Running Stats

Computing data statistics.

`WelfordStatistics`

Compute Welford statistics iteratively.

The Welford algorithm is used to compute the mean and variance of an array iteratively. Based on the implementation from: https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm

`finalize()`

Finalize the Welford statistics.

Returns:

Type	Description
`tuple or numpy arrays`	Final mean and standard deviation.

`update(array, sample_idx)`

Update the Welford statistics.

Parameters:

Name	Type	Description	Default
`array`	`NDArray`	Input array.	required
`sample_idx`	`int`	Current sample number.	required

`compute_normalization_stats(image)`

Compute mean and standard deviation of an array.

Expected input shape is (S, C, (Z), Y, X). The mean and standard deviation are computed per channel.

Parameters:

Name	Type	Description	Default
`image`	`NDArray`	Input array.	required

Returns:

Type	Description
`tuple of (list of floats, list of floats)`	Lists of mean and standard deviation values per channel.

`finalize_iterative_stats(count, mean, m2)`

Finalize the mean and variance computation.

Parameters:

Name	Type	Description	Default
`count`	`NDArray`	Number of elements in the array. Shape: (C,).	required
`mean`	`NDArray`	Mean of the array. Shape: (C,).	required
`m2`	`NDArray`	Variance of the array. Shape: (C,).	required

Returns:

Type	Description
`tuple[NDArray, NDArray]`	Final channel-wise mean and standard deviation.

`update_iterative_stats(count, mean, m2, new_values)`

Update the mean and variance of an array iteratively.

Parameters:

Name	Type	Description	Default
`count`	`NDArray`	Number of elements in the array. Shape: (C,).	required
`mean`	`NDArray`	Mean of the array. Shape: (C,).	required
`m2`	`NDArray`	Variance of the array. Shape: (C,).	required
`new_values`	`NDArray`	New values to add to the mean and variance. Shape: (C, 1, 1, Z, Y, X).	required

Returns:

Type	Description
`tuple[NDArray, NDArray, NDArray]`	Updated count, mean, and variance.