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On the Theory of Bias Tuning in Event Cameras

David El-Chai Ben-Ezra, Daniel Brisk, Adar Tal

Abstract

This paper lays the foundation of a theory for bias tuning in neuromorphic cameras, a novel sensing technology also known as "event cameras". We begin by formulating the high-level effect of the sensitivity biases on the camera's event rate in mathematical terms. We then show that, as a corollary of the Poincare-Miranda theorem, the commonly used tuning principles of rate budgeting and polarity balancing lead to a unique configuration of the sensitivity biases. As a corollary, we show how by adopting these principles, the multi-variable bias-tuning problem reduces to a two-parameter problem that can be resolved experimentally.

On the Theory of Bias Tuning in Event Cameras

Abstract

This paper lays the foundation of a theory for bias tuning in neuromorphic cameras, a novel sensing technology also known as "event cameras". We begin by formulating the high-level effect of the sensitivity biases on the camera's event rate in mathematical terms. We then show that, as a corollary of the Poincare-Miranda theorem, the commonly used tuning principles of rate budgeting and polarity balancing lead to a unique configuration of the sensitivity biases. As a corollary, we show how by adopting these principles, the multi-variable bias-tuning problem reduces to a two-parameter problem that can be resolved experimentally.

Paper Structure

This paper contains 6 sections, 7 theorems, 23 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Event Camera Biases
  3. Sensitivity Bias Modeling
  4. The Existence and Uniqueness Theorem
  5. Determining Filter Biases: A Demonstration
  6. Conclusions

Key Result

Theorem 1

Given a scene, an event camera with standard behavior, and a choice of the filter biases, let $R_{P}(p,n)$ and $R_{N}(p,n)$ be the positive and negative event-rates as function of the sensitivity biases $p$ and $n$, respectively. Then, there exists a constant $K$ such that for every target event-rat

Figures (2)

  • Figure 5.1: Values of the sensitivity biases $p$ = bias_diff_on and $n$ = bias_diff_off as functions of the filter biases $l$ = bias_fo and $h$ = bias_hpf. For each sampled $(l,h)$, the sensitivity biases were tuned to maintain a polarity balanced event rate of approximately 100k events/sec.
  • Figure 5.2: Number of positive and negative events per period of the signal generated by the incandescent lamp, as a function of the filter biases.

Theorems & Definitions (16)

  • Theorem 1
  • Remark 2
  • Corollary 3
  • Remark 4
  • Corollary 5
  • Remark 6
  • Definition 7
  • Lemma 8
  • proof
  • Lemma 9
  • ...and 6 more