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_{1 D} (x; σ) = \frac{1}{\sqrt{2 π} σ} e x p (- \frac{x^{2}}{2 σ^{2}})

N-D Gaussian kernel:

G_{N D} (x; σ) = \frac{1}{(\sqrt{2 π} σ)^{N}} e x p (- \frac{x^{2}}{2 σ^{2}})