基于恒定动量矢量的快速大形变微分同胚非刚体标记点集匹配算法

Fast Large Deformation Diffeomorphic Landmarks Matching Algorithm Based on Stationary Momentum

目前经典的基于微分同胚非刚体变换的标记点匹配算法虽然克服了以往非微分同胚变换方法不能处理大形变非刚体变换的问题,但是普遍存在时空复杂度较高,算法收敛速度较慢以及匹配精确性和变换光滑性不能兼顾等问题.针对这些问题,本文提出了一种新的基于恒定动量矢量的快速大形变微分同胚非刚体标记点集匹配算法,该方法利用拉格朗日坐标系下的恒定动量矢量以及时间依赖的多尺度再生核来构造速度矢量场,然后采用基于规则化控制参数的确定性退火机制来搜索最优动量矢量,从而得到最终的微分同胚变换形变场.最后实验验证了本文所提新算法能使匹配的精确性和变换的光滑性达到较好的平衡兼顾,而且也较大程度地降低了算法的时间复杂度以及空间复杂度.

At present,the classical diffeomorphic landmarks matching algorithms can handle large non-rigid deformation problems that cannot be solved by the non-diffeomorphic algorithms,but there are still plenty of problems such as high spatial and temporal complexity,slow convergence speed and impossible to take into account accurate matching and smooth transformation,and so on.To solve these problems,this paper proposes a novel algorithm named as the fast large deformation diffeomorphic landmarks matching based on stationary momentum （SM-FLDDLM）.The SM-FLDDLM algorithm estimates the velocity vector fields by means of the Lagrange stationary momentum vector and time-dependent multi-scale reproducing kernels,and then uses the determin-istic annealing mechanism based on regularization control parameters to search for the optimal momentum vectors,resulting in a final diffeomorphic deformation fields.The results of comparative experiments show that the SM-FLDDLM method is not only suitable for the large deformation diffeomorphic non-rigid transformation,with a better balance between accurate matching and smooth defor-mation,but also considerably reduces the time and space complexity.