# PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility

## TL;DR

This paper classifies all minimal point-line problems in multi-view camera setups, revealing only 30 such problems with varying complexities, and provides tools for their detection and analysis.

## Contribution

It offers a complete classification of minimal point-line problems in multi-view geometry, including algebraic degrees and practical detection methods.

## Key findings

- Only 30 minimal problems exist for up to 6 cameras.
- The algebraic degrees quantify the problems' intrinsic difficulty.
- Several new minimal problems have small degrees suitable for practical applications.

## Abstract

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.