Index
Single Raster Analysis Tools I Basic descriptive statistics with HISTO	A-Z	Single Raster Analysis Tools III Using FILTER

Single Raster Analysis Tools II

• Thinness Ratio - a simple shape factor with AREA⁺⁺⁺, PERIM, SCALAR and OVERLAY

  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 elements, ...).

  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 facility.

  

  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 hand :-)

  1. 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)
  2. 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.
  3. 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 operation:

     

     The PERIM output is raised to the power of 2 again with SCALAR.

  4. 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 coincidences.

     

• 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: , A_P means the area of the polygon and A_C 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.

  

	Index
Single Raster Analysis Tools I Basic descriptive statistics with HISTO	A-Z	Single Raster Analysis Tools III Using FILTER