Using perspective transformations in scene analysis

Abstract

This paper briefly reviews in a self-contained manner the perspective transformation governing 2-D images taken of a 3-D world. Using coordinates of points, direction cosines of lines on the image, or 3-D models of objects, relationships are developed that permit determination of the perspective transformation parameters in closed form, as well as the 3-D coordinates of objects. Contents. I, Introduction; I.1, 3-D Scene Analysis. II, The Perspective Transformation in 2-D. III, The Perspective Transformation in 3-D. IV, Properties of the 3-D Perspective Transformation; IV.1, Lines to Lines; IV.2, Vanishing Points. V, Image Coordinates to 3-D Coordinates; V.1, Camera Geometry; V.2, Vanishing Point to Camera Parameters; V.3, The Inverse Projective Transformation; V.4, Using the Inverse Perspective Transformation; V.5, Using the Perspective Transformation; V.6, Models. VI, Example; VI.1, Example 1; VI.2, Example 2. Acknowledgement. References.