MATLAB: Smoothing 2D scattered points

filterimageimage processinginterpolationSignal Processing Toolboxsmoothing

Hi Friends,

Is there anyway to smooth 2D scattered points?

I drew my question in this picture:

on the left we have an scattered path of points, but, rationally one can think of a smoothed representing set of points (black dots) in the right picture.

Thank you very much.

Best Answer

Yes. You can use something like spline or sgolayfilt() to smooth both the x and y coordinates independently. See attached demo. Here is the main part:

% Now smooth with a Savitzky-Golay sliding polynomial filter
windowWidth = 45
polynomialOrder = 2
smoothX = sgolayfilt(x, polynomialOrder, windowWidth);
smoothY = sgolayfilt(y, polynomialOrder, windowWidth);

Attach your x and y data if you can't figure it out from the well commented demo code.

Related Solutions

MATLAB: Using polyfit to fit 5 individual lines that intersect the y-axis

A = importdata('VERY_EXPENSIVE.txt');
x = A(:,1);
y = A(:,2) ;
% 
xi = 0:50:250 ;
xi(1) = min(x) ; xi(end) = max(x) ;
yi = interp1(x,y,xi) ;
C = zeros(5,1) ;   % y-intercept 
hold on
for i = 1:5
    x1 = x(x>=xi(i) & x<xi(i+1)) ;
    y1 = interp1(x,y,x1) ;
    p = polyfit(x1,y1,1) ;
    C(i) = p(2) ;
    y2 = polyval(p,x1) ;
    plot(x1,y1,'.') ;
    plot(x1,y2,'-') ;
end

MATLAB: How can plot with smooth line

With your data, my demo would become this:

% Create the original knot points.
xInitial = [1.6 1.1 .6 .1 .4 .9 1.4 1.9];
yInitial = [1 1.5 2 2.5 3 3.5 4 4.5];
lengthX = length(xInitial);
% flip sideways so there is only 1 y for every x
x = yInitial;
y = xInitial;
% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);
grid on;
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;
newXSamplePoints = linspace(min(x), max(x), lengthX * samplingRateIncrease);
smoothedY = spline(x, y, newXSamplePoints);
% Now flip back
ySmooth = newXSamplePoints;
xSmooth = smoothedY;
% Plot smoothedY and show how the line is

% smooth, and has no sharp bends.

hold on; % Don't destroy the first curve we plotted.

plot(newXSamplePoints, smoothedY, '-ob');
title('Spline Interpolation Demo', 'FontSize', 20);
legend('Original Points', 'Spline Points');
figure;
plot(xInitial, yInitial, '-sr', 'LineWidth', 2);
% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(xSmooth, ySmooth, '-ob');
grid on;

You can also use a Savitzky-Golay filter to smooth curves, and I attach a demo for that.

Best Answer

Related Solutions

MATLAB: Using polyfit to fit 5 individual lines that intersect the y-axis

MATLAB: How can plot with smooth line

Related Question