medpy.filter.noise.immerkaer#

medpy.filter.noise.immerkaer(input, mode='reflect', cval=0.0)[source]#

Estimate the global noise.

The input image is assumed to have additive zero mean Gaussian noise. Using a convolution with a Laplacian operator and a subsequent averaging the standard deviation sigma of this noise is estimated. This estimation is global i.e. the noise is assumed to be globally homogeneous over the image.

Implementation based on [1].

Immerkaer suggested a Laplacian-based 2D kernel:

[[ 1, -2,  1],
 [-2,  4, -1],
 [ 1, -2, 1]]

, which is separable and can therefore be applied by consecutive convolutions with the one dimensional kernel [1, -2, 1].

We generalize from this 1D-kernel to an ND-kernel by applying N consecutive convolutions with the 1D-kernel along all N dimensions.

This is equivalent with convolving the image with an ND-kernel constructed by calling

>>> kernel1d = numpy.asarray([1, -2, 1])
>>> kernel = kernel1d.copy()
>>> for _ in range(input.ndim):
>>>     kernel = numpy.tensordot(kernel, kernel1d, 0)

Parameters:

inputarray_like: Array of which to estimate the noise.
mode{‘reflect’, ‘constant’, ‘nearest’, ‘mirror’, ‘wrap’}, optional: The mode parameter determines how the array borders are handled, where cval is the value when mode is equal to ‘constant’. Default is ‘reflect’
cvalscalar, optional: Value to fill past edges of input if mode is ‘constant’. Default is 0.0

Returns:

sigmafloat: The estimated standard deviation of the images Gaussian noise.