Savitsky-Golay Filter Problem - Smoothing 3D line

Question

William 2015-4-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/213049-savitsky-golay-filter-problem-smoothing-3d-line

评论： William 2015-4-23

I wanted to smooth a 3d line using the Savitzky-Golay filter, but for this example is seems to not work properly. Any ideas why, and how to fix it?

% Savitzky–Golay filter (sgolayfilt) - smoothing individual axes
windowWidth = 27;    %Standard example values
polynomialOrder = 3;
xsg=sgolayfilt(points(:,1),polynomialOrder, windowWidth);
ysg=sgolayfilt(points(:,2),polynomialOrder, windowWidth);
zsg=sgolayfilt(points(:,3),polynomialOrder, windowWidth);
xyzsg = [xsg,ysg,zsg];
clf()
hold on
plot3(points(:,1),points(:,2),points(:,3),'bo')
plot3(xyzsg(:,1),xyzsg(:,2),xyzsg(:,3),'gx')
hold off

Green crosses show the smoothed version - blue circles is the original data

Cheers

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Answer 1

Image Analyst 2015-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/213049-savitsky-golay-filter-problem-smoothing-3d-line#answer_176286

How many elements are in your array? 27 looks like an incredibly wide window for your data. I would have used a width of 5 to 9 elements. Try that and see how it works out.

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Image Analyst 2015-4-22

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This works beautifully. The red curve moves smoothly through the noisy original blue data points.

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clc;
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 2;
% Savitzky–Golay filter (sgolayfilt) - smoothing individual axes
storedStucture = load('dataline.mat');
points = storedStucture.points;
originalx = points(:, 1);
originaly = points(:, 2);
originalz = points(:, 3);
numPoints = length(originalx);
% The points are not in order.  We need to sort them.
% I'll assume that element 1 is at one end of the curve, then
% I'll take the closest of the remaining points to be the next one.
% And so on until there are no points remaining.
% Create a list of
output = zeros(1, numPoints);
% Start with the first element.
xSoFar = originalx(1);
ySoFar = originaly(1);
zSoFar = originalz(1);
remainingx = originalx(2:end); % Initialize remaining points.
remainingy = originaly(2:end); % Initialize remaining points.
remainingz = originalz(2:end); % Initialize remaining points.
for k = 1 : numPoints-1
  index = output(end);
  % Get this coordinate.
  thisX = xSoFar(k);
  thisY = ySoFar(k);
  thisZ = zSoFar(k);
  % Find distances in 3D space to all of the remaining points.
  distances = sqrt(...
    (thisX - remainingx).^2 + ...
    (thisY - remainingy).^2 + ...
    (thisZ - remainingz).^2);
  % Find the index in the remaining points of the
  % point that is closest to this one.
  [minDistance, indexOfMin] = min(distances);
  % Assign the closest coordinates to the next point
  xSoFar(k+1) = remainingx(indexOfMin);
  ySoFar(k+1) = remainingy(indexOfMin);
  zSoFar(k+1) = remainingz(indexOfMin);
  % Remove that point from the list of remaining points.
  remainingx(indexOfMin) = [];
  remainingy(indexOfMin) = [];
  remainingz(indexOfMin) = [];
end
% Now they're arranged properly and we can proceed.
% Rename the arrays for convenience
x = xSoFar;
y = ySoFar;
z = zSoFar;
% Plot them
plot3(x, y, z, 'b.-', 'LineWidth', 2)
grid on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
hold on;
% Do a Savitzky-Golay Filter.
windowWidth = 9;    %Standard example values
polynomialOrder = 3;
% Filter each coordinate list in turn.
xsg=sgolayfilt(x, polynomialOrder, windowWidth);
ysg=sgolayfilt(y, polynomialOrder, windowWidth);
zsg=sgolayfilt(z, polynomialOrder, windowWidth);
% Plot the smoothed curve.
plot3(xsg, ysg, zsg,'r*-', 'LineWidth', 2, 'MarkerSize', 3)
hold off