``Kirsch edge operator'' - Kirsch edge operator

VFX name:

iKirschEdge

IMPROMPTU Equivalent:

Kirsch_edge_detection

purpose:

Calculate the edge strengths (or direction) of voxels in a 3-D grayscale volume using the Kirsch edge operator [1]. This operator is a slightly cruder approximation to a local directional derivative than the Sobel operator [1,24].

input:

An 8-bit 3-D grayscale volume.

output:

An 8-bit volume.

parameters:

Default parameters menu is

x_filter_dimension = 3
y_filter_dimension = 3
z_filter_dimension = 3
num_of_directions = 13
function = gradient
threshold = 0

The Kirsch operator is made up of a number of templates. Each template focuses on the edge strength in one direction. For each voxel, the Kirsch algorithm cycles through the desired number of directions and assigns an attribute (as specified by the parameter ``function'') of the best direction to the voxel. The best direction is the direction indicating the largest edge strength (gradient magnitude). The ``num_of_directions'' option can toggle to the following options:

1.

3 - the x, y, and z orthogonal directions.

2.

9 - covers the directions above and the directions orthogonal to the normals along x = y, x = z, y = z, x = -y, x = -z, or y = -z.

3.

13 - covers the directions above and the directions orthogonal to vectors passing through the origin and any corner of a 3x3x3 cube.

The ``function'' parameter toggles between the values ``gradient'' and ``direction''. The option ``gradient'' indicates that the gradient magnitude of the best Kirsch template is written into the output. The option ``direction'' indicates that the direction of the best Kirsch template is written into the output; for this option, a value of ``14'' indicates the opposite direction of ``1'', the value ``15'' indicates the opposite direction of ``2'', and so forth.

When you use the ``function = gradient'' option, you can zero out low-valued gradient values by setting the ``threshold'' parameter.

comments:

See below.

1.

This is a fairly time-consuming operation.

2.

Double edge responses are possible for larger (filter dimension >3) operators. Be careful using large operators.