I am looking for projective invariant properties of quadrilaterals or even a group of quadrilaterals. Example:
In Multiple View Geometry in Computer Vision by Hartley and Zisserman I read that
Concurrency, collinearity, order of contact: intersection (1 pt contact); tangency (2 pt contact); inflections (3 pt contact with line); tangent discontinuities and cusps. cross ratio (ratio of ratio of lengths)
are invariant but I don't know how to use these properties as numeric values. I am not a mathematician so it is hard for me to understand how I could use for example concurrency or collinearity. Say I have an image that shows one quadrilateral and a second image that shows the same quadrilateral after a projective transformation. Can I somehow say e.g. the cross ratio of both quadrilaterals is 0.5 and so this is one invariant characteristic of the given quadrilateral?