outputs spectra of size measurements of the textures in the image.
Image granularity is a texture measurement that tries a series of structure elements of increasing size and outputs a spectrum of measures of how well these structure elements fit in the texture of the image. Granularity is measured as described by Ilya Ravkin (references below). The size of the starting structure element as well as the range of the spectrum is given as input.
- Granularity: The module returns one measurement for each instance of the granularity spectrum.
- Serra J. (1989) Image Analysis and Mathematical Morphology, Vol. 1. Academic Press, London
- Maragos P. "Pattern spectrum and multiscale shape representation", IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, N 7, pp. 701-716, 1989
- Vincent L. (2000) "Granulometries and Opening Trees", Fundamenta Informaticae, 41, No. 1-2, pp. 57-90, IOS Press, 2000.
- Vincent L. (1992) "Morphological Area Opening and Closing for Grayscale Images", Proc. NATO Shape in Picture Workshop, Driebergen, The Netherlands, pp. 197-208.
- Ravkin I, Temov V. (1988) "Bit representation techniques and image processing", Applied Informatics, v.14, pp. 41-90, Finances and Statistics, Moskow, (in Russian)
Select an image to measure
Select the grayscale images whose granularity you want to measure.
Subsampling factor for granularity measurements
If the textures of
interest are larger than a few pixels, we recommend you subsample the image with a factor
<1 to speed up the processing. Down sampling the image will let you detect larger
structures with a smaller sized structure element. A factor >1 might increase the accuracy
but also require more processing time. Images are typically of higher resolution than is
required for granularity measurements, so the default value is 0.25. For low-resolution images,
increase the subsampling fraction; for high-resolution images, decrease the subsampling
fraction. Subsampling by 1/4 reduces computation time by (1/4)3
because the size
of the image is (1/4)2
of original and the range of granular spectrum can
be 1/4 of original. Moreover, the results are sometimes actually a little better
with subsampling, which is probably because with subsampling the
individual granular spectrum components can be used as features, whereas
without subsampling a feature should be a sum of several adjacent
granular spectrum components. The recommendation on the numerical value
cannot be determined in advance; an analysis as in this reference may be
required before running the whole set.
, slides 27-31, 49-50.
Subsampling factor for background reduction
It is important to
remove low frequency image background variations as they will affect the final granularity
measurement. Any method can be used as a pre-processing step prior to this module;
we have chosen to simply subtract a highly open image. To do it quickly, we subsample the image
first. The subsampling factor for background reduction is usually [0.125 – 0.25]. This is
highly empirical, but a small factor should be used if the structures of interest are large. The
significance of background removal in the context of granulometry is that image
volume at certain granular size is normalized by total image volume, which depends on
how the background was removed.
Radius of structuring element
This radius should correspond to the radius of the textures of interest after
subsampling; i.e., if textures in the original image scale have a radius of 40
pixels, and a subsampling factor of 0.25 is used, the structuring element size should be
10 or slightly smaller, and the range of the spectrum defined below will cover more sizes.
Range of the granular spectrum
You may need a trial run to see which granular
spectrum range yields informative measurements. Start by using a wide spectrum and
narrow it down to the informative range to save time.