Thread Subject:

Fractal Dimension

Hi,

Can anybody give me some hints for calculating the fractal dimension
of a picture using Matlab?

Thanks.

Bye

Stelian wrote:
>
>
> Hi,
>
> Can anybody give me some hints for calculating the fractal
> dimension
> of a picture using Matlab?
>
> Thanks.
>
> Bye

Recall the definition and you can do it by a for-loop.

If you have a coastline, with aproximate fractal shape, saved as
polygone vectors (x,y), you should calculate the circumference L of
that object with different step-lengths h. Then by plotting log(L)
vs. log(h) the slope should represent the fractal dimension (maby
there was some constant also -google that).
     Well it could happens (most-likely except for some easy figures
like the Koch-star) that the fractal is not self-similar, i.e., the
fractal dimension is not linear (look at the plot and you will see!).

/Per

Hi all,

Inspiration can be found from the following links

Higuchi Algorithm
http://www.lyapunovpress.com/pdf/HiguchiFD.pdf 
 
Katz Algorithm
http://www.lyapunovpress.com/pdf/KatzFD.pdf  
 
Petrosian Algorithm
http://www.lyapunovpress.com/pdf/PetrosianFD.pdf 
 
Sevick Algorithm
http://www.lyapunovpress.com/pdf/SevickFD.pdf 
 
Brahim

> Hi,
>
> Can anybody give me some hints for calculating the fractal dimension
> of a picture using Matlab?
>
> Thanks.
>
> Bye

I understand what you are saying, but until then, how do I extract
the coastline of the shape I'm interested in, from the picture, in
order to aply the algorithm?

thx

Per Sundqvist wrote:
>
>
> Stelian wrote:
>>
>>
>> Hi,
>>
>> Can anybody give me some hints for calculating the fractal
>> dimension
>> of a picture using Matlab?
>>
>> Thanks.
>>
>> Bye
>
> Recall the definition and you can do it by a for-loop.
>
> If you have a coastline, with aproximate fractal shape, saved as
> polygone vectors (x,y), you should calculate the circumference L of
> that object with different step-lengths h. Then by plotting log(L)
> vs. log(h) the slope should represent the fractal dimension (maby
> there was some constant also -google that).
> Well it could happens (most-likely except for some easy
> figures
> like the Koch-star) that the fractal is not self-similar, i.e., the
> fractal dimension is not linear (look at the plot and you will
> see!).
>
> /Per

hi Stelian,
i wrote this code to trace the perimeter out a few years back:
          j

function perim= trimperim(name)

if nargin<1, error('no file name');end;

[origim,map]=imread(name);
if origim(1,1)==1, origim=1-origim;end;
        [h,w]=size(origim);
 
% trim
        rows=sum(origim');
        cols=sum(origim);
        
firstrow=min(find(rows>0));
        dirlist=[0 1;1 0;0 -1;-1 0];
        start=max(find(origim(firstrow,:)==1));
        y=start;x=firstrow;dirj=4;
        perim=zeros(h,w);
        perim(x,y)=1;
        startx=x;starty=y;count=0;
        while x ~= startx | y ~= starty | count<4,
        checkpos=[x y]+ dirlist(rem(dirj,4)+1,:);
        if origim(checkpos(1),checkpos(2))==1,
            x=checkpos(1);y=checkpos(2);
            perim(x,y)=1;count=count+1;
            dirj=rem(dirj,4)+1;
        else
           newpos=[x y]+ dirlist(dirj,:);
           if origim(newpos(1),newpos(2))==1,
              x=newpos(1);y=newpos(2);
              perim(x,y)=1;count=count+1;
              else
              dirj=mod(dirj-2,4)+1;
          end;
       end;
    end;

Thanks for the source code, but it returns only zeros. i don't know
what i'm doing wrong. What kind of picture should i use? I tried with
grayscale pictures.

Stelian

j wrote:
>
>
> hi Stelian,
> i wrote this code to trace the perimeter out a few years back:
> j
>
> function perim= trimperim(name)
>
> if nargin<1, error('no file name');end;
>
> [origim,map]=imread(name);
> if origim(1,1)==1, origim=1-origim;end;
> [h,w]=size(origim);
>
> % trim
> rows=sum(origim');
> cols=sum(origim);
>
> firstrow=min(find(rows>0));
> dirlist=[0 1;1 0;0 -1;-1 0];
> start=max(find(origim(firstrow,:)==1));
> y=start;x=firstrow;dirj=4;
> perim=zeros(h,w);
> perim(x,y)=1;
> startx=x;starty=y;count=0;
> while x ~= startx | y ~= starty | count<4,
> checkpos=[x y]+ dirlist(rem(dirj,4)+1,:);
> if origim(checkpos(1),checkpos(2))==1,
> x=checkpos(1);y=checkpos(2);
> perim(x,y)=1;count=count+1;
> dirj=rem(dirj,4)+1;
> else
> newpos=[x y]+ dirlist(dirj,:);
> if origim(newpos(1),newpos(2))==1,
> x=newpos(1);y=newpos(2);
> perim(x,y)=1;count=count+1;
> else
> dirj=mod(dirj-2,4)+1;
> end;
> end;
> end;

Stelian wrote:
> What kind of picture should i use?

2 colours, all pixels should be either 1 or 0, if i recall
correctly... you should go through the code line by line, to check it
does what you need; i give no warranty that it works properly or
gives the correct answers!

j wrote:
>
>
> Stelian wrote:
>> What kind of picture should i use?
>
> 2 colours, all pixels should be either 1 or 0, if i recall
> correctly... you should go through the code line by line, to check
> it
> does what you need; i give no warranty that it works properly or
> gives the correct answers!

If your image is pretty smooth in the interior of that perimeter then
you can use gradient filters on that image (convolve image with the
filter matrix) and then finding out where that gradient is greater
than certain threshold should give you the perimeter. But I am making
the assumption that you image intensity makes a sharp change at the
perimeter.

Gagan

please tell me how will I detect the following in MATLAB,

       function perim= trimperim(name)

**********************************

j <jpreen@gmail.com> wrote in message <eef1b9b.3@webx.raydaftYaTP>...
> hi Stelian,
> i wrote this code to trace the perimeter out a few years back:
> j
>
> function perim= trimperim(name)
>
> if nargin<1, error('no file name');end;
>
> [origim,map]=imread(name);
> if origim(1,1)==1, origim=1-origim;end;
> [h,w]=size(origim);
>
> % trim
> rows=sum(origim');
> cols=sum(origim);
>
> firstrow=min(find(rows>0));
> dirlist=[0 1;1 0;0 -1;-1 0];
> start=max(find(origim(firstrow,:)==1));
> y=start;x=firstrow;dirj=4;
> perim=zeros(h,w);
> perim(x,y)=1;
> startx=x;starty=y;count=0;
> while x ~= startx | y ~= starty | count<4,
> checkpos=[x y]+ dirlist(rem(dirj,4)+1,:);
> if origim(checkpos(1),checkpos(2))==1,
> x=checkpos(1);y=checkpos(2);
> perim(x,y)=1;count=count+1;
> dirj=rem(dirj,4)+1;
> else
> newpos=[x y]+ dirlist(dirj,:);
> if origim(newpos(1),newpos(2))==1,
> x=newpos(1);y=newpos(2);
> perim(x,y)=1;count=count+1;
> else
> dirj=mod(dirj-2,4)+1;
> end;
> end;
> end;