基于角点检测及几何约束的仿射变换参数估计

Parametric Estimation of Affine Transformations Based on Corner Detection and the Geometric Constraints

本文针对机器视觉现有方法对目标的姿态判定及不同视角间仿射变换参数估计存在的对应特征点提取困难、计算复杂度高等不足,提出一种新的算法。算法引入角点和凸壳等概念,检测目标图像和模板图像的角点,分别组成特征点集并构造点集凸壳,由计算几何原理可知凸壳上的点在仿射变换前后具有对应性。当凸壳内部有内点时,分别对凸壳上的点、凸壳内部的点、凸壳的形心的横坐标和纵坐标构建方程,利用此方程组求解得到仿射变换6个未知参数;当凸壳内部无内点时,采用多项式理论再构建一组二次方程,以达到求解仿射变换参数的目的。实验结果表明,本方法不需要搜索特征点集间一一对应关系,只需点群子集间整体对应,估计得到的仿射变换参数精确,计算复杂度远低于基于区域的同类算法。

An improved algorithm of estimating the affine transformation aligning a known 2D shape and its distorted observation is proposed in this paper,as existing algorithms have difficulty of finding correspondences and the high computational complexity in solving this kind of registration problem.The concept of corner points and the convex hull of point set are introduced to set up a group of leaner equations in the proposed approach.The corner points of the template image and observation are detected firstly,then the feature point sets are determined and the convex hulls are constructed.It is a principle in computational geometry that the convex hulls are correspondent before and after the affine transformation.An affine transformation includes six unknown parameters,which need six equations to solve the six parameters.When there are interior points inside the convex hull,the points on convex hull,the centroid of the hull and the interior points can be used to construct six equations with the horizontal and vertical coordinates.When there are no interior points inside convex hull,a pair of extra quadratic equations should be built with horizontal and vertical coordinates using the polynomial theory to solve the six parameters.The main advantage of the proposed algorithm is that only the correspondence of point sets instead of the one-to-one correspondence of feature points between the template image and observation are needed to be found.Experimental results show that the proposed algorithm is more accurate in parametric estimation,and its computational complexity is much lower than that of the region-based approach.