Find the function in: MachineVision.rpy/ImageNet_pkg/Common/INCALC/noise

This function is used to generate the Gaussian and Uniform distribution random numbers.

Gaussian distribution, is a continuous probability distribution that has symmetric distribution about its mean.The graph of this probability distribution is look like a bell-shaped, and is known as the Gaussian function or bell curve .Where parameter μ is the mean (location of the peak) and σ 2 is the variance (the measure of the width of the distribution). The distribution with μ = 0 and σ 2 = 1 is called the standard normal.

Effect of the σ 2 on the width of distribution. Source: Wikipedia

About 68% of values drawn from a normal distribution are within one standard deviation σ > 0 away from the mean μ; about 95% of the values are within two standard deviations and about 99.7% lie within three standard deviations. This is known as the 68-95-99.7 rule, or the empirical rule, or the 3-sigma rule.

Normal distributions accounts for about 68% of the set (dark blue), while two standard deviations from the mean (medium and dark blue) account for about 95%, and three standard deviations (light, medium, and dark blue) account for about 99.7%. Source: Wikipedia

The result of RandNumber function for about 10,000 iteration with μ = 0 and σ 2 = 5 is quite familiar with the bell curve as shown in the figure.

Gaussian Number distributions of 'noise' Function

let X and Y will be unit normal random variables (mean = 0 and variance = 1), and these can be easily modified for different mean and variance.

X' = mean + sqrt(variance) * X and Y' = mean + sqrt(variance) * Y