Camera Location and Aperture Characterization Using the Transformation between a 2D Plane and the Image Captured by the Camera

Abstract

This paper uses as starting point the transformation matrix defined in the homogeneous space that associates the points of a 2D plane (that represents the model) with those of another 2D space (the image one), this transformation characterizing the camera capture process. This transformation (an homography from 2D to 2D) is coming from previous work and is used within the scope of the SimulFoot project. The final objective is to reconstruct a 3D model from TV soccer scenes, making it important to characterize the transformation between a 2D plane (the soccer field) and the camera image. We suppose the transformation (from image to field) is a conic projection whose center is S and projection plane is P in the model 3D space. We formulate two additional hypotheses related to the reference system of P: its origin is the orthogonal projection of S on P, and its first basis vector is parallel to the horizontal plane xOy. In fact, these conditions are often verified in soccer scenes since the camera is fixes on a tripod. In this communication, we give the camera location and aperture expressions on the only basis of the transformation matrix values.