05/13/2008

Morphological Parameters for Particles  Illustrations
These are some morphological parameters (statistics or 'stats') that Lispix can calculate and display.
Some of these parameters, such as length and width, are basic, exact, well defined, and determined directly from the convex hull, which is quickly calculated from the particle boundary.
To display using the Blob Tool: draw / convex hulls
The Convex Hull, green, is calculated from the
particle outline using a fast and exact algorithm1.
Maximum Inscribed Circle, red,calculated from maximum of the
Euclidian Distance Map2 of the mask.
Bounding rectangle, yellow. The bounding rectangle, yellow,
is calculated from the particle outline.
Note that it depends on the particle orientation.
Convex Hull references and algorithms.
To display using the Blob Tool: draw / maximum caliper diameters.
Particle length (maximum caliper diameter) is the distance between the most separated points of the convex hull, and thus of the outline.
Max.
caliper diameters for smaller particles.
To display using the Blob Tool: draw / minimumcaliper diameters.
Particle width (minimum caliper diameter), yellow line, is calculated using the convex hull3,4. This is the minimum separation, for any particle orientation, for parallel lines that just touch each side of the particle.
The line of support, tan line, a segment of the convex hull, is one of the parallel lines, i.e., one of the ‘sides’ of the ‘caliper’