利用薄板样条函数实现非刚性图像匹配算法

A New Non-Rigid Image Matching Algorithm Using Thin-Plate Spline

提出了一种利用薄板样条函数实现非刚性图像匹配的新方法 .该方法是将图像表示成由特征点构成的特征点集 ,利用薄板样条 (TPS)能够将形变清楚地分解为仿射分量和非仿射分量的独特性质 ,应用TPS函数来表征特征点集之间的非刚性映射 ,并将TPS映射参数的求解嵌入到确定性退火技术的框架中 .首先提出基于TPS弯曲能的非刚性匹配的能量函数 ,然后采用确定性退火技术 ,迭代求解点集之间的匹配矩阵和映射参数 .与其它的非刚性匹配算法相比 ,该算法不仅保证了图像特征点之间的一一对应的双向约束 ,同时避免了陷入局部极小 ,而且具有较强的鲁棒性 .实验结果证实了所提算法的有效性和鲁棒性 .

A novel,robust algorithm for solving the non-rigid matching between two images is proposed.This method represents the image by sets of feature points.Due to a special characteristic of the thin-plate spline(TPS)-it can decompose a deformation into the affine and non-affine components.TPS for non-rigid spatial mapping is chosen.A convex TPS bending energy function describing the problem is derived and a one-to-one two-way matching constraint on the match matrix is enforced.By minimizing the above bending energy,we can jointly estimate the TPS mapping parameters and match matrix between the two feature point-sets of the images.We utilize the deterministic annealing which emerged from the statistical physics to solve the optimization problem.Embedded within a deterministic annealing framework,and by introducing an annealing temperature to control the degree of fuzziness of the match matrix,the algorithm not only improves the robustness but also reduces the chances of getting trapped in local minima.We compare our method with the polynomial quasi-exhaustive exploration (PQEE) algorithm proposed by Michigan University,and the results show that PQEE's performance deteriorates much faster with the increase of degrees of deformation,amounts of noise and percentage of outliers.We also conduct experiments on matching of hand-shapes images and registration of anatomical brain MR images.The experimental results demonstrate the validation and robustness of the algorithm.