The simple cell operator is inspired by the function of a neuron in the
primary visual cortex of monkeys. The operator acts as a line or edge
detector, by responding to lines or edges with a specific orientation and
spatial-frequency. The operator consists of a linear filtering step (Gabor
filters) followed by two nonlinearities: contrast normalisation and
thresholding.
Below you can experiment with the simple cell operator, using your own
images. Please, specify values of the parameters and an input image and
press the button 'submit image'. The image you selected is transfered to our
computer where the computations are carried out. After approximately 30
seconds the results will be shown in your browser.
In reference [7] you can
read more about the simple cell operator and its properties.
Here is a description of the parameters:
| Periodicity | specifies the period or wavelength of the grating pattern to be detected in the input image. The periodicity is given in pixels. |
| Bandwidth | specifies the spatial-frequency bandwidth of the filters in octaves. |
| Phase | specifies the phase-offset of the receptive field profile. A zero phase offset results in a symmetric receptive field profile while an offset of pi divided by two will result in an anti-symmetric receptive field profile. |
| Result | specifies the way the filtering results are presented. Currently there are two options: presenting the results of 8 filters with 8 orientations or present the superposition of those 8 orientations in a single output image. |
| Image file | The name (including the path)
of the GIF image file on your local computer on which the calculations
will be performed. The image must be square and its size should be a power
of two (not larger than 512x512). Press the 'Browse' button to upload one of your own files. |
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The primary visual cortex (also called striate cortex or V1, for visual area 1) consists of about 200 million neurons in total and receives its input from the lateral geniculate nucleus (LGN) [Hubel88]. About 80 percent of the cells are selective for orientation of the visual stimulus. Those cells that are selective for the same orientation are located near each other and form so-called orientation channels. Hubel and Wiesel classified the orientation selective cells in two classes: simple and complex cells. The classification criterion they used is based on the structure of the so-called receptive field of the cells, i.e. the region of the visual field in which a stimulus can evoke a change in the firing rate of the cell. Simple cells differ from complex cells in the fact that they show distinct excitatory and inhibitory regions in their receptive fields.
Though simple cells have a particular orientation and spatial frequency to which they are optimally tuned, i.e. their peak or preferred orientation and spatial frequency, they may also respond to stimuli with off-peak orientations or off-peak spatial frequencies. For off-peak stimuli, however, the cell response will be lower than the maximal cell response. How strong a cell will respond to an off-peak stimulus depends on the difference between the actual and the preferred orientation and spatial frequency and on the so-called orientation bandwidth and spatial frequency bandwidth of the cell. The orientation bandwidth of a cell is the range of stimulus orientations (measured in degrees) in which the cell response is at least half of its maximal response. Likewise, the spatial frequency bandwidth is defined as the range of spatial frequencies (measured in octaves) in which the cell response is at least half of its maximal response. One cannot speak about `the' spatial frequency or orientation bandwidth of simple cells. The half-response spatial frequency bandwidth of simple cells in monkey striate cortex was measured to vary between 0.6 and 2.5 octaves with a mean of 1.4 octaves [Albrecht79,Devalois82a]. Andrews and Pollen (1979) found simple cells in cat striate cortex with spatial frequency bandwidths varying from 1.1 to 1.9 octaves with a mean of 1.5 octaves. The orientation bandwidth of simple cells lies in the range from 10°-80° with a median of about 40° in monkey striate cortex [Devalois82b] and from 10°-56° in cat striate cortex (mean 28°) [Watkins74]. There appears to be a strong correlation between the average spatial frequency bandwidth and the preferred spatial frequency of a cell. On a logarithmic scale, the spatial frequency bandwidth decreases linearly with the preferred spatial frequency as was reported by Kulikowski and Bishop (1981) and DeValois et al. (1982a).
One can compute the response s of a simple cell modelled by a receptive field function g(x,y) to an input image with luminance distribution f(x,y) as follows:
First, an integral
In order to normalise the simple cell response with respect to the contrast of the input image, r is divided by the average gray level within the receptive field. The average a is computed using the Gaussian factor of the function g:
