图像匹配中具有仿射不变性特征的定量分析

A Quantificational Analysis of Affine Invariant Features for Image Matching

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,这可以用平面单应映射来表示,而目前大多特征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匹配算法的复杂度,还能保证迭代过程收敛的稳定性,然而并没有人对这一近似的可行性及合理性给出定量的讨论和分析。本文首先回顾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给出定量分析,通过椭圆曲线规范化方法推导出这一近似所造成定位误差的解析表达式,指出用仿射变换模型近似单应映射的合理性;然后用真实图像的实验结果验证了本文分析方法的正确性;最后给出相应的分析结果和结论。

There are geometrical deformations between corresponding feature windows on different images of the same scene surface, which can be represented by a homography on 2D plane. But most of the state-of-the-art matching methods approximate the homography by 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 convergence of 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 feature was proposed, the analytic expression of location error was deduced by normalization of conic method. Experimental results of real images demonstrate the feasibility and correctness of our method. Finally ,the paper gives some conclusions based on the above analysis both on theory and in practice.