Image Erosion without using MATLAB function 'imerode'

In MATLAB, ‘imerode’ is a function used to make the objects thin. MATLAB code without using 'imerode' function and explanation is provided here. The input image is binary.

MATLAB CODE:

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

%Structuring element

B=[1 1 0];

%Pad array with ones on both sides

C=padarray(A,[0 1],1);

%Intialize the matrix D of size A with zeros

D=false(size(A));

for i=1:size(C,1)

    for j=1:size(C,2)-2

        In=C(i,j:j+2);

        %Find the position of ones in the structuring element

        In1=find(B==1);

        %Check whether the elements in the window have the value one in the

        %same positions of the structuring element

        if(In(In1)==1)

        D(i,j)=1;

        end

    end

end

display(D);

Explanation:

1.     Consider a matrix A and a structuring element B.

2.     Initialize a matrix D of size A with zeros.

3.     Construct a window of size B with the elements of matrix A.

4.     Check whether the ones in the structuring element B overlap the ones in the window.

5.     If it overlaps, then update D with one else zero.

Example 2:

A=imread('circles.png');

figure,imshow(A);

Original Image

%Structuring element

B=getnhood(strel('disk',11));

m=floor(size(B,1)/2);

n=floor(size(B,2)/2);

%Pad array on all the sides

C=padarray(A,[m n],1);

%Intialize a matrix with size of matrix A

D=false(size(A));

for i=1:size(C,1)-(2*m)

    for j=1:size(C,2)-(2*n)

       

        Temp=C(i:i+(2*m),j:j+(2*n));

       

        D(i,j)=min(min(Temp-B));

      

    end

end

figure,imshow(~D);

After Erosion

  

Image Dilation without using 'imdilate' function

           In MATLAB, ‘imdilate’is the function that dilates the image using a structuring element. Let’s learn how this function works using some examples and codes.

MATLAB CODE:

Example 1:

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

%Structuring element

B=[1 0 0; 0 1 0; 0 0 1];

%Pad zeros on all the sides

C=padarray(A,[1 1]);

%Intialize a matrix of matrix size A with zeros

D=false(size(A));

for i=1:size(C,1)-2

    for j=1:size(C,2)-2

        %Perform logical AND operation

        D(i,j)=sum(sum(B&C(i:i+2,j:j+2)));

    end

end

display(D);

Example 2:

A=imread('text.png');

Original Image

A=im2bw(A);
%Structuring element

B2=getnhood(strel('line',7,90));

m=floor(size(B2,1)/2);

n=floor(size(B2,2)/2);

%Pad array on all the sides

C=padarray(A,[m n]);

D=false(size(A));

for i=1:size(C,1)-(2*m)

    for j=1:size(C,2)-(2*n)

        Temp=C(i:i+(2*m),j:j+(2*n));

        D(i,j)=max(max(Temp&B2));

    end

end

figure,imshow(D);

Dilated Image

Example 3:(Method 2)

A=imread('text.png');

A=im2bw(A);
%Structuring element

B=[1 1 1 1 1 1 1;];
C=padarray(A,[0 3]);

D=false(size(A));

for i=1:size(C,1)

    for j=1:size(C,2)-6

        D(i,j)=sum(B&C(i,j:j+6));

    end

end

figure,imshow(D);

Dilated image

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     1     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.

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

                                           

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.

MATLAB CODE:

A=imread('coins.png');
figure,imshow(A); title('Original Image');

                                 

%Convert the Image to binary
B=im2bw(A);
 
%Fill the holes
C=imfill(B,'holes');
 
%Label the connected components
[Label,Total]=bwlabel(C,8);
figure,imshow(C); title('Labelled Image');

%Rectangle containing the region
Sdata=regionprops(Label,'BoundingBox');
 
%Crop all the Coins 
for i=1:Total
    Img=imcrop(A,Sdata(i).BoundingBox);
    Name=strcat('Object Number:',num2str(i));
    figure,imshow(Img); title(Name);
end

Another Example:

'coins.png'

Labeled Image

Text On Sphere - MATLAB CODE

Text on Sphere-MATLAB CODE

              We can see how to wrap a text around a sphere. First obtain the x,y and z co-ordinates of  the sphere.These co-ordinates can be used as an input for surface object.

Surface object generates sphere using the co-ordinates.  Example:[x,y,z]=sphere(25); surface(x,y,z);

Now read a text image and convert it into binary.  Label the components in the image. You can also check how to label components without BWLABELfunction in MATLAB.   Now use the labeled image as a CDATA value in surface object.

Example: surface(x,y,z, ‘CDATA’,matrix);

MATLAB CODE:

%Input a text image
A=imread('quotes.png');

         

A=~im2bw(A);
B=bwlabel(A,8);
F=double(B);
mytext=flipud(F);


% Create the surface.
[x,y,z] = sphere(100);


figure,surface(x,y,z,'CData',mytext,'FaceColor','texturemap','FaceLighting','phong','EdgeLighting','phong','EdgeColor','none');

%set the colormap. Some built-in colormaps are pink, copper, jet, hot...

%colormap pink

%Here I created my own colormap, the colors are white[1 1 1], black[0 0 0] and %blue [0 0 1]. Initialize the map with zeros(black) for 256x3 matrix. %Add blue 
%color to some components(words). Initialize the first row with [ 1 1 1](white).

map=zeros([253 3]);
map(1,:)=0;
map(50:80,3)=1;
colormap(map);



%Create light object
light('position',[1 2 0 ],'Style','infinite','color',[0.8 0.7 0.8]);
light('position',[-2 -3 0 ],'color',[0.8 0.7 0.8]);


%Specify the viewpoint
axis square off
view(12,0);

Another Example: To create a GLOBE from a WORLD MAP

INPUT IMAGE

To convert a RGB image into SPHERE:
MATLAB CODE:

A=imread('mountain.jpg');
[mytext,map]=rgb2ind(A,256);
mytext=flipud(mytext);

% Create the surface.
[x,y,z] = sphere(100);

figure,surface(x,y,z,'CData',mytext,'FaceColor','texturemap','FaceLighting','phong','EdgeLighting','phong','EdgeColor','none');
%set the colormap. 

colormap(map);


%Create light object
light('position',[1 2 0 ],'Style','infinite','color',[0.8 0.7 0.8]);
light('position',[-2 -3 0 ],'color',[0.8 0.7 0.8]);


%Specify the viewpoint
axis square off
%view(12,0);
view(180,0);

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