A Vision-Based Closed-Form Solution for Measuring the Rotation Rate of an Object by Tracking One Point

TL;DR

This paper introduces a closed-form, vision-based method to measure an object's rotation rate by tracking a single point, independent of object shape or prior scene knowledge, suitable for real-time processing.

Contribution

It provides an analytical solution for rotation rate measurement using only one tracked point under orthographic projection, without needing object shape or scene information.

Findings

Method accurately estimates rotation rate in simulations

Effective on real video data

Can distinguish points from different rigid bodies

Abstract

We demonstrate that, under orthographic projection and with a camera fixated on a point located on a rigid body, the rotation of that body can be analytically obtained by tracking only one other feature in the image. With some exceptions, any tracked point, regardless of its location on the body, yields the same value of the instantaneous rotation rate. The proposed method is independent of the shape of the 3D object and does not require a priori knowledge about the scene. This algorithm is suited for parallel processing and can achieve segmentation of the scene by distinguishing points that do not belong to the same rigid body, simply because they do not produce the same value of the rotation. This paper presents an analytical derivation, simulation results, and results from real video data.