I'm writing a connected component system and one of the descriptors I can easily compute is the surface area along with the component's rectangular bounding box.
What is surface area divided by bounding area called? (or any mixture of these two parameters).
For example, if my object were a rectangle, this parameter would be 1.0.
Extent or rectangularity, apparently:
Extent of an image object is defined as area of the image object divided by the area of its bounding rectangle.
Source: Question text in https://dsp.stackexchange.com/questions/49026/what-is-the-application-difference-between-extent-and-solidity-in-image-processi
Rectangularity is the ratio of the object to the area of the minimum bounding rectangle.
Source: Page 45 in http://www.cyto.purdue.edu/cdroms/micro2/content/education/wirth10.pdf
But the definitions I've run across do not always fully specify the rectangle. The ambiguity is related to the concept of "ferret box". Ferret boxes' edges do not have to be parallel to the image axes like good old bounding boxes. So depending on which you choose, your "extent" value might change.