# Distribution of degrees of freedom over structure and motion of rigid bodies

## TL;DR

This paper investigates the minimal data requirements for recovering structure and motion of rigid bodies from multiple frames, establishing the minimum points and frames needed and presenting solutions for different data configurations.

## Contribution

It determines the minimum number of points and frames required for structure and motion recovery and provides closed-form and linear solutions for these cases.

## Key findings

- 3 frames and 3 points are the minimum for recovery
- Linearization possible with 4 points or 4 frames
- No recovery from only 2 frames regardless of points

## Abstract

This paper is concerned with recovery of motion and structure parameters from multiframes under orthogonal projection when only points are traced. The main question is how many points and/or how many frames are necessary for the task. It is demonstrated that 3 frames and 3 points are the absolute minimum. Closed-form solution is presented. Furthermore, it is shown that the task may be linearized if either four points or four frames are available. It is demonstrated that no increase in the number of points may lead to recovery of structure and motion parameters from two frames only. It is shown that instead the increase in the number of points may support the task of tracing the points from frame to frame.