I'm trying to use the concept of lacunarity to classify images, as per how a few research papers have done it. To verify whether my equations and implementation are correct, I'm trying to verify the output of my program - for images with same fractal dimension, lacunarity is inversely proportional to the denseness of an image - denser the image, lower is its lacunarity.
For example, if I plot two triangular Koch curves, one with order 4 and another with order 6(order meaning iterations), both would have the same fractal dimension. Then you would expect the image with order 4 to have comparatively higher lacunarity since its less dense.
Now, after computing the lacunarity, there are two possible plots you can get - non-normalized and normalized lacunarity. When I plot the non-normalized lacunarity, I get the correct output - the order 4 curve has higher lacunarity. Whereas when I plot the normalized lacunarity, the plots exchange their positions and the order 6 curve ends up having higher lacunarity which seems incorrect.
The research papers that I'm referring are only using normalized lacunarity in their applications. I'm not sure where am I making an error.
Lacunarity is defined as follows -
For a m x n binary image, you define box size r, where r ranges from, for example, from 1 to 100.
Lacunarity is defined for every r. For a given r, it is computed as the ratio of (A+B)/B
Where A = Variance of X
B = Square of the mean of X
Where X = no. of 1s within a box of size r x r. So you compute mean and variance over all possible boxes of size r x r in the m x n matrix. Then r is varied from 1 to 100 for example, and hence lacunarity value is computed for 100 values of r, after which you can plot lacunarity.
Normalized lacunarity is obtained by dividing Lacunarity[r] by Lacunarity for all r.
So I need help with 2 questions:
 Am I making an error in the concept of lacunarity being inversely proportional to denseness, or is it that I'm making some mistake while plotting normalized lacunarity itself?
 Is there a way I can verify that I am implementing lacunarity calculation correctly? For example, if there are standard images whose lacunarity plots are well known. I can plot lacunarity for those standard images and verify that I am getting a similar lacunarity plot.