Filtering outlier in 2D coordinate data

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Hi experts,
I need your help to remove some outliers in my 2D coordinate data shown below.
At, at least, four locations, there are some outliers that need to be removed from my data. Please see some spikes in the plots (in red circles).
Does anyone have an algoritm, or can suggest one, that can be used to detect and move (or replace) those values?
Note that I may have several problems with slightly different cases, e.g. the number of points of the outliers may be more or less than the one shown here.
PS.
I have attached a txt file containing the 2D coordinate in this post.
  6 Comments
BeeTiaw
BeeTiaw on 17 May 2019
Edited: BeeTiaw on 17 May 2019
I can assure you that the spikes will not more than, even, 10%. Let's just stick to the problem I have at the moment. Thanks.

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Accepted Answer

Image Analyst
Image Analyst on 17 May 2019
Well this works for "the problem I have at the moment", though there are even simpler methods, and more sophisticated methods. I think this one is a good mix:
clc; % Clear command window.
clear; % Delete all variables.
close all; % Close all figure windows except those created by imtool.
workspace; % Make sure the workspace panel is showing.
fontSize = 18;
markerSize = 10;
% Read in data.
data = load('Data.txt');
x = data(:,1);
y = data(:,2);
% Smooth the shape with a median filter.
windowWidth = 9;
% for windowWidth = 9 : 2 : 9 % Try different values
smoothedx = medfilt1(x, windowWidth);
smoothedy = medfilt1(y, windowWidth);
figure;
plot(x, y, 'b.-', 'MarkerSize', markerSize);
hold on;
plot(smoothedx, smoothedy, 'r.-', 'MarkerSize', markerSize);
grid on;
legend('Original', 'Smoothed');
caption = sprintf('Median Window Width = %d', windowWidth)
title(caption, 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% end
% Find where shape deviates from smoothed shape the most.
figure;
residuals = sqrt((x-smoothedx) .^ 2 + (y - smoothedy) .^ 2);
plot(residuals, 'b.-', 'MarkerSize', markerSize);
title('Residuals', 'FontSize', fontSize);
grid on;
hold on;
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
% Find all residuals more than 0.01.
spikeIndexes = residuals > 0.01;
xSpike = x(spikeIndexes);
ySpike = y(spikeIndexes);
% Plot them
figure;
plot(x, y, 'b.-');
grid on;
hold on;
plot(xSpike, ySpike, 'ro', 'MarkerSize', markerSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);
0000 Screenshot.png
  2 Comments
Image Analyst
Image Analyst on 19 May 2019
You're welcome. Thanks for accepting. Just realize that it may not work for shapes where the spikes are of different widths, and you might need to adjust the parameters until you get exactly 4 regions. You can determine the number of regions with either bwlabel() or findgroups().

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