一种评价仿射不变性特征定位误差的新方法

A Novel Method for Evaluating the Location Error of Affine Invariant Features

特征点匹配是计算机视觉中的一个基本问题。不同视点图像中相应特征点邻域窗口之间存在几何上的透视畸变,这可用平面单应映射来表示,而目前大多匹配算法将该映射用仿射变换模型来近似,即用具有仿射不变性的特征进行图像的匹配。仿射变换的线性特点不仅能降低算法复杂度,还能保证迭代过程收敛的稳定性,然而并没有人对该近似的可行性及如何减小近似误差给出定量分析。本文首先回顾了各种几何层次上的特征点匹配策略,重点针对具有仿射不变性特征点的定位误差进行研究和定量分析,通过本文提出的椭圆曲线规范化法推导出该近似所造成相应特征点定位误差的解析表达;然后用真实图像的实验结果验证了本文分析方法的必要性和正确性;最后给出相应的分析结果和结论,并指出提高大基线图像特征点匹配精度的相应措施。

Feature matching is a fundamental problem in computer vision. There are geometrical deformations, named plane homography, between corresponding feature windows on different images of the same patch on scene surface. But most of the state-of-the-art matching schemes approximate the homography with an affine transformation model, namely affine invariant features. The linear character of affine model not only reduces the complication of matching process, but ensures a good and stable convergence of the unmanageable iteration. However, there are no quantificational discussions about this approximation by far. In this paper, an overview of invariant features under different geometric groups was given first, and then a quantificational analysis of affine invariant features was proposed. The analytic expression of location error was deduced by our novel method, named normalization of conic equations. Experimental results of real images demonstrate the correctness and necessity of our method. Finally, some valuable conclusions and suggestions based on the above analysis are deduced both on theory and in practice.