摘要
根据嘉当分解定理得到非紧致李群SL(3,R)上的最短测地线方程,从而得到黎曼指数映射,在内蕴几何优化算法框架下,提出了一种基于黎曼流形二阶最小化的投影图像配准算法。由于考虑了投影变换参数的几何结构,所以与基于向量空间的高斯-牛顿配准算法相比,这种配准算法的综合性能有较大的提高;由于利用图像配准的具体特点,避免了赫森矩阵的烦琐计算,同时参数寻优沿测地线方向,所以与基于李群上的高斯-牛顿算法相比,这种配准算法对目标投影变形也有更好的适应性。从理论和实验两个层面综合分析了所提算法的有效性和优越性。
The Riemannian exponential mapping on SL（3,R） that represents the geodesic of the optimal transformation is obtained from the minimal geodesic equation based on Cartan decomposition theorem.A second-order minimization projective registration algorithm based on the Riemannian manifold within the intrinsic geometric optimization framework is proposed.Compared with the Gauss-Newton registration algorithm based on vector space,the general performance of our proposed algorithm shows much more improvement because of considering the geometric structure of the projective parameters.Compared with the Gauss-Newton algorithm based on the Lie group,our registration algorithm shows more adaptability to the projective warps because of utilizing the specific properties of the image registration to avoid calculating the Hessian matrix,and searching the optimum parameters along the shortest geodesic.Theoretical analysis and comparative experiments demonstrate the effectiveness and superiority of the proposed algorithm.
出处
《仪器仪表学报》
EI
CAS
CSCD
北大核心
2010年第6期1323-1329,共7页
Chinese Journal of Scientific Instrument
关键词
黎曼流形
图像配准
射影变换
几何优化
李群
Riemannian manifold
image registration
projective transformation
geometric optimization
Lie group
