Gaussian Function

--- https://en.wikipedia.org/wiki/Gaussian_blur

aka bell curve

definition

G^ss p = --ss\tt/ -- [:p2 -- 2ss2], where

• G^ss is the gaussian function with standard deviation ss
• p = (x ...) is a point

note :p2 == :["abs" p]2 and therefore G^ss (x ...) == G^ss ("abs" x)

note

the gaussian function above can be broken down as follows:

x. --[x2] is the basic shape of the gaussian function

x. --[x2 -- 2ss2] stretches the gaussian function horizontally so it has a standard deviation ss

x. --ss\tt/ -- [x2 -- 2ss2] stretches the gaussian function vertically so it integrates to 1, making it a probability density function

p. --ss\tt/ -- [:p2 -- 2ss2] extends the gaussian function to take euclidean vectors as input while still returning a real number

--- me and https://youtu.be/cy8r7WSuT1I?t=130