Notes

Making a Square Wave with Sinusoids

Fourier theorem tells us that the function at the bottom of the image (luminance as a function of space) can be approximated by summation of sinusoids. Square Waves in 2-D: by adding sine waves components we can obtain a square waves.

Responses of a Ganglion Cell to Edges

By making the assumption that the system is linear and that the receptive field is approximated by a "Mexican hat" we can see estimate the response of ganglion cells to edges. We can image an edge that is moving over the receptive field, we notice that the maximum response is obtained when the edge is bordering the on-center such that it covers the off-center and leaves the on-center fully illuminated. As soon as the edge covers the on-center, the response drops.

Chevreuil Illusion - Mach Bands If you look at the edges of the image to the right, you should notice that the contour to the edge appears brighter on the left than on the right. These slight increases/decreases are due to the shape (center/surround) of the ganglion cells receptive fields.

Sensitivity for Different Spatial Frequencies Spatial Frequency Tuning of a Ganglion Cell This represents again the responses to different spatial frequencies of the single ganglion cells receptive fields.

Spatial Frequency Sensitivity Curve of a Whole Brain Same kind of slide as before, but rather than being for a single cell, represents the overall spatial frequency sensitivity curve for a whole observer (person). To measure this kind of curve, you present on a screen a sinusoidal wave, then you make it flatter and flatter until it becomes undetectable (no more contrast respect to the background). However, if the frequency is increased over a certain frequency, the brain is incapable of detecting them and you will end up seeing it as a continuous stream rather than single sinusoidal waves.

Contrast Sensitivity Varies with Spatial Frequency On the x-axis the frequency of the sinusoidal waves increases, while on the y-axis the contrast decreases. The contrast sensitivity function represents what is in principle visible for an observer.

One Interpretation of the Contrast Sensitivity Curve

This picture shows spatial frequency against contrast sensitivity in a whole observer (Macaque monkey in this case). The curves without datapoints are the contrast sensitivity curves of a cortical cell/neuron, and what can be seen is that the cells are highly selective for spatial frequency. So, each individual cell sees only a small range of spatial frequency. Hence, the overall contrast sensitivity of an observer derives from the sum of many individual cells contrast sensitivities.