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## Smooth Contour Data with Convolution Filter

This example shows how to use a convolution filter to remove high-frequency components from a matrix to smooth the matrix for contour plotting.

The conv2 and filter functions can remove high-frequency components from a matrix representing a continuous surface or field to make the underlying data easier to visualize.

Create a function of two variables and plot the contour lines at a specified, fixed interval.

Z = peaks(100);
clevels = -7:1:10; % contour levels for all plots

figure
contour(Z,clevels)
axis([0,100,0,100])
title('Peaks Surface (underlying data)')

Add uniform random noise with a mean of zero to the surface and plot the resulting contours. Irregularities in the contours tend to obscure the trend of the data.

ZN = Z + rand(100) - .5;

figure
contour(ZN,clevels)
axis([0,100,0,100])

Specify a 3-by-3 convolution kernal, F, for smoothing the matrix and use the conv2 function to attenuate high spatial frequencies in the surface data. Plot the contour lines.

F = [.05 .1 .05; .1 .4 .1; .05 .1 .05];
ZC = conv2(ZN,F,'same');

figure
contour(ZC, clevels)
axis([0,100,0,100])
title('Noisy Surface (smoothed once)')

Smooth the surface one more time using the same operator and plot the contour lines. A larger or more uniform kernal can achieve a smoother surface in one pass.

ZC2 = conv2(ZC,F,'same');

figure
contour(ZC2, clevels)
axis([0,100,0,100])
title('Noisy Surface (smoothed twice)')