利用消失点列的射影不变量描述平面直线关系

消失点或消失直线蕴含了一组平行直线或一组平行平面的方向信息.同一平面上的所有直线对应的消失点共线于该平面的消失直线.消失线上的四点交比是射影不变量,该不变量与各点所对应的直线夹角存在内在联系.由此,本文提出了一种利用消失点列的射影不变量提取平面直线夹角的方法.在无需校准或3D重建的条件下,该方法可用于描述平面上直线间的相互关系,诸如平行、垂直、相交等.将本方法应用于真实图像的直线关系解释中,实验结果验证了方法的有效性.

Description of Planar Line Relationship by Projective Invariant of Vanishing Points

A vanishing point or a vanishing line indicates the direction information of a s et of parallel lines or a set of parallel planes.The vanishing points of all lines in the same plane are colinear at the vanishing line of the plane.The cross ratio of four points in the vanishing line is a projective invariant.It is related inherently with the intersection angles among the lines that the vanishing point s correspond.So,this paper presents an approach based on the projective invariants of vanishing points to calculate the intersection angles of planar lines.With out any calibration or 3D reconstruction,the approach can be used to describe the relationship between planar lines,such as parallelism, perpendicularity or intersection, and so on.Our method is applied to some real images for interpreting the relationship of lines,and the experimental results verify its efficacy.