Mach Bands: How Many Models are Possible? Recent Experiemental Findings and Modeling Attempts

Mach bands are illusory bright and dark bands seen where a luminance plateau meets a ramp, as in half-shadows or penumbras. A tremendous amount of work has been devoted to studying the psychophysics and the potential underlying neural circuitry concerning this phenomenon. A number of theoretical models have also been proposed, originating in the seminal studies of Mach himself. The present article reviews the main experimental findings after 1965 and the main recent theories of early vision that have attempted to discount for the effect. It is shown that the different theories share working principles and can be grouped in three clsses: a) feature-based; b) rule-based; and c) filling-in. In order to evaluate individual proposals it is necessary to consider them in the larger picture of visual science and to determine how they contribute to the understanding of vision in general.Air Force Office of Scientific Research (F49620-92-J-0334); Office of Naval Research (N00014-J-4100); COPPE/UFRJ, Brazi

Lateral inhibition: inherent recurrent processes in coherent optical propagation

Processes that are analogous to the neural process of recurrent lateral inhibition can be found in optical systems that consist of a shift-invariant system and a Fabry-Perot cavity. The properties of the optical recurrent system are derived and demonstrated by computer simulation. The simulation shows that optical lateral inhibition can be used to enhance the outline of an amplitude object and to make phase-only objects directly detectable and visible. The optical recurrent system is compared with frequency-plane spatial filtering. Requirements and practical limitations for the design of an optical recurrent system are also discussed

Analysis and Synthesis of the Dynamic Response of Retinal Neurons

theory of linear systems analysis is developed in a form directly applicable to the treatment of the Limulus retina. The dynamics of the retina may conveniently be characterized by means of a spatiotemporal transfer function, which summarizes the response of the system to moving sinusoidal gratings ( analysis ). The response of the retina to an arbitrary stimulus may then be calculated by addition of the response to suitably weighted sinusoidal stimuli ( synthesis ). Responses were obtained from the in-situ retina by means of extracellular recording of impulse activity in single optic nerve fibers. Test ommatidia were chosen in the interior of the retina, to avoid asymmetries introduced by the edge of the retina. Stimuli which varied in both space and time were produced under computer control on the screen of a display oscilloscope, and were conveyed to the Limulus eye by means of a fiber-optic taper. Transfer functions were measured using counterphase modulation of cosine gratings according to a sum-of-sinusoids temporal signal, a procedure equivalent to the use of moving gratings, for ommatidia with symmetrical receptive fields. By means of these transfer functions, the responses of the Limulus eye to visual stimuli moving at various velocities were predicted in a parameter-free Fourier synthesis calculation. There was good agreement between these predictions and the measured responses to these stimuli. A quantitative model for the dynamic, integrative action of the Limulus retina is developed, based on the original formulation for the steady state given by the Hartline- Ratliff equations. The model comprises an excitatory generator potential, and dynamic processes of self and lateral inhibition. An explicit expression for the spatiotemporal transfer function is obtained in terms of transfer functions for the generator potential, self-inhibitory, and lateral-inhibitory transductions, and spatial transforms of the lateral inhibitory kernel and the point-spread characteristic of the experimental and physiological optics. Explicit functional forms for these component transductions are adopted. The parameters which occur in these expressions serve to incorporate information about the subcellular physiology of retinal neurons into the quantitative description of the function of the retina as a whole. Procedures are described for the estimation of these parameters from empirical transfer function data. Transfer functions calculated from the model on the basis of parameters obtained with these procedures show good agreement with the corresponding empirical transfer functions. The parameter values obtained in this way are, in general, quite consistent with the results of many more direct (and frequently more invasive) measurements reported in the literature. In particular, the inhibitory kernel, as determined from our transfer function measurements, shows a small crater in the vicinity of the test-ommatidium. The dynamical model can be used to describe the response of the retina in the vicinity of its boundary, as well as in the interior. An analysis, based on the Wiener-Hopf technique, is given for the response of peripheral retinal neurons. The predictions derived from this theory were compared with experiment through the use of illumination patterns in which one half of the retina was kept in darkness, while the remaining half was presented with a moving stimulus. This procedure permitted the calibration of model transfer functions by means of methods appropriate only for interior ommatidia, while simulating the neural environment at the edge of a homogeneous retina. Significant differences between the responses to stimuli which moved toward and away from the simulated edge were observed experimentally, in good agreement with the predictions of the theory. Similar behavior was also observed at the actual anatomical boundary of the eye

Dynamics of Excitation and Inhibition in the Light-Adapted Limulus Eye in situ

The dynamics of spike discharge in eccentric cell axons from the in situ lateral eye of Limulus, under small sinusoidal modulation of light to which the eye is adapted, are described over two decades of light intensity and nearly three decades of frequency. Steady-state lateral inhibition coefficients, derived from the very low-frequency response, average 0.04 at three interommatidial spacings. The gain vs. frequency of a singly illuminated ommatidium is described closely from 0.004 to 0.4 cps by the linear transfer function s0.25; this function also accounts approximately for the measured phase leads, the small signal adaptation following small step inputs, and for Pinter's (1966) earlier low-frequency generator potential data. We suggest that such dynamics could arise from a summation in the generator potential of distributed intensity-dependent relaxation processes along the dendrite and rhabdome. Analysis of the dynamic responses of an eccentric cell with and without simultaneously modulated illumination of particular neighbors indicates an effect equivalent to self-inhibition acting via a first-order low-pass filter with time constant 0.42 sec, and steady-state gain near 4.0. The corresponding filters for lateral inhibition required time constants from 0.35 to 1 sec and effective finite delay of 50–90 msec

A Quantitative Description of the Dynamics of Excitation and Inhibition in the Eye of Limulus

By means of intracellular microelectrode techniques, we have measured the dynamics of the several processes which translate light stimulation into spike activity in the Limulus eye. The transductions from light to voltage and from voltage to spike rate, and the lateral inhibitory transduction from spike rate to voltage, we have characterized by transfer functions. We have checked the appropriateness of treating the eye as a system of linear transducers under our experimental conditions. The response of the eye to a large spot of light undergoing sine flicker has been correctly predicted