Matlab bottom source code realizes image corrosion and expansion operation (consistent with Halcon effect)

Theoretical basis

       The operation of mathematical morphology is based on the two basic operations of corrosion and expansion , Several other commonly used mathematical morphological operations are introduced , The most common basic operations are seven , Namely ： inflation , corrosion , Open operation , Closed operation , hit , Refinement and coarsening , They are the basis of all morphology , Using these operations and their combinations, we can analyze and process the shape and structure of the image , Common in image preprocessing , Segment the back image , feature extraction , boundary detection , Lay the foundation for image filtering .
       Corrosion is one of the two most basic operations in mathematical morphology , The function of corrosion in mathematical morphology is to eliminate the boundary points of objects , Shrink the boundary inward , Objects smaller than structural elements can be removed . In this way, structural elements of different sizes are selected , You can remove objects of different sizes . For example, there is a small channel between the two areas , The two areas can be separated by corrosion . The mathematical expression of corrosion is
                                                      $S=X⨂B=\left\{x,y\mid B_{xy}\subseteq X\right\}$
       Expansion is another basic operation in mathematical morphology besides corrosion . The role of expansion in mathematical morphology is just opposite to that of corrosion , It is an extension of the boundary points of binary objects , Merge all the background points in contact with the object into the object . If the distance between two objects is relatively close , Then the expansion operation may connect two objects , Inflation is very useful for filling holes . The mathematical expression of inflation is ：
                                                      $S=X⨁B=\left\{x,y\mid B_{xy}\cap X\ne \phi \right\}$

Image corrosion operation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Image etching 
%Author:Zhu
% Time ：2022.6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc;
image = imread("F:\\fabrik.png");
image_matrix=image(:,:,1);
image_matrix=double(image_matrix);
[height,width,channels]=size(image);
image_out = zeros(height,width);

% The size of the input convolution kernel 
maskHeight=11;
maskWidth=11;

% Current pixel value 
currentPixel=0;

for i=(maskHeight+1)/2:height-(maskHeight+1)/2
    for j=(maskWidth+1)/2:width-(maskWidth+1)/2
        minValue = 255;
        % Update Max 
        for k=1:maskHeight
            for p=1:maskWidth
                currentPixel = image_matrix(i-(maskHeight+1)/2+k,j-(maskWidth+1)/2+p);
                if(currentPixel<minValue) minValue = currentPixel; end end end % Update the value of the convolution kernel Center  image_out(i,j)=minValue; end end % Image edge pixel modification  for i=1:height for j=1:width if(i>(maskHeight+1)/2 && i<height-(maskHeight+1)/2 && j>(maskWidth+1)/2 && j<width-(maskWidth+1)/2)
            image_out(i,j)= image_out(i,j);
        else
            image_out(i,j)= image_matrix(i,j);
        end
    end
end

% Display images 
image_out = uint8(image_out);
subplot(1,2,1);
imshow(image);
subplot(1,2,2);
imshow(image_out);

Image expansion operation

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Image expansion 
%Author:Zhu
% Time ：2022.6
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc;
image = imread("F:\\fabrik.png");
image_matrix=image(:,:,1);
image_matrix=double(image_matrix);
[height,width,channels]=size(image);
image_out = zeros(height,width);

% The size of the input convolution kernel 
maskHeight=11;
maskWidth=11;

% Current pixel value 
currentPixel=0;

for i=(maskHeight+1)/2:height-(maskHeight+1)/2
    for j=(maskWidth+1)/2:width-(maskWidth+1)/2
        maxValue = 0;
        % Update Max 
        for k=1:maskHeight
            for p=1:maskWidth
                currentPixel = image_matrix(i-(maskHeight+1)/2+k,j-(maskWidth+1)/2+p);
                if(currentPixel>maxValue)
                    maxValue = currentPixel;
                end
            end
        end
        % Update the value of the convolution kernel Center 
        image_out(i,j)=maxValue;
    end
end

% Image edge pixel modification 
for i=1:height
    for j=1:width
        if(i>(maskHeight+1)/2 && i<height-(maskHeight+1)/2 && j>(maskWidth+1)/2 && j<width-(maskWidth+1)/2)
            image_out(i,j)= image_out(i,j);
        else
            image_out(i,j)= image_matrix(i,j);
        end
    end
end

% Display images 
image_out = uint8(image_out);
subplot(1,2,1);
imshow(image);
subplot(1,2,2);
imshow(image_out);

Halcon operator

* Corrosion image 
gray_erosion_rect (Image, ImageMin, 11, 11)
* Dilated image 
gray_dilation_rect (Image, ImageMax, 11, 11)

Halcon Compare with the image effect of the source code

Halcon Corrosion effect

Matlab Source code corrosion effect

Halcon Expansion effect

Matlab Source expansion effect