Mathematical biophysics of color vision

A neural mechanism is studied in which three primary receptors interact in such a manner that only a small region is in activity for a given colored stimulus. The similarity to the color triangle is noted. The introduction of an additional primary receptor may or may not change the dimensionality of sensation space in this mechanism. Problems of discrimination of color, absolute judgment of saturation, and hue are discussed.     

Mathematical biophysics of color vision II: Theory of color changes induced by the alternation of colors at various frequencies.

A model previously introduced to account for a number of phenomena of color vision is studied for the conditions in which the alternation of colors is periodic. The case of three primary receptors having no differences in their time constants is considered for the situations such as the temporal alternation of two primaries, a primary and a neighboring binary, a primary and white, a binary and white, etc. Using the same mathematical model which was used to account for the enhancement effect of interrupted illumination, it is found possible to account for observed changes in hue in a qualitative manner. A method is suggested for measuring the color changes quantitatively. This method is readily adapted for demonstration purposes. The model shows that there should be differences between “primaries” and “binaries” with respect to change in hue. In principle, therefore, comparison between theory and experiment should yield information regarding the physiological primaries. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18 (600) 1454.     

Color perception and the limits of color constancy

Summary A summary of colorimetry is given and the limits of color constancy mechanism under changing illuminations are discussed.     

Color vision: how the cortex represents color

Our understanding of how we see color has benefited from the long tradition of visual psychophysics. More recently, models and methods from psychophysics are guiding modern neuroimaging experiments on color vision. Combining the two techniques can lead to discoveries that neither can make alone.     

Color vision: color categories vary with language after all

An intriguing new study with Russian and English participants has provided compelling support for the view that 'categorical perception' of color categories is verbally mediated and varies with culture and language.     

Mathematical biophysics of growth

The rate of growth of a tissue is studied mathematically in its dependence on the metabolism of the cells. A high glycolytic coefficient, which facilitates cell division, as has been shown before, does in this way also increase indirectly the rate of growth of the tissue. There is however also a possible direct effect of glycolysis on the rate of growth, which is also studied analytically. Equations are derived, giving the total rate of growth of a tissue in its dependence on the glycolytic coefficient.     

On the biophysics of vision

A photochemical system is considered which is similar to that of S. Hecht but which includes an intermediate substance between visual purple and visual white. This intermediate is assumed to change the embrane voltage of the photoreceptors. A simple model is presented from which one may calculate the frequency of the impulses resulting from the application of light. It is found that this physicochemicai model enables one to account for a considerable number of physiological phenomena of vision. Among these are the light and dark adaptation phenomena. By introducing a simple assumption regarding spatial interaction one can account for some psychological phenomena such as the effect of intensity, light-dark ratio, shape, and area on the critical flicker frequency. A number of other phenomena are discussed in terms of the model. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. AF 18(600)-1454. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

Color categorization and color constancy in a neural network model of V4

We develop a neural network model that instantiates color constancy and color categorization in a single unified framework. Previous models achieve similar effects but ignore important biological constraints. Color constancy in this model is achieved by a new application of the double opponent cells found in the blobs of the visual cortex. Color categorization emerges naturally, as a consequence of processing chromatic stimuli as vectors in a four-dimensional color space. A computer simulation of this model is subjected to the classic psychophysical tests that first uncovered these phenomena, and its response matches psychophysical results very closely.     

Mathematical biophysics of cell division

The new fundamental equation, based on the principle of maximum energy exchange, is applied to the case of elongation and constriction of a cell. A simple case is treated as an illustration, and it is shown that the elongation curves thus obtained are of the same character as in the old theory.     

Mathematical biophysics of automobile driving

In a previous paper (Rashevsky, 1959,Bull. Math. Biophysics,21, 299–308) we derived an approximate expression for the maximal speed of driving in terms of the reaction time of the driver. In the present paper the possible effects of unevennesses of the pavement, of such distracting stimuli as road signs etc. on the reaction time are studied theoretically, using previous developments of the mathematical biophysics of the central nervous system. In this manner expressions are derived which determine the maximal safe speed in terms of road conditions and other distracting stimuli. Effects of those conditions on fatigue are also discussed.     

Physiological mechanisms of color constancy

Color constancy is the term given to the ability to recognize the color of objects correctly under different conditions of illumination. For this purpose the visual system must determine the character of the illumination, introduce a correction for it into the spectal composition of the light received from the object, and hence recreate the true color of its surface. Behavioral experiments on fish showed that they possess constant color vision of objects. Electrophysiological experiments on ganglion cells of the color type showed that the simplest mechanisms of correction for illumination are found at the retinal level. An investigation of model algorithms providing for color constancy showed thatthe presence of color vision makes it much easier to recognize the three-dimensional form of objects. This fact compels a reexamination of established views regarding the place and role of color vision in functions of the animal visual system as a whole.Institute for Problems in Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 7, No. 1, pp. 21–26, January–February, 1975.     

Color constancy in goldfish: the limits

Color constancy was investigated in behavioral training experiments on colors ranging from blue to yellow, located in the color space close to Planck's locus representing the main changes in natural skylight. Two individual goldfish were trained to peck at a test field of medium hue out of a series of 13-15 yellowish and bluish test fields presented simultaneously on a black background. During training the tank in which the fish were swimming freely was illuminated with white light. Correct choices were rewarded with food. During the tests differently saturated yellow or blue illumination was used. The degree of color constancy was inferred from the choice behavior under these illuminations. Perfect color constancy was found up to a certain degree of saturation of the colored light. Beyond this level test fields other than the training test field were chosen, indicating imperfect color constancy. Color constancy was quantified by applying color metrics on the basis of the goldfish cone sensitivity functions.     

Mathematical biophysics of some neural nets

Methods are considered for constructing neural nets of the McCulloch-Pitts type giving arbitrary time delays between stimuli and their responses. By introducing cycles of neurons, the problem is treated from the standpoint of economizing on the number of neurons required. A generalization is effect that will realize any unique temporal response pattern from a unique stimulus.     

Evolution of color vision.

Color vision is achieved by comparing the inputs from retinal photoreceptor neurons that differ in their wavelength sensitivity. Recent studies have elucidated the distribution and phylogeny of opsins, the family of light-sensitive molecules involved in this process. Interesting new findings suggest that animals have evolved a strategy to achieve specific sensitivity through the mutually exclusive expression of different opsin genes in photoreceptors.     

Color constancy: the role of low-level mechanisms

Color constancy (CC) is an important psychophysical phenomenon, which has been studied extensively. However, it is not clearly understood. This study presents a novel biological model for the contribution of low level mechanisms to CC. The model is based on two chromatic adaptation mechanisms in the color-coded retinal ganglion cells, 'local' and 'remote', which cause a 'curve-shifting' effect at each receptive field subregion. Simulations are employed for calculating the perceived image and measuring the degree of CC using both 'human-perception' and 'machine-vision' indices. The results indicate that the contribution of adaptations to CC is significant, robust and in agreement with experimental findings. The model is successful in performing CC under multiple chromatic illumination sources, a condition which mimics common natural environments.     

Mathematical biophysics of cell respiration II

The recent approximate method developed by N. Rashevsky in his bookMathematical Biophysics is shown to lead to results equivalent to those obtained in the preceding paper on cell respiration. An estimate is made of the value of the total diffusion resistance to lactic acid for unfertilizedArbacia eggs. Several more general reactions are treated to illustrate the effect of intermediate products. Expressions for the glycolytic coefficient are derived in terms of the parameters of the cell.