Image fractal dimension value

I have interest in fractal dimension (FD) as I was reading this paper https://translational-medicine.biomedcentral.com/track/pdf/10.1186/1479-5876-8-140.pdf

I run the code below on the right figure (Koch snowflake) https://translational-medicine.biomedcentral.com/articles/10.1186/1479-5876-8-140/figures/1 but I get different results, any idea why? Any recommendation of introductory book covering this issue with matlab?

clc;
clear all;
close all;

fileName='E:/fd126.png'
I = (imread(fileName));
I = imfill(I,'holes');
figure
imshow(I);
BW = imbinarize(I);

BoxCountfracDim(BW)  %using Hausdorff (Box-Counting) Fractal Dimension with multi-resolution calculation version 1.0.0.0 by Tan Nguyen

hausDim(BW) %using Hausdorff (Box-Counting) Fractal Dimension version 1.2.0.0 by Alceu Costa

[John D'Errico]

What result do you get? How far is it off? Do you accept that this computation could some some degree of error in it? How can we know what you think is the wrong number?

[Image Analyst]

If you want us to run the code you should attach BoxCountfracDim and hausDim. Otherwise I'm not doing anything.

Answer 1

[yanqi liu]

yes，sir，may be should use image as same，such as

clc; clear all; close all;

fileName='12967_2010_Article_2115_Fig1_HTML.webp.jpg';
[I,map] = imread(fileName,'jpg');
if ~isempty(map)
    I = ind2rgb(I,map);
end
figure
imshow(I);
BW = im2bw(I,0.9);
bws = imfill(~BW,'holes');
bw1 = bwperim(bwareafilt(bws,1));
[r,c] = find(bw1);
bw1 = bw1(min(r):max(r),min(c):max(c));
bw2 = bwperim(bwareafilt(bws,1,'smallest'));
[r,c] = find(bw2);
bw2 = bw2(min(r):max(r),min(c):max(c));
figure;
subplot(1,2,1); imshow(bw1);
subplot(1,2,2); imshow(bw2);

BoxCountfracDim(bw1)  %using Hausdorff (Box-Counting) Fractal Dimension with multi-resolution calculation version 1.0.0.0 by Tan Nguyen

hausDim(bw1) %using Hausdorff (Box-Counting) Fractal Dimension version 1.2.0.0 by Alceu Costa

BoxCountfracDim(bw2)  %using Hausdorff (Box-Counting) Fractal Dimension with multi-resolution calculation version 1.0.0.0 by Tan Nguyen

hausDim(bw2) %using Hausdorff (Box-Counting) Fractal Dimension version 1.2.0.0 by Alceu Costa

ans =

1.0495

ans =

1.0495

ans =

1.2097

ans =

1.2097

>>

now，we can see

first， 1.0495

second， 1.2097

as similar with 1 and 1.26

[Image Analyst]

Can you attach BoxCountfracDim() and hausDim()?

[yanqi liu]

yes，sir，here is 2 functions，get them by file exchange platform