Wednesday, November 21, 2012


Auto Cropping- Based on labeling the connected components 

 This post is about labeling the connected components in a binary image and crop the connected components based on the label. The main two functions used for this simple operation are ‘bwlabel’ and ‘regionprops’. 

  I used ‘bwlabel’ to label the connected components.  After labeling, I used ‘regionprops’ function to find the rectangle containing the region.  To find the rectangle points, I used ‘BoundingBox’ property.Then the labeled components are automatically cropped and the image is displayed. To crop an image, ‘imcrop’ function is used.


figure,imshow(A); title('Original Image');


%Convert the Image to binary
%Fill the holes
%Label the connected components
figure,imshow(C); title('Labelled Image');

Add caption

%Rectangle containing the region
%Crop all the Coins 
for i=1:Total
    Name=strcat('Object Number:',num2str(i));
    figure,imshow(Img); title(Name);

Add caption

Another Example:


Labeled Image

Bit-Plane Slicing 

Digitally, an image is represented in terms of pixels.

These pixels can be expressed further in terms of bits.
Consider the image ‘coins.png’ and the pixel representation of the image.

Consider the pixels that are bounded within the yellow line. The binary formats for those values are (8-bit representation)

The binary format for the pixel value 167 is 10100111
Similarly, for 144 it is 10010000
This 8-bit image is composed of eight 1-bit planes.
Plane 1 contains the lowest order bit of all the pixels in the image.

And plane 8 contains the highest order bit of all the pixels in the image.

Let’s see how we can do this using MATLAB
A=[167 133 111
      144 140 135
      159 154 148]

B=bitget(A,1);  %Lowest order bit of all pixels
‘bitget’ is a MATLAB function used to fetch  a bit from the specified position from all the pixels.
B=[1 1 1
      0 0 1
      1 0 0]
B=bitget(A,8);%Highest order bit of all pixels
B=[1 1 0
      1 1 1 
      1 1 1]
%Bit Planes from 1 to 8. Output Format: Binary

subplot(2,2,1);imshow(logical(B));title('Bit plane 1');
subplot(2,2,2);imshow(logical(B));title('Bit plane 2');
subplot(2,2,3);imshow(logical(B));title('Bit plane 3');
subplot(2,2,4);imshow(logical(B));title('Bit plane 4');

subplot(2,2,1);imshow(logical(B));title('Bit plane 5');
subplot(2,2,2);imshow(logical(B));title('Bit plane 6');
subplot(2,2,3);imshow(logical(B));title('Bit plane 7');
subplot(2,2,4);imshow(logical(B));title('Bit plane 8');

Image reconstruction using n bit planes.

1.     The nth plane in the pixels are multiplied by the constant 2^n-1
2.     For instance, consider the matrix
A= A=[167 133 111
      144 140 135
      159 154 148] and the respective bit format
3.     Combine the 8 bit plane and 7 bit plane.
For 10100111, multiply the 8 bit plane with 128 and 7 bit plane with 64.
4.     Repeat this process for all the values in the matrix and the final result will be
[128 128 64
 128 128 128
128 128 128]
%Image reconstruction by combining 8 bit plane and 7 bit plane
Image reconstructed using 8 and 7 bit planes
‘bitset’ is used to set  a bit at a specified position. Use ‘bitget’ to get the bit at the positions 7 and 8 from all the pixels in matrix A and use ‘bitset’ to set these bit values at the positions 7 and 8 in the matrix B.
%Image reconstruction by combining 8,7,6 and 5 bit planes
Image reconstructed using 5,6,7 and 8 bit planes

Find Area, Perimeter, Centroid, Equivdiameter, Roundness and Bounding Box without Using MATLAB Function ‘regionprops’ 


In MATLAB, the function ‘regionprops’ is used to measure the image properties. Here are some basic properties computed without using the function.
          Read an image and find the connected components using ‘bwlabel’ function.
Using the Labeled matrix as an input, the properties can be measured.

A=[1 0 0 1
      1 1 1 1
      0 0 1 1]

To find Area:
·        The total number of ‘ON’ pixels in the image.

The number of ones in the matrix is 8.
To find Centroid:
·        Find the row and column having pixel value one. Eg.[row,column]=find(label==1)
Row=[ 1     2     2     2     3     1     2     3]
Column=[ 1     1     2     3     3     4     4     4]
·        Find the mean of the row and column having pixel value one.
Mean of Row=2 and mean of column= 2.75
To find the Bounding Box:
·        We need 4 points, starting position(x,y) , length and breadth.
·        Minimum value of row and column minus 0.5 gives starting position(x,y) respectively
·        Minimum value of  row=1-0.5=0.5
·        Minimum value of column=1-0.5=0.5
·        Maximum value of column – minimum value of column+1 gives breadth of the box
·        Maximum value of column=4
·        Max value-min value of column=3+1
·        Maximum value of row- minimum value of row +1gives length of the box
·        maximum value of row=3
·        Max value – Min value=2+1
·        Bounding Box value for the given example:0.5000    0.5000    4.0000    3.0000
·        For more details on how to draw a rectangle check here:

To find the Perimeter
·        Find the boundary of the labeled component
Boundary pixels:
     1     1
     2     2
     2     3
     1     4
     2     4
     3     4
     3     3
     2     2
     2     1
     1     1
·        Find the distance between the each adjoining pair of pixels around the border of the region.
·        Use the distance formula:
·        For instance, calculate the distance between the two points (1,1) and (2,2). distance=sqrt((2-1).^2+(2-1).^2)=1.41
·        Similarly, the distance is computed for all the pixel positions.
·        The perimeter for the given example is 10.2426
To find the Roundness:
·        Roundness of  an object can be determined using the formula: 
        If the Roundness is greater than 0.90 then, the object is circular in shape.
     Result= (4*8*3.14)/10.2426.^2=0.9582

To find the Equivdiameter
·        Formula: sqrt(4*Area/pi).
     Equivdiameter for the given example:3.1915


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