Limits in Perception

Essays in Honour of Maarten A. Bouman

A.J. van Doorn, W.A. van de Grind, J.J Koenderink

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000722963
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This book presents an analysis of limits in perception from the vantage point of the physicist, the engineer, the psychophysicist, the psychologist and the theorist. Limits in perception find their causal explanation at many logically and/or physically different levels. Some of the most fundamental bottlenecks are due to the quantum mechanical and atomistic structure of the microworld. Other simple constraints are due to the material constitution of sensory organs. For instance, the fact that the eye is predominantly composed of water limits both the optical quality and the available spectral window. The engineer uses knowledge on such limits to design equipment that optimizes human performance in daily life. Examples include room acoustics and visual displays. Psychophysicists and psychologists deal with limits on a quite different logical level. These limits constrain much of our perceptually guided behaviour. The book includes chapters on such topics as movement perception, binocular vision, illusory phenomena, language and perception, the perception of time. A few concluding chapters on fundamental limits imposed by information theoretical constraints on the coding and representation of sensed structure are included. Limits in Perception will be important reading material for scientists and/or engineers in the following fields: perception, experimental psychology, sensory biology, physics, neuroscience, human engineering, artificial intelligence, robotics, ophthalmology, audiology, psychonomics and ergonomics, remote sensing.

PART I

A PHYSICIST’S APPROACH TO LIMITS IN PERCEPTION

The “external senses”.
(Taken from Johann Amos Comenius: Orbis Sensualium Pictus, Chapter XLI. Nuremberg, 1658.)

We cannot perceive all physical events around us and this is clearly a fortunate circumstance. It would not be of any survival value to perceive the discrete and essentially chaotic microstructure of extended media and radiation fields. The transduction processes, which link our nervous systems to the rest of the world, are tuned to coherence, relations, structure. It is the space-time coincidence of quanta, not the single events, that forms the basis of vision. Brownian motion is a nuisance rather than a signal or information to the senses. The haphazard processes of the world limit the sensitivity of our perceptual systems at the low-energy end. Other limits are inherent in the delicate biological materials, which cannot endure strong radiation, too high or too low temperatures, high pressure or shocks. The phylogenetical process that structured our perceptual systems and our bodies has so to speak ‘internalized’ the properties of surrounding and biological materials. The spectral transmission and dispersion of water not only limits the spectral sensitivity of the eyes of aquatic animals but also of our, partly water-filled, bowl-like eyes. The mechanical properties of bone and membranes, muscles and cilia determine functional limits of the inner ear, cochlea, semicircular canals and the like. The physical properties of biological materials thus influence our limits in perception. Other limits are related to packing density or mosaic structures of receptor arrays, to the availability and stability-lability of pigment molecules (think of the four basic types of photoreceptors), the flow of air in the nose or saliva in the mouth. Physical limits in perception are numerous and often require much ingenuity to be uncovered and studied quantitatively. The physicist has developed most of the tools required to study such limiting factors and brings to this study her extensive, quantitative and well-tested theories on the structure of the world. The following four chapters on optical limits and the limits set by the quantum structure of light give the flavour of this approach. Obviously a full treatment would require four libraries instead of book chapters. Even writing about physical limits must have its physical limits, however.

1

DEVELOPMENT AND PRESENT STATUS OF THE QUANTUM CONCEPT IN VISUAL PSYCHOPHYSICS

PETER ZUIDEMA

GENERAL INTRODUCTION

After the introduction of the quantum character of light by Planck in 1900 the Utrecht physiologist Zwaardemaker was in 1909 probably the first to express the available values of the minimum energy for light perception in quanta. The quantum theory of vision was born. In his textbook on physiology (Zwaardemaker, 1921) he concluded that the threshold condition for the energy transfer from light flashes to the sensory system was fulfilled by a mere two quanta and that it was set by the end-organs.

In this chapter I will follow the further development of the quantum concept in vision as it is revealed particularly by psychophysical experiments with human observers. In an extensive review paper Bouman et al. (1984) place the quantum theoretical approach to visual perception in a more general context. Here I will evaluate the present status of the quantum concept and discuss how it has been and still is a fruitful guideline for research on the limits of visual perception at low luminance levels.

The statistical nature of light

In the thirties the consequences of the statistical nature of light were incorporated in studies of the visual system. Bowling Barnes and Czerny (1933) first raised the question of whether quantal fluctuations could be seen. From the irregular percept of a flashed multi-spot stimulus they concluded qualitatively that the statistical nature of light could indeed be seen.

Brumberg and Vavilov (1933) were the first to introduce a quantitative method for estimating the minimum threshold of perception. They assumed that for brief flashes the threshold of the visual system could be fixed at a value k quanta and that the distribution of the number of quanta per flash could be approximated by a Gaussian distribution. They then deduced the following relation between the probability of detection P, the threshold k and the mean number of quanta in the flash × (expressed as a factor with respect to k):

$\text{P}=0\text{.5}-0\text{.5}\sqrt{\left(\text{k/2}\right)}\left(1-\text{x}\right)/\sqrt{\text{x}}$

(1)

They were apparently the first to realize that owing to the statistical nature of light there is a continuous change of the probability of perception from 0 to 100% with increasing mean luminance of the light source. The slope of the relation between P and $\left(1-\text{x}\right)/\sqrt{\text{x}}\text{equals}0\text{.5}\sqrt{\text{k/2}}$, and it thus reveals the threshold k of the visual system. They verified relation (1) experimentally by asking subjects to indicate whether or not they saw the stimulus flash in a series with the same mean intensity.

Fig. 1. The probability of detection W as a function of (1–x)/√x. The straight line is the best fit with the theory (see text). (From Brumberg and Vavilov, 1933)

Figure 1 shows some of their results for light with a wavelength of 510 nm. From the slope of these curves they estimated the minimum threshold k to be 47, which was in agreement with values estimated by Barnes and Czerny (1933).

In the same paper Brumberg and Vavilov reported another experiment based upon the physical properties of light sources. They used a coherent light source and a Fresnel biprism in order to create two coherent light-spots. Most of the time the subject observed these spots as uncorrelated fluctuating spots, a behaviour which led Brumberg and Vavilov to the following conclusion: “Wenn Fresnel diese, sonst so leicht reproduzierbare Erscheinung, hätte beobachten können, so hätte natürlich das Schicksal der Lichttheorie eine ganz andere Wendung genommen!” (If Fresnel had been able to observe this so easily reproducible appearance, the theory of light would have followed a quite different course).

Unfortunately it was a long time before the work of the Russians Brumberg and Vavilov came to the knowledge of Western scientists. In the forties Hecht (1942) in New York and van der Velden (1944) in Utrecht used the same principle as that used by Brumberg and Vavilov. Both Hecht and van der Velden used the more appropriate cumulative Poisson distribution for the emission of quanta from an incandescent lamp in order to deduce the relation between the probability of seeing and the mean number of quanta supplied in a brief, small flash. However, van der Velden concluded that this so-called frequency-of-seeing (FOS) curve best fitted a threshold of two quanta (k = 2), whereas Hecht concluded that the threshold was set by the coincidence of a number of quanta varying between 5 and 7. They both defined “the” absolute threshold energy as the mean energy at the corneal level for which 60% of the flashes was observed.

Van der Velden explored a third way of estimating the number of quanta necessary for a percept. He calculated the probability of detecting a flash with a duration of T seconds on the assumption that the quantal effect remained effective only for τ seconds and that the coincidence of two such effects within these τ seconds was a sufficient condition for perception (the two-quanta hypothesis). He found that his experimental data for flashes with varying duration fitted the theoretical two-quanta curve (see Fig. 2). He proved the same with a similar experiment in the spatial domain. We shall now look more ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• List of Contributors
• Preface: Maarten Bouman and the Limits of Perception
• List of Publications
• List of Doctoral Dissertations Supervised
• Part 1: A Physicist’s Approach to the Limits in Perception
• Part 2: An Engineer’s Approach to the Limits in Perception
• Part 3: Psychophysical Approaches to the Limits in Perception
• Part 4: Psychological Approaches to the Limits in Perception
• Part 5: Theoretical Approaches to the Limits in Perception
• Subject Index