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: https://www.imageeprocessing.com/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);

%Refer:https://www.imageeprocessing.com/2011/06/how-to-draw-in-matlab.html

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