Abstract—A common task in computer graphics is the mapping of digital high dynamic range images to low dynamic range display devices such as monitors and printers. This task is similar to the adaptation processes which occur in the human visual system. Physiological evidence suggests that adaptation already occurs in the photoreceptors, leading to a straightforward model that can be easily adapted for tone reproduction. The result is a fast and practical algorithm for general use with intuitive user parameters that control intensity, contrast, and level of chromatic adaptation, respectively. Index Terms—Tone reproduction, dynamic range reduction, photoreceptor physiology. 1

Abstract—We present a novel model for the mammalian retina and analyze its behavior. Our outer retina model performs bandpass spatiotemporal filtering. It is comprised of two reciprocally connected resistive grids that model the cone and horizontal cell syncytia. We show analytically that its sensitivity is proportional to the space-constant-ratio of the two grids while its half-max response is set by the local average intensity. Thus, this outer retina model realizes luminance adaptation. Our inner retina model performs high-pass temporal filtering. It features slow negative feedback whose strength is modulated by a locally computed measure of temporal contrast, modeling two kinds of amacrine cells, one narrow-field, the other wide-field. We show analytically that, when the input is spectrally pure, the corner-frequency tracks the input frequency. But when the input is broadband, the corner frequency is proportional to contrast. Thus, this inner retina model realizes temporal frequency adaptation as well as contrast gain control. We present CMOS circuit designs for our retina model in this paper as well. Experimental measurements from the fabricated chip, and validation of our analytical results, are presented in the companion paper [Zaghloul and Boahen (2004)].

ABSTRACT Identifying the basic module of enzymatic amplification as an irreversible cycle of messenger activation/ deactivation by a “push-pull ” pair of opposing enzymes, we analyze it in terms of gain, bandwidth, noise, and power consumption. The enzymatic signal transduction cascade is viewed as an information channel, the design of which is governed by the statistical properties of the input and the noise and dynamic range constraints of the output. With the example of vertebrate phototransduction cascade we demonstrate that all of the relevant engineering parameters are controlled by enzyme concentrations and, from functional considerations, derive bounds on the required protein numbers. Conversely, the ability of enzymatic networks to change their response characteristics by varying only the abundance of different enzymes illustrates how functional diversity may be built from nearly conserved molecular components.

abstract We determined the Ca2� dependence and time course of the modulation of ligand sensitivity in cGMP-gated currents of intact cone photoreceptors. In electro-permeabilized single cones isolated from striped bass, we measured outer segment current amplitude as a function of cGMP or 8Br-cGMP concentrations in the presence of various Ca2� levels. The dependence of current amplitude on nucleotide concentration is well described by the Hill function with values of K1/2, the ligand concentration that half-saturates current, that, in turn, depend on Ca2�. K1/2 increases as Ca2� rises, and this dependence is well described by a modified Michaelis-Menten function, indicating that modulation arises from the interaction of Ca2� with a single site without apparent cooperativity. CaKm, the Michaelis-Menten constant for Ca2� concentration is 857 � 68 nM for cGMP and 863 � 51 for 8Br-cGMP. In single cones under whole-cell voltage clamp, we simultaneously measured changes in membrane current and outer segment free Ca2� caused by sudden Ca2� sequestration attained by uncaging diazo-2. In the presence of constant 8Br-cGMP, 15 ��, Ca2� concentration decrease was complete within 50 ms and membrane conductance was enhanced 2.33 � 0.95-fold with a mean time to peak of 1.25 � 0.23 s. We developed a model that assumes channel modulation is a pseudo–first-order process kinetically limited by free Ca2�. Based on the experimentally measured changes in Ca2� concentration, model simulations match experimental data well by assigning the pseudo-first-order time constant a mean value of 0.40 � 0.14 s. Thus, Ca2�-dependent ligand modulation occurs over the concentration range of the normal, dark-adapted cone. Its time course suggests that its functional effects are important in the recovery of the cone photoresponse to a flash of light and during the response to steps of light, when cones adapt. key words:

A B ST RACT Visual pigment bleaching desensitizes rod photoreceptors greatly in excess of that due to loss of quantum catch. Whether this phenomenon also occurs in cone photoreceptors was investigated for isolated salamander red-sensitive cones. In parallel experiments, (a) visual pigment depletion by steps of bleaching light was measured by microspectrophotometry, and (b) flash sensitivity was measured by recording light-sensitive membrane current. In isolated cones, visual pigment bleaching permanently reduced flash sensitivity significantly below that due to the reduction in quantum catch, and there was little spontaneous recovery of visual pigment. The "extra " desensitization due to bleaching was most prominent up to bleaches of ~ 80 % visual pigment and reached a level ~ 1 log unit beyond that due to loss of quantum catch. At higher bleaches, the effect of loss of quantum catch became more important. Bleaching did not greatly reduce the maximum lightsuppressible membrane current. A 99 % reduction of the visual pigment permanently reduced the circulating current by only 30%. Visual pigment bleaching speeded up the kinetics of dim flash responses. All electrical effects of bleaching were reversed on exposure to 11-c/s retinal, which probably caused visual pigment regeneration. Light adaptation in photopic vision is known to involve significant visual pigment depletion. The present results indicate that cones operate with a maintained circulating current even after a large pigment depletion. It is shown how Weber/Fechner behavior may still be observed in photopic vision when the contributions of bleaching to adaptation are included.

. This paper presents an efficient, biologically-inspired early vision architecture, the dynamic retina, that is well-suited to highly active and responsive vision platforms. The dynamic retina exploits normally undesirable camera motion as a necessary step in detecting image contrast, by using dynamic receptive fields instead of traditional spatial-neighborhood operators. We analyze the continuous miniature "noise" movements made by active imaging systems, and show that they can be exploited to detect contrast. We then develop an appropriate photoreceptor response function, based on light-adaptation models for vertebrate receptors. Together, the movements and response function over time compute image contrast. The dynamic retina is also useful for motion analysis, since moving objects processed by the system leave a clear signature from which motion parameters can be extracted. Results from a number of experiments with real video sequences demonstrate the effectiveness of the system f...

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber’s Law. The current paper develops a new segmentation model based on the integration of both Weber’s Law and the celebrated Mumford–Shah segmentation model (Comm. Pure Applied Math., 42, pp. 577-685, 1989). Explained in details are issues concerning why the classical Mumford–Shah model lacks light adaptivity, and why its “weberized ” version can more faithfully reflect human vision’s superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein’s distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford–Shah model with Bose–Einstein noise. In particular, Ambrosio-Tortorelli’s Γ-convergence approximation theory is adapted (Boll. Un. Mat. Ital., 6-B, pp. 105-123,1992), and stable numerical algorithms are developed for the associated pair of nonlinear Euler-Lagrange PDEs.

A neuromorphic model for achromatic and chromatic surface representation of natural images

The dynamic range of the human visual system should be an important parameter in the design of high dynamic range (HDR) display devices. A good display should at least approximate this range. However, the literature reports a simultaneous dynamic range between 2 and 4 log units of luminance, leaving ambiguity as to what dynamic range HDR display devices should cater for. In this paper we present a sequence of psychophysical experiments, carried out with the aid of a high dynamic range display device, to determine the simultaneous dynamic range of the human visual system under full adaptation to a given background luminance. Our findings show that the human visual system is capable of distinguishing contrasts over a range of 3.7 log units under specific viewing conditions. Further, we show how the dynamic range is affected by stimulus duration, contrast of the stimulus as well as background illumination, thereby accounting for the differences reported in the literature and providing guidance for display design.

designs that model the properties of the outer