smoothdata2

Create a matrix containing noise, and visualize the matrix along the z-dimension using a surface plot.

A = peaks;
rng(0,"twister")
A = A + 0.5*randn(size(A));

surf(A)

Smooth the data using a moving average.

B = smoothdata(A);

Visualize the smoothed data.

surf(B)

In this example, explore and compare 2D smoothing methods. Each method has its own advantages and is suitable for different types of data and noise characteristics.

Create a matrix of data that is discretized and has sharp edges, and visualize the matrix using a surface plot.

[bins,edges] = discretize(peaks,10);
A = edges(bins);

surf(A)

Smooth the data using moving statistic smoothing methods.

B = smoothdata2(A);
B2 = smoothdata2(A,"movmedian");

Compare the results of the smoothing methods by visualizing the smoothed data. The moving mean method is preferable to the moving median method for discretized 2D data with sharp edges. While the moving median method is robust against outliers, it may not adequately address the sharp edges in the data due to its focus on the middle value alone.

tiledlayout(2,1)

nexttile
surf(B)
title("Mean")

nexttile
surf(B2)
title("Median")

Create a matrix with sharp variations occurring over an area smaller than the size of the smoothing window.

x = 1:59;
y = sin(x/5*pi);
A2 = y + y';

figure
surf(A2)

Smooth the data using a moving statistic smoothing method and a local regression smoothing method.

B3 = smoothdata2(A2,"movmean",9);
B4 = smoothdata2(A2,"gaussian",9);

Compare the results of the smoothing methods by visualizing the smoothed data. The Gaussian smoothing method is better suited than the moving mean method for smoothing data with sharp variations due to its ability to preserve the sharp features while reducing noise. Unlike the moving mean method, which applies a simple average over the window, Gaussian smoothing uses a weighted average that assigns higher weights to nearby points.

tiledlayout(2,1)

nexttile
surf(B3)
title("Mean")

nexttile
surf(B4)
title("Gaussian-Weighted Average")

Create a matrix containing noise, and visualize the matrix along the z-dimension using a heatmap chart.

A = peaks(25);
rng(0,"twister")
A = A + 6*randn(size(A));

heatmap(A)

Smooth the data by averaging over each 2-D window of A. Define the moving window as a 2-by-3 block of entries neighboring the current element.

B = smoothdata2(A,"movmean",{2 3});

Smooth the data over a larger moving window that is a 4-by-4 block of entries.

B2 = smoothdata2(A,"movmean",4);

Compare the results of the window sizes by visualizing the smoothed data.

tiledlayout(2,1)

nexttile
heatmap(B,Title="2-by-3 Window")

nexttile
heatmap(B2,Title="4-by-4 Window")

Create a matrix containing noise, and visualize the matrix using a filled 2-D contour plot.

A = peaks;
rng(0,"twister")
A = A + 4*randn(size(A));

contourf(A);
colorbar

Smooth the data by averaging over each 2-D window of A. smoothdata2 determines the window size heuristically based on the input data and the default window size factor 0.25. Return the window size.

[B,winsize] = smoothdata2(A);
winsize

winsize=1×2 cell array
    {[3]}    {[3]}

Smooth using a larger window size, resulting in more smoothing, by specifying a larger window size factor.

[B2,winsize2] = smoothdata2(A,SmoothingFactor=0.5);
winsize2

winsize2=1×2 cell array
    {[5]}    {[5]}

Compare the results of the window size factors by visualizing the smoothed data.

tiledlayout(2,1)

nexttile
contourf(B)
title("Window Size Factor 0.25")
colorbar

nexttile
contourf(B2)
title("Window Size Factor 0.5")
colorbar

Create a matrix of nonuniformly spaced data. Specify the sample points in vectors xs and ys.

t = linspace(0,10,30);
xs = cumsum(sin(pi/11*t));
ys = xs;
A = sin(xs'/5)*cos(ys/5);

rng(0,"twister")
A = A+randn(size(A))*0.5;

Visualize the matrix using a mesh surface plot.

m = mesh(xs',ys,A,FaceAlpha=0.5);
m.FaceColor = "flat";
view(0,90)

Smooth the data using linear regression over each 2-D window of A. Specify the window size, and specify the x-axis and y-axis locations of the data.

B = smoothdata2(A,"loess",{[2 3],[4 3]},SamplePoints={xs,ys});

Visualize the smoothed data.

m2 = mesh(xs',ys,B,FaceAlpha=0.5);
m2.FaceColor = "flat";
view(0,90)