PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility
This provides a foundational classification for multi-view geometry in computer vision, enabling more efficient 3D reconstruction and image matching.
The authors completely classified minimal problems for calibrated perspective cameras observing generic arrangements of points and lines, finding only 30 total minimal problems with specific bounds on cameras, points, and lines. They provided algebraic degrees for all problems, showing how difficulty grows with views and identifying several new practical problems with small degrees.
We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there are only 30 minimal problems in total, no problems exist for more than 6 cameras, for more than 5 points, and for more than 6 lines. We present a sequence of tests for detecting minimality starting with counting degrees of freedom and ending with full symbolic and numeric verification of representative examples. For all minimal problems discovered, we present their algebraic degrees, i.e. the number of solutions, which measure their intrinsic difficulty. It shows how exactly the difficulty of problems grows with the number of views. Importantly, several new minimal problems have small degrees that might be practical in image matching and 3D reconstruction.