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Run Length Encoding


Consider a matrix A with 15 elements,
A= [10 10 9 9 9 9 4 0 0 0 0 0 10 10 10]
In the given example,
10 has occurred 2 times, 9 has occurred 4 times, 4 has occurred once, 0 has occurred 5 times and 10 has occurred 3 times.
After Run length encoding, we obtain the matrix without any repetition in the adjacent elements, [10     9     4     0    10].  And the occurrences of each element [2     4     1     5     3]
Thus the matrix is reduced to 10 elements from 15 elements.
Let’s see how to code this reduction method.
Consider the above matrix A,
1.     Find the difference between adjacent elements. Use the function ‘diff(A)’ to find the difference. 
[0    -1     0     0     0    -5    -4     0     0     0     0    10     0     0]
2.     Convert it to logical format.  The elements without repetition are denoted with one and the repeated elements with zero.
 [0         0     0     0     1     1     0     0     0     0     1     0     0     1]
3.     Find the position of the elements that has the value one in the above step.
[2     6     7    12    15].
4.     Find the unique element values using the positions obtained from the above step. In the matrix A, the element at the position 2 is 10, the element at the position 6 is 9, the element at the position 7 is 4, the element at the position 12 is 0 and the element at the position 15 is 10.
[10     9     4     0    10]
5.     The first element in the matrix is 10, it has occurred 2 times. We obtained the occurrence of the first element alone from the matrix in the step 3. For the remaining elements, find the difference of the matrix in the step 3.
i.e. diff([2     6     7    12    15]); The result after concatenating the first element of the matrix obtained in step 3 with difference for the matrix in the step 3 is [2     4     1     5     3]
6.     Thus in the step 4 we obtain the elements without repetition,
[10     9     4     0    10] and the occurrences in step 5, [2     4     1     5     3].

MATLAB CODE:
A=[5 2 2 2 3 3 3 3 4 4 1 1 1 1 1 1 1 6 6 4 4]
F=[logical(diff(A)) 1];
In=find(F~=0);

Ele=A(In);

C=[In(1) diff(In)];

Result=zeros([numel(Ele) 2]);
Result(:,1)=Ele;
Result(:,2)=C;
display(Result);

SAMPLE OUTPUT:
Result =

     5     1
     2     3
     3     4
     4     2
     1     7
     6     2
     4     2
EXPLANATION:
5  has occurred 1 times, 2 has occurred 3 times, 3 has occurred 4 times, 4 has occurred 2 times, 1 has occurred 7 times, 6 has occurred 2 times and 4 has occurred 2 times.
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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.

Example:
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: http://angeljohnsy.blogspot.in/2011/06/how-to-draw-in-matlab.html



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: 
     Roundness=(4*Area*pi)/(Perimeter.^2) 
        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
   

MATLAB CODE:

%Measure Basic Image Properties without using 'regionprops' function
%Measure Area, Perimeter, Centroid , Equvidiameter, Roundness and Bounding Box
clc
%Read Original Image
I=imread('coins.png');
%Convert to Binary
B=im2bw(I);
                                                 
%Fill the holes
C=imfill(B,'holes');
                                                    
 %Label the image
[Label,Total]=bwlabel(C,8);
%Object Number
num=4;
[row, col] = find(Label==num);

                                         
                                        
                                   
                               





%To find Bounding Box
sx=min(col)-0.5;
sy=min(row)-0.5;
breadth=max(col)-min(col)+1;
len=max(row)-min(row)+1;
BBox=[sx sy breadth len];
display(BBox);
figure,imshow(I);
hold on;
x=zeros([1 5]);
y=zeros([1 5]);
x(:)=BBox(1);
y(:)=BBox(2);
x(2:3)=BBox(1)+BBox(3);
y(3:4)=BBox(2)+BBox(4);
plot(x,y);

                              

%Find Area
Obj_area=numel(row);
display(Obj_area);
%Find Centroid
X=mean(col);
Y=mean(row);
Centroid=[X Y];
display(Centroid);
plot(X,Y,'ro','color','r');
hold off;
                                  

%Find Perimeter
BW=bwboundaries(Label==num);
c=cell2mat(BW(1));
Perimeter=0;
for i=1:size(c,1)-1
Perimeter=Perimeter+sqrt((c(i,1)-c(i+1,1)).^2+(c(i,2)-c(i+1,2)).^2);
end
display(Perimeter);
                                

%Find Equivdiameter
EquivD=sqrt(4*(Obj_area)/pi);
display(EquivD);


%Find Roundness
Roundness=(4*Obj_area*pi)/Perimeter.^2;
display(Roundness);
                          


%Calculation with 'regionprops'(For verification Purpose);
%Sdata=regionprops(Label,'all');
%Sdata(num).BoundingBox
%Sdata(num).Area
%Sdata(num).Centroid
%Sdata(num).Perimeter
%Sdata(num).EquivDiameter
                                           


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