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A biologically inspired algorithm to deal with filter-overlap in retinal models
BMC Neuroscience volume 10, Article number: P126 (2009)
A multi-filter LN retinal model to simulate parallel processing by a population of retinal ganglion cells was proposed in  to test rank-order codes , a spike-latency based neural code. Dealing with filter-overlap in this model has been an area of concern [3, 4]. This is because data redundancy induced by over-sampling of a point in space affects the quantity of salient information during rapid information transmission . We propose a Filter-overlap Correction algorithm (FoCal) to deal with this problem of over-sampled data. The algorithm is based on the lateral inhibition technique  used by sensory neurons to deal with data redundancy , so that only salient information is transmitted through the optic-nerve bottleneck for rapid object detection and recognition.
where r is the response of a receptor unit, e is the excitation supplied by the external stimulus on the receptor, K is the coefficient of inhibitory influence of one receptor over the other, and r0 is the threshold frequency. Let Φ1 and Φ2 be two filters sampling an image at spatial locations (x, y) and (x+1, y) respectively on a digital raster, the respective coefficients of filtering c1 and c2 representing the spiking latency of the retinal ganglion cells corresponding to the filters. The filter overlap is written as O1,2 = O2,1 = ⟨Φ1, Φ2⟩. Let c1 > c2. The smaller coefficient is corrected for the effect of this overlap thus
where r2 simulates the overlap corrected response latency of the ganglion cell corresponding to Φ2. However, we introduce lateral inhibition post-spiking whereas it is pre-spiking in biology. Thus, we substitute the stimulus strength e2 with the corresponding coefficient of filtering c2. The threshold frequency is also irrelevant in our case. Further, we implement a winner-take-all mechanism in each iteration of the algorithm: the largest coefficient inhibits all others, the degree of inhibition being proportional to O, which corresponds to K. This reduces redundancy in the coefficient set and helps prioritise salient information, thus enabling rapid recovery of perceptually important information  in rank-order encoded images.
Results and conclusion
Using a data set of 65 images, we obtain the mean perceptually-important information recovery plot as shown (Figure 1). The error-bars show the standard deviation across the data set. We observe an increase of more than 20% in the total information recovered. Moreover, the rate of information recovery is much faster, with 80% recovery using the top 10% of the coefficients, which is a 30% increase compared to rank-order encoding without using FoCal. Based on these results, we argue that FoCal provides a general method for coping with non-orthogonal basis functions for current and future biologically inspired visual models.
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