``morphological_gradient'' - morphological gradient

VFX name:

iMorphGradient

IMPROMPTU Equivalent:

Morphological_gradient

purpose:

Calculate the morphological gradient, a measure of edge strength, for the voxels in a grayscale volume [25]. The specific operation done here is the following:

$$\rm local\ max\left\{local\ average\ volume\right\} - local\ min\left\{local\ average\ volume\right\} \rightarrow volume$$

where volume is the input volume, local average refers to the (pseudo) lowpass filtering operation of local averaging, and local max/min refer to the operation of local maximum/minimum.

The ``local average'' step is optional. If left out, the morphological gradient reduces to

$$\rm local\ max\left\{ volume \right\} - local\ min\left\{ volume \right\} \rightarrow volume$$

input:

An 8-bit grayscale volume.

output:

An 8-bit grayscale volume.

parameters:

Default parameters menu is

x_filter_dimension = 3
y_filter_dimension = 3
z_filter_dimension = 3
function = unsmoothed
threshold = 0

The ``function = unsmoothed'' option does not use the local average before doing the maximum or minimum operations; the option ``function = smoothed'' does.

The parameter ``threshold'' can be used to zero out points will small morphological gradient.

comments:

See below.

1.

A moderate speed function, much faster than the Kirsch and difference-of-Gaussians operations.

2.

Using the ``smoothed'' option (i.e., using the local averaging before the max or min) gives smoother results.

3.

The gradient values are semi-comparable to the Kirsch operator. The Kirsch operator is more directionally focused and will give larger gradient values at edges.