On the probabilistic multi-view geometry

Where the classic multi-view geometry is deterministic in assessing the geometric constraints and relationships between several images, there has recently been proposed a modern, probabilistic approach for multi-view geometry. This approach is essentially a novel direction in a branch of integral geometry that in the modern form studies integral transforms modeled with the Radon or Radon-like transforms. Where the classic way in geometric computer vision is, for instance, to take a point in an image and transfer it into another view, the probabilistic way is to replace the point coordinates by a 2D location distribution and transfer it into the other view by dualizing the uncertainty distribution of the multi-view geometric entity with respect to the underlying geometric incidence relation. Most importantly, the dual distributions open the way for a complete probabilistic treatment of multilinear geometric relations where everything is modeled with probability distributions. In the talk, we will present the mathematical construction of the approach, show some real examples, and discuss possible future research directions around this topic.