Visual Navigation with a 2-pixel Camera---Possibilities and Limitations

TL;DR

This paper explores the theoretical possibilities and limitations of using a minimal two-pixel camera for visual navigation, introducing Eulerian and Lagrangian optical flow concepts and discussing their practical challenges.

Contribution

It introduces the concepts of Eulerian and Lagrangian optical flow sensing in the context of minimal camera systems and analyzes their potential and limitations for navigation.

Findings

Eulerian optical flow can provide reliable steering signals with a two-pixel camera.

Implementing Eulerian sensing is challenging due to hardware and computational constraints.

Lagrangian optical flow is standard but confounded by rotational motion effects.

Abstract

Borrowing terminology from fluid mechanics, the concepts of {\em Eulerian} and {\em Lagrangian optical flow sensing} are introduced. Eulerian optical flow sensing assumes that each photoreceptor in the camera or eye can instantaneously detect feature image points and their velocities on the retina. If this assumption is satisfied, even a two pixel imaging system can provide a moving agent with information about its movement along a corridor that is sufficiently precise as to be used as a robustly reliable steering signal. Implementing Eulerian optical flow sensing poses significant challenges, however. Lagrangian optical flow, on the other hand, tracks feature image points as they move on the retina. This form of visual sensing is the basis for many standard computer vision implementations, including Lukas-Kanade and Horn-Schunck. Lagrangian optical flow has its own challenges, not least of which is that it is badly confounded by rotational components of motion. Combined steering and sensing strategies for mitigating the effects of rotational motions are considered.