The distance parameter used to construct a GLCM specifies the scale at which the texture is analysed. An optimal choice of this distance is dependent on the inherent scale of the textures being analysed. Many implementations consider only a distance of 1. We show here that significant improvements can be made by careful choice of the distance parameter.
Consider the brick textures in the mortar test suite. These textures contain a regular, repeated pattern of mortar which is dependent on the brick lengths and widths. The tests in this suite seek to classify textures with different brick widths (and hence mortar spacings). We would expect that in many cases, a selection of distance can be found which will give us perfect results.
In particular, we show results for the test, stagMort01. This
test is a two way classification of two mortar patterns - one with
constant 7 pixel horizontal mortar spacing and the other with
alternating horizontal mortar spacings of 4 and 10 pixels. The
vertical mortar spacings are constant 11 pixels. Note that the mortar
densities are identical in each class. A 64x64 pixel sample of each
texture is shown below.
We can hypothesize that GLCM will best distinguish between these
textures when its distance parameter is equal to the mortar-to-mortar
distance in one of the textures. Thus, we would expect good
discrimination for distances of 4, 7 and 10 pixels.
The figure below shows the performance results on this test as the
distance parameter is varied from 1 to 20 pixels. Our hypothesis is
confirmed with perfect performance at distances of 4, 7, and 10
pixels. We also obtain perfect discrimination at a distance of 18
pixels, being the width of 2 narrow bricks and 1 wide brick in the
alternating width images. A very poor score is achieved at a distance
of 14, which is the width of two adjacent bricks in both images. We
see that the results are consistently poor except
where the distance is optimal.
