Fractal box counts

I tried to measure fractal dimension for erythrocytes, but it is always deal with the cells as background. I made particle select after threshold. Each time I run fractal box counting it give me the wrong fractal dimension. I explored that the program deals with the cell as background. Could you please help me and give the standard procedure to measure fractal dimension

It would help if you could post a sample image. The Analyze>Tools>Fractal Box Count command requires an 8-bit binary (black and white) image, which can be created by thresholding the image using the Image>Adjust>Threshold tool and applying the threshold by clicking on the “Apply” button. You will need to check “Black backround” in the Fractal Box Count dialog if the cells in the binary image are white.

Many thanks Wayne for your attention here is an example of the image. What you mention is exactly what I have been done before, but It did not work. I would like to calculate fractal dimension for each cell in the image individually.

I do not see an easy way to calculate the fractal dimension of each cell. The Fractal Box Count command is not designed to handle multiple objects in an image.

In principle you can segment the image to extract each cell in it’s own image and then apply
the fractal box count on the cell images. Not long ago there was a thread about how to extract individual particles (e.g. you cells) into images, see:

However you have a lot of overlaps in your example image which you have to deal with, too. For a possible solution, see the great plugin from @twagner to at least extract a single overlapping cell (not the suggested Ellipse) :

But do you really need a fractal analysis? Some default shape parameters available in the particle analysis of ImageJ might be sufficient, see:

For additional morhological parameters see also the Morphological plugin collection from @gabriel:

Finally have a look at the plugin MorphoLibJ from @iarganda and D. Legland :


Fractals are hierarchical structures that show repeating detail over a large number of scales.
In blood smears the shape of the erythrocytes do not look fractal at all, but pretty Euclidean (and I would venture to say that you will get near D=1.0 for all of them when measuring their boundaries).
Also you need high magnification images, so you can investigate box ranges of more than one order or magnitude, but at the same time not too small, so you can avoid the problem of image pixellation.
E.g. boxes ranging from 1 to 10 pixels would not be useful as they do not capture the increase of detail that you see on larger ranges and you end up with curved plots.
Maybe this paper is useful to clarify some of points raised above (by the way, nice feature in the editor, you add an URL and it shows you the abstract! Clicking on the title takes you to Pubmed, and from there to the journal PDF):


Dear Gabriel
Thanks a lot for your help notes. You paid my attention to many important points. Thanks again

Dear friends,
I have read the concept of fractal analysis for binary images. I want to measure fractal dimension for dendritic nanostructures which are grayscale images from SEM. I want to know how I can change the parameters in box counting scan to measure fractal dimension? Do I need to threshold the grayscale images or convert them to binary images? is it possible to use the same setting as binary images for them?

So the “Black background” means to treat the black color as background and calculate the white color. Is that true?
And if does not tick the “Black background”, it means treat the black color as the analysis object?

Select “Black background” to treat black as the background and do not select it to treat white as the background.