In many computer vision applications, one acquires images of planar surfaces from two different vantage points. One can use a projective transformation to map pixel coordinates associated with a particular planar surface from one image to another. The transformation, called a homography, can be represented by a unique, to within a scale factor, 3 × 3 matrix. One requires a different homography matrix, scale differences apart, for each planar surface whose two images one wants to relate. However, a collection of homography matrices forms a valid set only if the matrices satisfy consistency constraints implied by the rigidity of the motion and the scene. We explore what it means for a set of homography matrices to be compatible and show that two seemingly disparate definitions are in fact equivalent. Our insight lays the theoretical foundations upon which the derivation of various sets of homography consistency constraints can proceed.

在许多计算机视觉应用中，人们从两个不同的有利位置获取平面图像。可以使用投影变换将与特定平面相关联的像素坐标从一个图像映射到另一个图像。这种变换称为单应性，可以由3×3矩阵的比例因子唯一表示。对于每个要关联两个图像的平面，都需要一个不同的单应性矩阵，各个尺度的差异分开。但是，仅当单应性矩阵的集合满足运动和场景的刚性所隐含的一致性约束时，它才形成有效集合。我们探索了一组单应性矩阵兼容的含义，并证明了两个看似完全不同的定义实际上是等效的。