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The receptive field of a visual neuron is the particular region in which a stimulus will modify the firing of that neuron. Retinal ganglion cells have a coaxial-shaped structure formed by the central excitatory and outer inhibitory regions. These regions respond oppositely to light. This shape can be mathematically modeled by a balanced Difference of Gaussian (DOG) function. In digital image processing, the DOG filter is used for detecting objects' edges.
Bacteriorhodopsin (bR) is a photosensitive protein which resembles the visual pigment rhodopsin. When bR is illuminated, it generates a positive transient photocurrent, and, when light is switched off, a negative transient photocurrent is produced. This peculiar behavior is similar to the response of ganglion receptive fields.
In this study, we fabricate a two-dimensional binarized DOG (b-DOG) filter, in which the central part mimics the excitatory part of the ganglion cell receptive fields, whereas the outer ring reproduces the effect observed in their outer inhibitory regions. This filter consists of photosensitive protein bR films and electrolyte solution that are sandwiched between ITO electrodes.
To analyze the spatial-temporal frequency sensitivity, we use moving sine wave gratings with different pitches with a controlled scanning speed. When the temporal frequency is kept constant, the spatial frequency sensitivity matched with the Fourier transform of the b-DOG function. On the other hand, when the spatial frequency does not vary, the temporal frequency sensitivity corresponded well with the Fourier transform of Difference of Gamma function. Difference of Gamma function is known as the impulse response of the visual nerve of animals. We separately analyze the independent spatial and temporal frequencies collected from the spatial-temporal characteristics of the filter. The spatial-temporal frequency characteristics of b-DOG filter are similar to those of the X-type retinal ganglion cells. However, unlike the retinal ganglion cell, the b-DOG filter is a perfect linear filter.
The analog image processing using this b-DOG filter is performed by scanning a standard test image. It is found that an edge can be detected just by scanning the image and plotting the zero-crossing point. With increasing input image size, the spatial frequency peak detected by the b-DOG filter shifts towards higher frequencies. Since there are only sharp edges where high spatial frequency components are present, the detected results of the analog filter are similar to that of the digital filter. Consequently, the phase difference between the input and output image is approximately the same for all pixels, and it agrees with the digital edge detection results.
Some illusion images are scanned on the b-DOG filter to verify the occurrence of the illusion similar to vision. The Hermann grid illusion generated with lower-order vision was observed. It is found that no luminance information is necessary for the Herman grid illusion, because this b-DOG filter does not extract image luminance.
The visual function elements similar to X-type retinal ganglion cells prepared in this study are useful to constructively understand the visual information processing mechanism of the organism.
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