From filters to features:Scale-space analysis of edge and blur coding in human vision

To make vision possible, the visual nervous system must represent the most informative features in the light pattern captured by the eye. Here we use Gaussian scale-space theory to derive a multiscale model for edge analysis and we test it in perceptual experiments. At all scales there are two stages of spatial filtering. An odd-symmetric, Gaussian first derivative filter provides the input to a Gaussian second derivative filter. Crucially, the output at each stage is half-wave rectified before feeding forward to the next. This creates nonlinear channels selectively responsive to one edge polarity while suppressing spurious or "phantom" edges. The two stages have properties analogous to simple and complex cells in the visual cortex. Edges are found as peaks in a scale-space response map that is the output of the second stage. The position and scale of the peak response identify the location and blur of the edge. The model predicts remarkably accurately our results on human perception of edge location and blur for a wide range of luminance profiles, including the surprising finding that blurred edges look sharper when their length is made shorter. The model enhances our understanding of early vision by integrating computational, physiological, and psychophysical approaches. © ARVO

Irregularity in the cortical spike code : noise or information?

How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1) and extrastriate cortex (MT) of awake, behaving macaque monkey, and compared them to analytical predictions. We measured two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized Coefficient of Variation (C_v) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., C_v ≈ 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and-fire neuron (Knight, 1972). Both this and related models predicted very low firing variability ( C_v ≪ 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the C_v and the variability in the number of spikes were both very low, in agreement with the integrate-and- fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley- like currents (I_(Na) and very strong I_(DR) were placed on the distal basal dendrites. Now the simulated neuron acted more as a millisecond-resolution detector of dendritic spike coincidences than as a temporal integrator, thereby increasing its bandwidth by an order of magnitude above traditional estimates. This hypothetical submillisecond coincidence detection mainly uses the cell's capacitive localization of very transient signals in thin dendrites. For millisecond-level events, different dendrites in the cell are electrically isolated from one another by dendritic capacitance, so that the cell can contain many independent computational units. This de-coupling occurs because charge takes time to equilibrate inside the cell, and can occur even in the presence of long membrane time constants. Simple approximations using cellular parameters (e.g., R_m, C_m, R_i, G_(Na) etc) can predict many effects of dendritic spiking, as confirmed by detailed compartmental simulations of the reconstructed pyramidal cell. Such expressions allow the extension of simulated results to untested parameter regimes. Coincidence-detection can occur by two methods: (1) Fast charge-equilization inside dendritic branches creates submillisecond EPSPs in those dendrites, so that individual branches can spike in response to coincidences among those fast EPSP's, (2) strong delayed-rectifier currents in dendrites allow the soma to fire only upon the submillisecond coincidence of two or more dendritic spikes. Such fast EPSPs and dendritic spikes produce somatic voltages consistent with intracellular observations. A simple measure of coincidence-detection "effectiveness" shows that cells containing these hypothetical dendritic spikes are far more sensitive to coincident EPSPs than to temporally separated ones, and suggest a conceptual mechanism for fast, parallel, nonlinear computations inside single cells. If a simplified model neuron acts as a coincidence-detector of single pulses, networks of such neurons can solve a simple but important perceptual problem-the "binding problem" -more easily and flexibly than traditional neurons can. In a simple toy model, different classes of coincidence-detecting neurons respond to different aspects of simple visual stimuli, for example shape and motion. The task of the population of neurons is to respond to multiple simultaneous stimuli while still identifying those neurons which respond to a particular stimulus. Because a coincidence-detecting neuron's output spike train retains some very precise information about the timing of its input spikes, all neurons which respond the same stimulus will produce output spikes with an above-random chance of coincidence, and hence will be easily distinguished from neurons responding to a different stimulus. This scheme uses the traditional average-rate code to represent each stimulus separately, while using precise single-spike times to multiplex information about the relation of different aspects of the stimuli to each other: In this manner the model's highly irregular spiking actually reflects information rather than noise.</p