Model of visual adaptation and contrast detection GEORGE SPERLINGl BELL TELEPHONE LABORATOR1ES A three-component model of spatial other hand, shunting models of lateral vision is proposed, consisting of (1) a interaction intrinsically are models of feedback stage, (2) a feedforward stage, adaptation. (3) a threshold detector. The components :7' correspond to physiological processes; in I'~ Boundary Detection particular, the feedforward control signal o----l When viewing the boundary between I : corresponds to the "surround's" signal in I two adjacent, uniform fields of slightly the receptive fields ofretinal ganglion cells. FEEDFOAWAAD 1~ FEEDBACK different luminances, Os see an illusory The model makes appropriate qualitative ---_/ '---- light band near the boundary on the light predictions of" (1) a square-root law side and an illusory dark band near the ( ~Q a: QY2) for detection at low luminances, Fig. 1. Electronic analogue of shunting boundary on the darker side (Fig. 2). These (2) a Weber law (t:.Q a: Q) at high synaptic inhibition. The input current is H; illusory light-dark bands are called Mach luminances, (3) additivity of threshold the output voltage is G; the triangle bands because of their similarity to the masking effects at high background indicates an isolating transconductance. light-dark bands observed by Mach at luminances, (4) receptive fields that, in the The shunt path is R, which is controlled by discontinuities in luminance gradients dark, consist only of an excitatory center inhibition, I. Inhibition may arrive either (Ratliff, 1965). and that, in the light, also contain via feedforward or feedback paths; I Because of Mach bands, the apparent inhibitory surrounds, (5) the variation of increases the conductance (diminishes R) contrast between two fields ofnearly equal spatial characteristics of receptive fields of the shunt path proportionally to its own luminance is greatest at the boundary depending on the temporal characteristic strength. between them. Thus, in searching for a of the test stimulus used to measure them, liminal test field superimposed on a (6) the subjective appearance of Mach Eccles, and Fatt (1955) first established masking field, it usually is the boundary of bands, (7) sine-wave contrast-threshold the basic mechanism of neural inhibition. the test that the 0 detects (Lamar et al, transfer functions, (8) the frequent failure This mechanism may be called shunting 1947). For a boundary to be detected, it is of disk-detection experiments to inhibition (Furman, 1965) because assumed that the excitation in the light demonstrate inhibitory surrounds, and inhibitory signals cause a portion of the band (plus-zone, z+) must differ by a (9) various second-order threshold effects, excitatory signals to be diverted, or criterion amount from the excitation in the such as reduced spatial integration for shunted. An electronic analog of shunting z+ long-duration stimuli, reduced temporal inhibition is an RC·stage in which the value ------/--­ integration for large-area stimuli, and the of R is decreased by inhibition (Fig. 1). At ~~ increased effect of background luminance high levels of inhibitory input, the net Q on the detection of large-area stimuli. effect is analagous to arithmetic division of z Predictions areimproved by assuming there excitation by inhibition. exist various sizes of receptive fields that .r:": determine thresholds jointly. Lateral Interaction -----~/// All visual systems of more than one Q I. INTRODUCTION receptor exhibit phenomena of lateral l- This article describes a shunting interaction; namely, the outputs of the feedback-plus-feedforward model of visual adjacent receptors combine at various contrast detection." Shunting networks levels in the nervous system. A priori, at a derive from neurophysiology, where they particular level, lateral interaction may be describe a kind of synaptic inhibitory characterized as feedback or feedforward, process. Though nonlinear, the and as shunting or subtractive (Furman, mathematical analysis of the steady-state 1965), although these categories are not response of the shunting networks is exhaustive. For example, the lateral basically simple. On the other hand, human interaction in the eye of Limulus has been contrast detection is basically complex, characterized as feedback and subtractive probably involving several different (Hartline & Ratliff, 1958).3 Fig. 2. Mach bands at a boundary (a), mechanisms. Whereas a complete model for Various subtractive models of lateral and at the ends of gradients (b) and (c). contrast would be correspondingly interaction have been proposed for vision The anaular curves indicate the stimulus complex, the model proposed here is (e.g., Schade, 1956; von Bekesy, 1960; retinal illuminance £(x) as a function of x; neither complex nor exact. The Lowry & DePalma, 1961; Rodieck, 1965; the short horizontal lines indicate Q(x)=O. justification for proposing it is that, for a Nachmias, 1968). A desirable feature of The smooth curves are G(x), the model of its simplicity, it has remarkable these models is that, because they are predictions by the model of the retinal correspondences to vision. linear, the full power of linear analysis response to £(x). G(x) corresponds applies. Unfortunately, linear models do approximately to the subjective appearance Shunting Inhibition not handle the problem oflight adaptation, of the stimulus. In (a), the light band z+ Fatt and Katz (1953) and Coombs, except by ad hoc mechanisms. On the and the dark band z_ are indicated. Perception &Psychophysics, 1970, Vol. 8 (3) 143 jDIAM(WH Fig. 3. Example of an excitatory >1 weightinS function WJI(r) and of an r- --, inhibitory weighting functiOR WI[r]. Both I I functions are two-dimensional normal I distributions-; 3. These functions I or/ou = are used in all numerical examples of this article; The indicated effective diameters of wH and WI are 2OUv'2 aad 201..fi, respectively. ------DIAM (WI> ------ Equation 3 arises from the circuit of Fig. 1. which describes shunting inhibition. For H dark band (minus-zone, z_). An expression are not interested in these details may skip and I constant in time, Eq.3 reduces to for the difference in excitation between z+ to Section 111. G = R• H/(I +kl), For convenience, the and z_ is derived from the feedforward parameter R is absorbed into G so that-for shunting model. lIa. Basic Assumptions steady inputs-Eq. 3 reduces to the form (1) Excitation: At each point in space II. FEEDFORWARD MODEL x,y and at each instant in time t, excitation H (3a) Outline H is given by the weighted sum of retinal G=I+k1' Let ~(x,y), the illuminance distribution illuminance ~ in a spatial and temporal on the retina, be the input to the model. region around x,y,t, namely It is interesting to note that a similar The input undergoes a transformation equation for lateral interaction originally (feedforward neural field) so that H(x,y,t) = ~ (x',,/,t') wH was proposed by Mach one hundred years corresponding to each point x,y there f {[ ago (Mach, 1868; Ratliff, 1965).4 ultimately is an output G(x,y). The output (4) Prior adaptation. The adaptation G is composed of an excitation term H and (x-x',y-y'}vH (t-t') dx' dy' dt'. mechanism proposed by Fuortes and an inhibition term I. The excitation term H Hodgkin (1964) consists of a cascade of n is given by a weighted sum ofilluminances (l) RC stages in each of which the R is falling on the excitatory area around x,y; controlled by shunting feedback from the inhibition is given by the weighted sum of Here WH represents the excitatory final stage. This n-stage feedback system is illuminance falling on a larger, concentric area-weighting function, VH represents the described by equations of the form inhibitory area(Fig. 3). Inhibition interacts excitatory temporal-weighting function, with excitation by feedforward shunting to and R represents integration over the area produce the net output G. A detector scans of the retina. G(x,y) to find the point z+ where G(z) is a By defining the symbol * to denote the maximum and the point z_ where G(z) is a operation of convolution, Eq. 1 can be j=I,···,n minimum. When .lG, rewritten as where X = t/RC and Yo = ~ (Sperling & .lG = max G(z) - min G(z) H(x,y,t)= ~x,y,t) * wH(x,y) * vH(t). Sondhi, 1968). For constant input i', the output Y is defined by = G(z+) - G(z_), (Ia) (4) exceeds a threshold criterion e, detection is The definition of H by an integral is an signaled. approximation to a sum that involves an In the case of prior adaptation, the ~ of the receptor elements; because these are Eqs, 1 and 2 is replaced by Y of Eq, 4. Adaptation numerous, the approximation is good. (5) Boundary detection. The detector As a complication, the input to the (2) Inhibition. Inhibition I(x,y,t) is given locates the point z; with maximum output feedforward neural field may not be ~(x,y) by in the light band near the boundary and directly, but some transformation of ~. the point z_ with minimum output in the There are good reasons for supposing that I(x,y,t)= ~(x,y,t) ... wI(X,y) * vIet) (2) dark band of the boundary. It forms the the H and I terms of the feedforward field difference .lG = G(z+) - G(z_), adds a are not composed simply of weighted sums where WI and VI are the inhibitory random variable N to this difference, and of ~, but that a feedback transformation area-weighting and temporal-weighting produces a detection response if (adaptation) precedes the feedforward functions. Figure 3 illustrates the wH and .lG + N;;;' e. The criterion E may vary from transformation (Sperling' & Sondhi, 1968). WI that are used in the examples of this experiment to experiment but is assumed If the initial adaptation is taken to be the article.