Reprints 101-120

Date:
1980-1992
Reference:
PP/CRI/M/1/6
Catalogue details

Licence: In copyright

Credit: Reprints 101-120. Source: Wellcome Collection.

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    Theory To approach this problem we need to use a computational approach. The underlying idea is that the nervous system is a very complex information-processing machine. While we cannot always say exactly how visual information is handled, we can be sure that once informa tion is lost in a pathway it cannot be recovered. But to assess whether information is lost or only concealed we need some theoretical results, and to this we must now turn. Viewed in this way, the retina is a device for sampling the visual image at intervals which, from the point of view of hyperacuity, might appear somewhat coarse. Is it possible to sample a continuous distribu tion and yet not lose any information? The mathematical answer to this is well known. Provided that the pattern does not change too abruptly in space the reconstruction can, in theory, be perfect. To make this more precise consider first the 1-dimensional (1-D) case. The condition imposed is that, if the pattern is analyzed into its Fourier components, they must be zero above a certain limiting spatial fre quency. For any general spatial pattern we can achieve this by passing it through a perfect low-pass filter (see Figure 2). This allows all spatial frequencies below the cutoff frequency of the filter to pass unaltered while reducing to zero all frequencies above this limit. The sampling theorem then says that for such a pattern we need only sample it at the (regular) intervals shown in Figure 3. That is, the sampling points must Figure 2 A perfect low-pass filter is shown on the left. Frequencies above / = V2 are blocked, whereas frequencies below are passed undistorted. The inverse Fourier trans form sine X is outlined on the right. The function sine has an infinite number of side lobes, not shown here, but indicated in Figure 3. Convolution of a 1-D pattern with the receptive field sine x is equivalent to filtering it with n(f).
    digitised image 1
    digitised image 2
    digitised image 3