不依赖于连续性假设的Correspondence Manifold研究

Research on Correspondence Manifold without Continuous Constraint

图像匹配是计算机视觉中的一个基本问题,现有方法一般基于极几何模型,在使用中往往存在效率不高和对有些错误匹配点无法剔除的问题,为此研究了图像匹配中的模型问题.首先通过分析图像对应点映射关系的特点及其在联合图像空间中所形成曲面的几何直观,给出了不依赖于连续性假设的对应流形(CM)定义;然后通过分析CM及其视图所体现的映射关系特点和完备性,直观地给出了基于对应函数的CM表征方案,据此将CM的学习归结为一般的函数回归问题;最后通过理论分析和实验方式探讨了CM模型相比于经典的极几何模型的优势.理论分析结果表明,CM模型在图像匹配关系的描述中给出的是充分必要约束,而极几何模型给出的是必要非充分约束;实际图像匹配的实验结果表明,基于CM的错误匹配剔除方法的准确性和稳健性比基于极几何模型的方法略好,且候选匹配中错误越多,CM的速度优势越明显.

Image registration is a fundamental problem in computer vision,and the epipolar geometry constraint is the most popular model in it,which usually suffers from the efficiency problem and accuracy problem in applications.Therefore,this work focuses on the model designing problem in image registration.Firstly,by analyzing the characteristics of the mapping between corresponding points and the geometric properties of the surface formed by corresponding points in 4-dimentional joint image space,we introduced the concept of correspondence manifold（CM）.Compared with the available method,the advantage of this definition is independent of the continuity hypothesis.Secondly,the concept correspondence view（CV） is introduced to describe the CM after studying the characteristics and completeness of the point mapping in CM and its upward views,based on which the estimation of CM can be converted into a regression problem.Finally,we compared the CM with the commonly used model epipolar geometry constraint theoretically and experimentally.The theoretical result is that CM is a sufficient and necessary constraint in correspondence problem,but epipolar geometry is a necessary but insufficient one.The experimental results on real images show that CM-based mismatch removing method is more accurate,robust and efficient than that based on epipolar geometry constraint.