COMPUTATIONAL PROJECTIVE GEOMETRY

A computational formalism is given to computer vision problems involving collinearity and concurrency of points and lines on a 2-D plane from the viewpoint of projective geometry. The image plane is regarded as a 2-D projective space, and points and lines are represented by unit vectors consiting of homogeneous coordinates, called N-vectors. Fundamental notions of projective geometry such as collineations, correlations, polarities, poles, polars, and conis are reformulated as "computational" processes in terms of N-vectors. They are also given 3-D interpretations by regarding 2-D images as perspective projection of 3-D scenes. This N-vector formalism is further extended to infer 3-D translational motions from 2-D motion images. Stereo is also viewed as a special type of translational motion. Three computer vision applications are briefly discussed-interpretation of a rectangle, interpretation of a road, and interpretation of planar surface motion. © 1991.