鲁棒精确的点模式仿射变换参数估计和对应性匹配

Exact and Robust Parameter Estimation and Correspondence Determination for Two Point Patterns under an Affine Transform

仿射变换下的点模式匹配和参数估计是计算机视觉中的重要研究课题 ,其关键是寻找对仿射变换不变的不变量。与传统使用矩或交比作为不变量不同 ,我们考虑一种具有仿射不变性的并且正交唯一和尺度归一的坐标系———本征坐标系 ,证明了仿射变换前后的两个点模式经白化变换后映射为由一旋转变换联系的两个本征点模式 ;并在此基础上 ,我们开发了无须点对应性仅需点模式整体对应的仿射参数估计算法 ,该算法能在仅已知两个点模式整体对应的条件下精确估计它们所历经的仿射变换参数的同时 ,正确地确定它们的逐点对应性 ;通过融合进随机采样最小子集型鲁棒估计技术 ,我们进一步开发出仿射参数的无对应性鲁棒精确复原算法。实验表明该算法具有计算简便、快速、有效 ,参数估计精度高 ,鲁棒性好 。

Matching and parameter estimation of two point patterns under an affine transform is a very important research topic in the field of computer vision. The key step is to find some invariant features. As contrast to traditional techniques employing geometric moments or cross ratios, the orthogonal, unique and normalized coordinate systems, i.e. the eigen ones, which are invariant for an affine transform, are considered. Then, it is shown that after whitening transform, the two point patterns, one of which is the affine transform of the other, are respectively mapped to the eigen point patterns, one of which is the rotation transform of the other. Based on this, and alogorithm exactly estimating the affine parameters and correctly determining point correspondence under the condition that the only known thing is that the two point patterns are totally corresponding is developed. By fusing it with a robust estimation technique of the type of randomly sampling minimal subsets, we develop the robust version of the algorithm. The experiments have demonstrated that the performance of the algorithm is very satisfactory.\;