How to form Adjacency matrix from CXX and CYY where CXX and CYY contains collectively some information??

Hi, I have 100 x 100 binary image, I have made 2 x 2 grid on it, within each grid I am taking centre-of-mass of the white pixels if they have any white pixels else represent the grid as NaN.x-coordinate mean in CXX and Y coordinate mean in CYY.. To get a grph I am plotting :-

plot(CYY,CXX,'k*');

But I need Adjacency Matrix of a graph..How can I get that.....

[Jan]

I cannot follow your descriptions. Please post an example input and the code. "I have mad a grid" can mean a variety of procedures. What does "represent the grid as NaN" mean? With some code it would be clear, what you are doing. But is the explanation needed at all? Maybe it is enough to state, that you have two vectors X and Y which contain coordinates and want the corresponding adjacency matrix? Does it matter, where the coordinates are coming from or that they are called "CXX"?

Answer 1

[Jan]

As posted in your other thread already, the methods shown here should solve your problem:

https://stackoverflow.com/questions/3277541/construct-adjacency-matrix-in-matlab

You have commented: "No help". So please explain, why these methods do not help you. What is the difference between these solutions and what you need?

[Mohammad Bhat]

Here is my code and I have attached figures:-

X = imread('e.jpg');

b = imresize(X,[100,100]);

% Binarization

th = graythresh(b);

I = im2bw(b,th);

% %thinning

kl=bwmorph(~I,'thin',inf);

%grid size

t1 = 5; % Grid Size choosen by USER we have fixed it 5 x 5

D = 100; % Height 5 and Breadth 5 of each grid in image Image

I = 1; % fix it 1

U1 = t1; % asign 5 to U1

J = 1; % FIX IT 1

U2 = t1; % assign 5 to U2

E = 1; % assign 1 to E

t2 = D/t1; % grid the 100 x 100 image into 5 x 5 therefore t2 = 20

%Z=1;

for iir=1:t2 %

    for jjr=1:t2  %    

 B(I:U1,J:U2)=R(I:U1,J:U2);   %     1 to 5 and 1 to 5

% vc=sum(B(I:U1,J:U2));

% Fd=sum(vc);

 [x,y]=find(B==1);

 CX=mean(x);

 CY=mean(y);

 CXXX(E)=CX;

 CYYY(E)=CY;

 CXX(iir,jjr)=CX;

 CYY(iir,jjr)=CY;

      T(I:U1,J:U2)=B(I:U1,J:U2);

      J=J+t1;

      U2=U2+t1;

E=E+1;

   clear B x y 

      end

I=I+t1;

U1=U1+t1;

J=1;

U2=t1;

end

%plot and grid

%figure,imshow®

hold on

M10 = size(R,1);

N10 = size(R,2);

a=t1;

b=t1;

for k = 1:a:M10

    x = [1 N10]; 

   y = [k k]; 

    plot(x,y,'Color','white');

    set(findobj('Tag','MyGrid'),'Visible','on')

end

for k = 1:b:N10

    x = [k k]; 

    y = [1 M10];

    plot(x,y,'Color','white');

    set(findobj('Tag','MyGrid'),'Visible','on')

end

z = imread('empty.jpg');

r = imresize(z,[50,50]);

%figure,imshow(r);

hold on

%baseFileName = sprintf('figure_%d.jpg',k);

%set(0, 'DefaultFigureVisible', 'off');

plot(CYY,CXX,'k*');

[Mohammad Bhat]

My actual values are in CXX and CYY, the variables which are not used above are used for further processing...

[Mohammad Bhat]

Here is the original figure,actually , I am following the following algorithm:-

1.for i = 1 to number of columns C= width of B/w do

2.for j=1 to number of rows R =height of B/h do

3.V=V U{(Xm,Ym) | (Xm,Ym) is the center of mass of segment Sij}

4.return G..

[Mohammad Bhat]

I have fixed grid or segment size as 5 x 5 and original image size is 100 x 100

[Mohammad Bhat]

In a segment where there is no information or foreground pixels there, centre-of-mass is equal to zero.I have computed center of mass of each segmented x-coordinates in CXX and Y-coordinates in CYY....I am ploting , i am getting desired graph...But I need Adjacency Matrix...How to get that

[Mohammad Bhat]

CXX values

[Mohammad Bhat]

CYY values

[Jan]

Please, Mohammad, format your code to make it readable, see http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup#answer_18099. Then use the chance to edit the comment. One large comment is easier to read than 7 comments.

 I need Adjacency Matrix...How to get that

Again: I have posted a link to a page already, which offers different methods to get this matrix. Please answer my question, why these methods do not solve your problem.

I think, it does not matter where your CXX and CYY comes from.

[Mohammad Bhat]

Sir, I have found some way, please check it,

     Adj=zeros(size(original_image));

1. I have CXX and CYY

2. XX =CXX;

3. XX(isnan(XX))=[] % for empty segments of image (zero foreground pixels) X-COORDINATE

4.YY=CYY;

5. YY(isnan(YY))=[] % SIMILARLY FOR Y COORDINATE

6. X=XX';

7. Y=YY';

8. H=[ X Y ]

9.F =CEIL(H)

10 FOR I = 1: LENGTH ( F )

        xy=F(I:I,:)

         ROW1=xy(1);

         COL1=XY(2);

         Adj(COL1,ROW1)=1;

END

5.

[Jan]

Or as Matlab code:

X   = ceil(CXX(isfinite(CXX)));
Y   = ceil(CYY(isfinite(CYY)));
Adj = zeros(size(original_image));
for k = 1:numel(X)
  Adj(X(k), Y(k)) = 1;
end

Or without a loop:

X = ceil(CXX(isfinite(CXX)));
Y = ceil(CYY(isfinite(CYY)));
Adj = zeros(size(original_image));
Adj(sub2ind(size(Adj), X, Y)) = 1;

Note that "Y" might be the 1st coordinate.

But the result is not the adjacency matrix! I suggest the 3rd time now to read https://stackoverflow.com/questions/3277541/construct-adjacency-matrix-in-matlab and check, if these methods to create the wanted matrix solve your problem. I cannot reconsider why you ignore this suggestion.

[Mohammad Bhat]

Sir, I went thru your suggestion,since I am new to this forum,I will not repreat mistakes,I got the desired Adjacency matrix,.....Thank you all for patience and tolerance....

[Jan]

@Mohammad: You are welcome. The purpose of this forum is solving Matlab problem and this includes finding out, what the actual problems are.