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