Coordinate-Free Carlsson-Weinshall Duality and Relative Multi-View Geometry

Matthew Trager, Martial Hebert, Jean Ponce; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 225-233

We present a coordinate-free description of Carlsson-Weinshall duality between scene points and camera pinholes and use it to derive a new characterization of primal/dual multi-view geometry. In the case of three views, a particular set of reduced trilinearities provide a novel parameterization of camera geometry that, unlike existing ones, is subject only to very simple internal constraints. These trilinearities lead to new "quasi-linear" algorithms for primal and dual structure from motion. We include some preliminary experiments with real and synthetic data.