscous Fluid B-spline Model
2009年14卷第4期页码：712
纸质出版：2009
DOI： 10.11834/jig.20090423
稿件说明：

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荣成城, 周健, 曹国刚, 罗立民. 基于粘滞流体B样条模型的快速非刚体配准方法[J]. 中国图象图形学报, 2009,14(4):712. DOI： 10.11834/jig.20090423.

RONG Chengcheng, ZHOU Jian, CAO Guogang, LUO Limin. Fast Non-rigid Image Registration Using Viscous Fluid B-spline Model[J]. Journal of Image and Graphics, 2009, 14(4): 712. DOI： 10.11834/jig.20090423.

摘要

基于粘滞流体模型的非刚体配准算法是一种适合个体差异较大配准场合的方法。其关键步骤为求解偏微分运动方程组，但原始算法中采用直接离散结合同步超松弛(SOR)的方法相当耗时。为了缩短求解时间，提出一种基于粘滞流体B样条模型的快速方法。首先利用B样条对速度场进行建模，将方程组未知量转为B样条系数，减小计算负担；接着利用B样条的一些重要性质，推导出基于快速傅里叶变换(FFT)的B样条系数求解方法，进一步加快求解速度。实验结果表明，新算法在保持原始算法相同配准精度的同时，具有很快的计算速度。

Abstract

Non-rigid image registration algorithm based on viscous fluid model is an appropriate method for registering objects with large difference.The critical part of the model is the viscous fluid kinematical partial differential equations（PDEs)

which are very time-consuming to be solved by direct discretization combined with successive over-relaxation method(SOR).In order to reduce the time cost

a fast method based on viscous fluid B-spline model is developed.Firstly

B-spline is used to model the vector fields in the PDEs

changing the unknowns to the coefficients of B-spline.Secondly

by using of fast Fourier Transform(FFT) and some special attributes of B-spline

formulas of directly calculating the coefficients are deduced.Experimental results show that new method is a fast non-rigid registration method without precision loss.