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Running Mean Std

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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:

  • tuple or numpy arrays –

    Final mean and standard deviation.

update(array, sample_idx)

Update the Welford statistics.

Parameters:

  • array (NDArray) –

    Input array.

  • sample_idx (int) –

    Current sample number.

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:

  • image (NDArray) –

    Input array.

Returns:

  • 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:

  • count (NDArray) –

    Number of elements in the array. Shape: (C,).

  • mean (NDArray) –

    Mean of the array. Shape: (C,).

  • m2 (NDArray) –

    Variance of the array. Shape: (C,).

Returns:

  • 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:

  • count (NDArray) –

    Number of elements in the array. Shape: (C,).

  • mean (NDArray) –

    Mean of the array. Shape: (C,).

  • m2 (NDArray) –

    Variance of the array. Shape: (C,).

  • new_values (NDArray) –

    New values to add to the mean and variance. Shape: (C, 1, 1, Z, Y, X).

Returns:

  • tuple[NDArray, NDArray, NDArray] –

    Updated count, mean, and variance.