Local Thresholding in blocks error

I'm trying to do Local Thresholding. I have to divide an image into SxS blocks and then apply the thresholding. But I get the error "Index in position 2 exceeds array bounds (must not exceed 1).", I think it has something to do with my for loop. Can anyone help me? I would be very grateful.

Here is my code:

function []=my_function(filename,S)
IM=imread(filename);
    if size(IM,3)==3 
        IC=rgb2gray(IM);
    else 
        IC=IM;
    end
    
TOtsu=graythresh(IC);

[NL,NC]=size(IC);
MNC=round(NC/S)*ones(S); 
MNC(:,S)=NC-(S-1)*round(NC/S);
MNL=round(NL/S)*ones(S); 
MNL(:,S)=NL-(S-1)*round(NL/S);
    
for f=1:S
    for g=1:S
        NLB=MNL(f,g); %lines of the block
        NCB=MNC(f,g); %columns of the block
    end
end  

ICblocks=[NLB;NCB];

for i=1:NLB
   for j=1:NCB
       if var(ICblocks(i,j))<1 %image is uniform
          if (ICblocks(i,j) < TOtsu)
                    IFinal(i,j) = 0; 
          elseif (ICblocks(i,j) > TOtsu)
                    IFinal(i,j) = 1;
           end
       else %image is not uniform
            IFinal(i,j)=imbinarize(IC,TOtsu);
       end
   end
end
subplot(1,2,1);imshow(IC);title('IC')   
subplot(1,2,2);imshow(IFinal);title('Threshold Local')   
end

Answer 1

[yanqi liu]

yes，sir，may be check the loop process，such as

filename = 'football.jpg';
S = 3;

IM=imread(filename);
if size(IM,3)==3
    IC=rgb2gray(IM);
else
    IC=IM;
end
sz = size(IC);
TOtsu=graythresh(IC);
IFinal = [];

for f=0:S-1
    for g=0:S-1
        recti = round([sz(2)/S*f+1, sz(1)/S*g+1, sz(2)/S-1, sz(1)/S-1]);
        ICfg = imcrop(IC, recti);
        TOtsufg=graythresh(ICfg);
        IFinal(recti(2):recti(2)+recti(4), recti(1):recti(1)+recti(3)) = imbinarize(ICfg,TOtsufg);
    end
end


subplot(1,2,1);imshow(IC);title('IC')
subplot(1,2,2);imshow(IFinal);title('Threshold Local')

[Joana Teixeira]

Hello! This code is changing the purpose that i want to do.

Answer 2

[Walter Roberson]

filename = 'football.jpg';
S = 3;

my_function(filename, S);

  Name            Size                Bytes  Class     Attributes

  IC            256x320               81920  uint8               
  ICblocks        2x1                    16  double              
  IM            256x320x3            245760  uint8               
  MNC             3x3                    72  double              
  MNL             3x3                    72  double              
  NC              1x1                     8  double              
  NCB             1x1                     8  double              
  NL              1x1                     8  double              
  NLB             1x1                     8  double              
  S               1x1                     8  double              
  TOtsu           1x1                     8  double              
  f               1x1                     8  double              
  filename        1x12                   24  char                
  g               1x1                     8  double              
  i               1x1                     8  double              
  j               1x1                     8  double              

  Name            Size                Bytes  Class     Attributes

  IC            256x320               81920  uint8               
  ICblocks        2x1                    16  double              
  IFinal          1x1                     8  double              
  IM            256x320x3            245760  uint8               
  MNC             3x3                    72  double              
  MNL             3x3                    72  double              
  NC              1x1                     8  double              
  NCB             1x1                     8  double              
  NL              1x1                     8  double              
  NLB             1x1                     8  double              
  S               1x1                     8  double              
  TOtsu           1x1                     8  double              
  f               1x1                     8  double              
  filename        1x12                   24  char                
  g               1x1                     8  double              
  i               1x1                     8  double              
  j               1x1                     8  double              

Index in position 2 exceeds array bounds. Index must not exceed 1.

Error in solution>my_function (line 34)
if var(ICblocks(i,j))<1 %image is uniform

function []=my_function(filename,S)
IM=imread(filename);
    if size(IM,3)==3 
        IC=rgb2gray(IM);
    else 
        IC=IM;
    end
    
TOtsu=graythresh(IC);

[NL,NC]=size(IC);
MNC=round(NC/S)*ones(S); 
MNC(:,S)=NC-(S-1)*round(NC/S);
MNL=round(NL/S)*ones(S); 
MNL(:,S)=NL-(S-1)*round(NL/S);
    
for f=1:S
    for g=1:S
        NLB=MNL(f,g); %lines of the block
        NCB=MNC(f,g); %columns of the block
    end
end  

Look at that loop. You are ovewriting all of NLB and all of NCB each iteration of the loops. f and g are each scalars, so you are overwriting them with scalars.

ICblocks=[NLB;NCB];

So after the loop, NLB and NCB are each scalars. You create a column vector from that, which is going to give you a 2 x 1 result in ICBlocks

for i=1:NLB
   for j=1:NCB

NLB and NCB are each scalars -- the last entries in the MNL and MNC arrays.

       whos
       if var(ICblocks(i,j))<1 %image is uniform

and you use them to try to index ICblocks, which is 2 x 1.

          if (ICblocks(i,j) < TOtsu)
                    IFinal(i,j) = 0; 
          elseif (ICblocks(i,j) > TOtsu)
                    IFinal(i,j) = 1;
           end
       else %image is not uniform
            IFinal(i,j)=imbinarize(IC,TOtsu);
       end
   end
end
subplot(1,2,1);imshow(IC);title('IC')   
subplot(1,2,2);imshow(IFinal);title('Threshold Local')   
end

[Walter Roberson]

Your MNL and MNC arrays are calculating the number of row and columns to use for each block, taking into account that the image might not be an exact multiple of the block size. That calculation in itself is not a bad thing.

You later take var() of something. You obviously want to take the variance of a block extracted from the image. To do that you need to know the starting and ending column numbers of the block, and the starting and ending row numbers of the block. But your code does not calculate starting and ending row numbers. You could try calculating them by taking your index and multiplying by the block size (with a small offset), but if you do that, then you lose the advantage of having stored the sizes in the arrays.

I would suggest that you cumsum() the MNL and MNC with a starting offset of 1. For example,

MNL = [3 3 3 2]

MNL = 1×4

3 3 3 2

Lbounds = cumsum([1, MNL])

Lbounds = 1×5

1 4 7 10 12

and now block #K vertically would be rows Lbounds(K):Lbounds(K+1)-1