``Grayscale_Erosion'' -- grayscale erosion

purpose:

Perform a grayscale erosion [27] on an input volume, using a specified structuring element with adjustable dimensions. Grayscale erosion is defined as

where is the eroded voxel intensity, is the original voxel intensity, b is the grayscale structuring element, and B is the domain of b, or the set of all values where b is defined.

Three structuring element shapes are currently available with this function:

1. sphere -- a structuring element of the form

   

   where D is the maximum intensity value for the structuring element, and a, b, and c are the x, y, and z filter dimensions, respectively.

2. paraboloid -- structuring element of the form

   

   where the parameters are the same as those defined above.

3. cone -- structuring element shaped as the elliptical cone given by

   

   where the parameters are the same as those defined above.

    

The domain B for these structuring elements is defined as all within the size of the structuring element where the equations have a real solution.

input:

An 8-bit grayscale volume.

output:

An 8-bit grayscale volume.

parameters:

Default parameter menu for this function is

x filter dim = 3
y filter dim = 3
z filter dim = 3
shape = sphere
max gray level = 3
no. of iterations = 1
input from vol # = 0
copy output to vol # = 0

The ``filter dim'' parameters specify the size of the structuring element in voxels. The x, y, and z values specified here correspond to the a, b, and c values used to compute the structuring element (see above).
The parameter ``shape = '' specifies the shape of the structuring element to be used when performing the erosion. The available structuring elements are a sphere, paraboloid, and cone.
The parameter ``max gray level'' corresponds to the D value (see above) used to set the highest intensity value within the structuring element.

comments:

 

1. This function can also be used to perform erosions using other structuring elements, although this is not currently a menu option within the ROI system. Other routines can be written to call the grayscale erosion function directly if different structuring elements are desired.
2. This function is very slow, taking about 3 minutes for a 100x100x100 image using a 7x7 structuring element.