基于黎曼流形的图像投影配准算法

Projective Registration Algorithm Based on Riemannian Manifold

提出了基于黎曼流形的图像投影配准优化方法,根据投影变换的特点,用SL(3)表征目标的图像投影变换,研究SL(3)的几何结构,通过变分的方法求出了SL(3)上的测地线,给出相应的黎曼指数映射,设计了一种新的基于SL(3)群上黎曼分析的平面投影配准算法,分析了算法的优点,并对其收敛性做出了证明.模拟图像数据和真实图像序列测试的对比实验结果表明,本文算法在效率和精度上较现有文献中基于欧氏空间的图像投影配准算法有显著提高,优于基于李群的图像配准算法.

A novel image projective registration algorithm based on Riemannian manifold is presented. We use SL（3） group as projective parametric transformation to exploit the geometric structure of the underlying space and get the geodesics on SL（3） through variation method. Then, we define the new Riemannian exponential mapping. Finally, we develop a new image projective registration algorithm based on Riemannian analysis on SL（3）. In addition, we analyze the advantage of our method and give a direct proof of local quadratic convergence of the algorithm. Comparative experiments have demonstrated that this method makes a more significant improvement on efficiency and accuracy than the image projective registration algorithm based on vector space and outperforms the projective registration algorithm based on Lie group.