Thinness Ratio - a simple shape factor with AREA+++, PERIM, SCALAR
Many shape descriptors have been introduced for different purposes. E.g. to
assist pattern recognition techniques in image processing, or make the approach to
explain function and/or genesis by form (classification of certain geomorphological
If you are interested in pattern analysis, take a look at FRAGSTATS - a
free software package available from ftp.orst.edu.
It calculates more than 90 indicative parameters for quantifying landscape structure.
BTW, IDRISI has implemented a module - PATTERN - which computes a handful
of these parameters. They are well documented and referenced in the on-line help
The thinness ratio is defined as , where
A means the area and P the perimeter. By this formula
we simply relate the area of a polygon to its perimeter. Again we will apply this method to the vegetation image (had no better dataset at
Calculating the Compactness Ratio with CRATIO
In the Analysis/Statistics submenue you will find CRATIO which
requires only input (the GROUPed vegetation image) and output image names,
a click on the OK button and it calculates the Compactness Ratio,
another shape describing factor. Its formula is quite simple:
, AP means the
area of the polygon and AC the area of a circle having the
same perimeter as that of the polygon. The 'most compact polygon' (one pixel) has a
theoretical compactness ratio of 0.886, so the reclassified images shows 5 classes. Higher
values indicate more compact areas.
- We need to isolate each single polygon first and attach to it a unique identifyer.
To achieve this, use GROUP. You have to name input and output images and
check, whether to Include diagonals or not. GROUP assigns each disjunctive
polygon a continuous unique id. It puts together polygons that have same values
and neighbouring cells in the north, east, south or west direction
(with checked Include diagonals additionally: NE, SE, SW and NW). In this
example I decide to include diagonals, as a diagonal corridor makes 35.36 m, what's
slightly above expected data resolution (ca. 25 m). The number of generated
unique polygons is the maximum value of the GROUPed image (can be found through
DESCRIBE or HISTO)
- Now feed AREA and PERIMeter with the GROUPed images - polygons
in the resulting image files contain their area resp. their perimeter give in
units you chose.
- To go on with the formula, take the AREA-image as input for SCALAR, a
rather straightforward module to apply simple arithmetics to an image and multiply
it subsequently by Pi and by 4 - all cellvalues are then treated with the same
The PERIM output is raised to the power of 2 again with SCALAR.
- We got two images now from one starting dataset - the scaled area and the
raised perimeter. OVERLAY completes the action allowing us to divide the
first by the last one.
To make the result clearer, I used a RECLASSification to 4 classes. The highest
ratio is 0.785 for a single pixel. The blue color indicates a high grade of
thinness whereas the tiny green spots show the opposite - compactness. The results
strongly depend on scale and resolution. In a later part of the tutorial we will
overlay the vegetation with the thinness ratio image to find out possible