Matching Constraints and the Joint Image

This paper studies the geometry of multi-image perspective projection and the matching constraints that this induces on image measurements. The combined image projections define a 3D joint image subspace of the space of combined homogeneous image coordinates. This is a complete projective replica of the 3D world in image coordinates. Its location encodes the imaging geometry and is captured by the 4 index joint image Grassmannian tensor. Projective reconstruction in the joint image is a canonical process requiring only a simple rescaling of image coordinates. Reconstruction in world coordinates amounts to a choice of basis in the joint image. The matching constraints are multilinear tensorial equations in image coordinates that tell whether tokens in different images could be the projections of a single world token. For 2D images of 3D points there are exactly three basic types: the epipolar constraint, Shashua’s trilinear one, and a new quadrilinear 4 image one. For images of line...

• Type: Conference
• Year: 1995
• Where: ICCV
• Authors: Bill Triggs
• Keywords: Computer Vision, ICCV 1995, Image, Image Coordinates, Joint Image