Efficient algorithm for online Variance over image batches

Question:

I have a large amount of images and want to calculate the variance (of each channel) across all of them.
I’m having problem finding an efficient algorithm / setup for that.

I read on of the Welford’s online algorithm but it is way to slow as it is not vectorized in this form accross a single image or a batch of images.
So I’m wondering how to improve the speed of it to either use vectorization or making use of inbuilt variance algorithms.

Asked By: Daraan

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Source

Answers:

These are the two functions needed to update/combine the mean and variances of two batches. Both functions can be used with vectors (the 3 color channels) and the mean and variance can be acquired from inbuilt methods like batch.var().

Equations taken from: https://notmatthancock.github.io/2017/03/23/simple-batch-stat-updates.html

   
# m amount of samples (or pixels) over all previous badges
# n amount of samples in new incoming batch
# mu1 previous mean
# mu2 mean of current batch
# v1 previous variance
# v2 variance of current batch

def combine_means(mu1, mu2, m, n):
    """
    Updates old mean mu1 from m samples with mean mu2 of n samples.
    Returns the mean of the m+n samples.
    """
    return (m / (m+n)) * mu1 + (n/(m+n))*mu2

def combine_vars(v1, v2, mu1, mu2, m, n):
    """
    Updates old variance v1 from m samples with variance v2 of n samples.
    Returns the variance of the m+n samples.
    """
    return (m/(m+n)) *v1 + n/(m+n) *v2 + m*n/(m+n)**2 * (mu1 - mu2)**2
Answered By: Daraan