Convolution

Convolution $*$

r (t) = s (t) * h (t) = \int s (τ) h (t - τ) d τ

Convolution in Computational Neuroscience:

In image processing, the retina functions as linear filters (receptive fields) that involves in convolutions.
For example, a low-pass filter can blur the image, i.e. remove high-contrast and high spatial patterns.

Example - Gaussian kernel

1-D Gaussian kernel:

G_{1D} (x; \sigma)=\frac{1}{\sqrt {2 \pi} \sigma} \ exp (- \frac {x^2}{2 \sigma {#2} })

N-D Gaussian kernel:

G_{ND} (x; \sigma)=\frac{1}{ (\sqrt {2 \pi} \sigma) {#N} } \ exp (- \frac {x^2}{2 \sigma {#2} })