# Explanation for Solidity and Extent

#1

I’d like to be able to illustrate/explain what measures from the MeasureObjectAreaShape mean. The manual gives definitions, but some of them are confusing.

*Solidity - Also known as convexity. The proportion of the pixels in the
convex hull that are also in the object. Computed as Area/ConvexArea.

*Extent - The proportion of the pixels in the bounding box that are also
in the region. Computed as the Area divided by the area of the bounding box.

What is the difference between Convex Area and Bounding box? what is the difference between a Region and an Object?

help on this matter as soon as possible would be greatly appreciated

p.s.The module gives me different measures for each of these when I input a 2d monolayer of epithelial cells.

#2

Here’s the answer, from one of our software engineers:

Both the solidity and extent are ratios of the area of your object (which Matlab refers to as region sometimes) and some other surrounding container. For Extent, the container is the enclosing rectangle and for Solidity, the container is the convex hull.

Extent is the easier of the two concepts: imagine the smallest rectangle that fits around your object. The extent is the area of your object divided by the area of this rectangle. Your cells will have relatively large extents if they are circular or elliptical and have no protrusions.

Solidity is a little more difficult, but potentially a better differentiator of cells with protrusions or irregular shape versus generally round cells. The containing shape is the convex hull. Imagine putting a rubber band around your cell’s shape. The rubber band will stretch in a straight line across indentations in the cell but will follow the rounded outside contours. The area within the rubber band is the area of the convex hull. The solidity should be one for something without any indentations and, for a cell with an indent, will have a value of one minus the proportion of the area within the rubber band not covered by the cell.

Here are a couple of links that may explain the convex hull in a more visual manner:
en.wikipedia.org/wiki/Convex_hull
en.wikipedia.org/wiki/File:ConvexHull.svg
softsurfer.com/Archive/algorithm … ex%20Hulls
cse.unsw.edu.au/~lambert/jav … xHull.html

–Lee Kamentsky

(via Kate)

#3

Thanks Kate and Lee, I guess the key to differentiating these is the phrase bounding box, aka rectangle, in the definition of extent.

#4

Hye,
coming back to this hold post because I would like to know if the extent of an object is computed using an axis-aligned bounding box or according to the object orientation as figured out in the following pictures ?

thanks

#5

Hi,
The extent is computed using the approach represented by the panel on the left.
-Mark