On the Modern Treatment of the Relationship between 3D scenes and 2D views and its applications in Computer Vision

The topic of representation, recovery and manipulation of three-dimensional (3D) scenes from two-dimensional (2D) images, provides a fertile ground for both theoretical questions related to the algebra and geometry of the problem and to practical applications such as Visual Recognition, Animation and View Synthesis, recovery of scene structure and camera ego-motion, object detection and tracking, multi-sensor alignment, etc.

The basic materials have been known since the turn of the century, but the full scope of the problem has been unraveled since 1992, first on the algebra of two views and then on the algebra of multiple views leading to a relatively mature understanding of what is known as ``multilinear matching constraints'', and the ``trilinear (trifocal) tensor'' of three or more views.

In the talk I will describe the modern treatment of the 3D-from-2D problem including the derivation of the tensor, its properties, tensor operators, Admissibility Constraints, Critical Configurations, the tensor embedding of the Fundamental matrix, and go briefly over the range of applications covering Visual Recognition, Interpretation of Motion, View Synthesis and Animation and 3D Reconstruction.