Smoothing data using convolution

         Convolution can be used to smooth two-dimensional data containing high-frequency components . Use peaks Function to create 2D data , And plot the data at each contour level .

Z = peaks(100);
levels = -7:1:10;
contour(Z,levels)

         As shown in the figure ：

         Insert random noise into the data and draw noisy contours .

Znoise = Z + rand(100) - 0.5;
contour(Znoise,levels)

         As shown in the figure ：

        MATLAB Medium conv2 The convolution() function computes the convolution of two-dimensional data using a specified kernel , The elements of this kernel define how to remove or enhance the features of the original data . The size of the core does not have to be the same as the input data . The small kernel is enough to smooth the data containing only a few frequency components . Larger cores can adjust the frequency response more accurately , To get a smoother output .

         Define a 3×3 nucleus K And use conv2 Yes Znoise Smooth the noisy data in . Draw smoothed contour lines .conv2 Medium 'same' Option to make the output the same size as the input .

K = (1/9)*ones(3);
Zsmooth1 = conv2(Znoise,K,'same');
contour(Zsmooth1, levels)

As shown in the figure ：

         use 5×5 Check the noisy data for smoothing , And draw new contours . 

K = (1/25)*ones(5);
Zsmooth2 = conv2(Znoise,K,'same');
contour(Zsmooth2,levels)

         As shown in the figure ：