``Grayscale_Opening'' - morphological grayscale opening

VFX name:

iGrayOpen

IMPROMPTU Equivalent:

Grayscale_Opening

purpose:

Perform a grayscale opening [27] on an input volume, using a specified structuring element with adjustable dimensions. The morphological grayscale opening of a volume v by a structuring element b is defined as

$$v_b = [v \ominus b] \oplus b$$

where v_b is the notation for v opened by b. The operators $\ominus$ and $\oplus$ correspond to grayscale erosion and dilation, respectively, which are described in sections 2.2.7 and 2.2.8.

input:

An 8-bit grayscale volume.

output:

An 8-bit grayscale volume.

parameters:

Default parameter menu for this function is

x_filter_dimension = 3
y_filter_dimension = 3
z_filter_dimension = 3
shape = sphere
max_gray_level = 3

The parameter ``shape'' specifies the shape of the structuring element to be used when performing the opening. The available structuring elements are a sphere, paraboloid, and cone.
The parameter ``max_gray_level'' corresponds to the highest intensity value within the structuring element.

The ``filter_dimension,'' ``shape,`` and ``max_gray_level'' parameters provide information about the filter size and structuring element used in the grayscale erosion and dilation functions that perform the opening. See Sections 2.2.7 and 2.2.8 for a more detailed explanation of these parameters.

comments:

1.

There is no ``iterations'' parameter with this function. Grayscale opening is idempotent.

2.

This function is very slow, taking up to 6 minutes for an opening with a 7x7 structuring element on a 100x100x100 volume.