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  • 傅里叶变换之低通滤波、sobel边缘检测之matlab实现

      滤波是傅里叶变换的一个主要应用,因为在频域中可以更好的理解图像以及了解如何对它进行处理。

    以下是低通滤波的:

    function output = low_filter(image,value)
    %Retain centred transform components inside circle of radius
    %
    %  Usage: new image = low_filter(image,number)
    %
    %  Parameters: image      - array of points 
    %              value      - radius of filter
    
    %get dimensions
    [rows,cols]=size(image); 
    
    %filter the transform
    for x = 1:cols %address all columns
      for y = 1:rows %address all rows
        if (((y-(rows/2))^2)+((x-(cols/2))^2)-(value^2))>0 
            output(y,x)=0; %discard components outside the circle
        else
            output(y,x)=image(y,x); %and keep the ones inside
        end
      end
    end

    计算哈特利变换

    输出真实的图像作为结果:

    function trans = Hartley(image)
    %  Usage: [new image] = Hartley(image)
    %
    %  Parameters: image      - array of points 
    
    %get dimensions
    [rows,cols]=size(image); 
    
    trans(1:rows,1:cols)=0;
    
    %compute transform
    for u = 1:cols %address all columns
        for v = 1:rows %address all rows
            sum=0;
            for x = 1:cols %address all columns 
                for y = 1:rows %address all rows
                    %Eq. 2.41
                    mux=2*pi*(u-1)*(x-1)/cols;
                    nvy=2*pi*(v-1)*(y-1)/rows;
                    sum=sum+(image(y,x)*(cos(nvy)+sin(nvy))*(cos(mux)+sin(mux)));
                end
            end
            trans(v,u)=sum/sqrt(rows*cols);
        end
    end
    

     sobel 边缘检测

    function edge = Sobel_edges(image)
    % Gives Sobel for Canny operator
    %
    %  Usage: [new image] = Sobel_edges(image)
    %
    %  Parameters: image      - array of points
    
    %get dimensions
    [rows,cols]=size(image);
    
    %set the output image to black (0)
    edge(1:rows,1:cols,3)=0;
    
    %then form the difference
    for x = 2:cols-1 %address all columns except border
      for y = 2:rows-1 %address all rows except border
        Sobel_y=image(y+1,x+1)+2*image(y+1,x)+image(y+1,x-1)-...
                 image(y-1,x+1)-2*image(y-1,x)-image(y-1,x-1);
        Sobel_x=image(y-1,x+1)+2*image(y,x+1)+image(y+1,x+1)-...
                 image(y-1,x-1)-2*image(y,x-1)-image(y+1,x-1);
        edge(y,x,1)=Sobel_x;
        edge(y,x,2)=Sobel_y;
        edge(y,x,3)=floor(sqrt(Sobel_x*Sobel_x+Sobel_y*Sobel_y));
      end
    end
    

     

    参考资料:计算机视觉特征提取与图像处理 Mark S.Mixon

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  • 原文地址:https://www.cnblogs.com/qianyuesheng/p/15003119.html
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