采用凹二次正则项的弹性点匹配算法

Non-rigid feature point matching algorithm using concave quadratic regularization term

现有的采用l1范数正则项的点匹配算法,其l1范数优化问题可等价为一个线性规划问题,但约束不满足完全的单模性,这导致解出的对应关系不是整数,需要后续的取整过程,这会给计算结果带来额外误差并使算法复杂化。为解决该问题,基于鲁棒点匹配算法的最新成果,提出一种新的正则项。该正则项是凹的,可以证明目标函数具有整数的最优解,所以算法无须后续处理,实现起来更简单。实验结果表明:相比采用l1范数正则项的算法,所提算法对于各种干扰均有更好的鲁棒性,特别对于野点干扰,误差只有对比算法的一半。

For the existing point matching algorithms adopting the l1 norm regularization terms,the corresponding l1 norm optimization problems are equivalent to linear programs.But the constraints do not satisfy the total unimodularity property,which causes the point correspondence solutions to be non-integers and post-processing is needed to convert the solutions to integers.Such processing brings error and complicates the algorithms.To resolve the above problem,based on the latest result with the robust point matching algorithm,a new regularization term was proposed.The new regularization term is concave and it can be proved that the objective function has integral optimal solutions.Therefore,no post-processing is needed and it is simpler to implement.The experimental results show that,compared with the algorithms adopting the l1 norm regularization terms,the proposed algorithm is more robust to various types of disturbances,particularly outliers,while its error is only half of the compared algorithms.