Move/delete/create some coordinates in order to make the curve more or less uniform

Question

Alberto Acri 2022-12-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1877407-move-delete-create-some-coordinates-in-order-to-make-the-curve-more-or-less-uniform

编辑： Alberto Acri 2022-12-16

coordinate_A.txt

Hello! As written in the title I am trying to figure out if there is a way to move/delete/create some coordinates in order to make the curve more or less uniform.

Below is an example (whose coordinates can be found in the attached .txt. text file).

I am trying to make the black curve more or less uniform with the coordinates marked by dots in red.

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Answer 1

Image Analyst 2022-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/1877407-move-delete-create-some-coordinates-in-order-to-make-the-curve-more-or-less-uniform#answer_1127187

编辑：Image Analyst 2022-12-13

在 MATLAB Online 中打开

coordinate_A.mat

The attached file is a .mat file, not a txt file. The attached data is not sorted. Is there anyway you could sort it clockwise? I got this but it's not good because your data is not sorted. I wanted to see if you had sorted data before I tried to sort it better.

data = load('coordinate_A.mat')

data = struct with fields:

out_both: [582×2 double]

x = data.out_both(:, 1);

y = data.out_both(:, 2);

% plot(x, y, 'c.', 'MarkerSize', 8)

hold on;

grid on;

axis equal

% The data is not sorted so we can't smooth it yet.

% Need to sort it clockwise.

% First need to find centroid

% Get left shape

leftIndexes = x < 250;

xLeft = x(leftIndexes);

yLeft = y(leftIndexes);

plot(xLeft, yLeft, 'b.');

hold on;

% Find centroid.

p = polyshape(xLeft, yLeft);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

[xCentroid, yCentroid] = centroid(p)

xCentroid = 141.9855

yCentroid = 229.7115

plot(xCentroid, yCentroid, 'r+', 'MarkerSize', 40, 'LineWidth',2);

% Get angles

angles = atan2d(yLeft-yCentroid, xLeft-xCentroid);

% Sort

[sortedAngles, sortOrder] = sort(angles, 'ascend');

% Sort x and y the same way.

xLeft = xLeft(sortOrder);

yLeft = yLeft(sortOrder);

% Smooth both

windowWidth = 5;

xSmooth = movmean(xLeft, windowWidth);

ySmooth = movmean(yLeft, windowWidth);

plot(xSmooth, ySmooth, 'r-', 'LineWidth',2)

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Mathieu NOE 2022-12-14

在 MATLAB Online 中打开

hello

the method based on poalr coordinates is quite sensitive to the shape of the curve

if the curve is mostly convex then all points of the curve can be "seen" from the centroid and then the method will work

with a more complex shape (with concave portions) this will fail;

now I cannot make any suggestion based on image processing as I don't have the toolbox (and not really expert in image processing)

here just for the sake of the demo, the centroid positions have been changed (from mean to median) and this suffice in that case to go from fail to success

I doubt you can always find a robust pseudo centroid position that make you "see" all points of your curve without being forced to see "below the horizon"

result with centroid /mean

result with centroid /median

data = load('coordinate_A.mat');
x = data.out_both(:, 1);
y = data.out_both(:, 2);
idx = x<250; % select left curve 
% idx = x>250; % select right curve 
x = x(idx);
y = y(idx);
% %% method 1 using boundary + smoothn  (https://fr.mathworks.com/matlabcentral/fileexchange/25634-smoothn/?requestedDomain=)
% [k,v] = boundary(x,y,0.75);
%  z = smoothn({x(k), y(k)},2);
%   figure(1),plot(x,y,'b*',x(k), y(k),'r*',z{1},z{2},'k','linewidth',2)
%% method 2 
% centroid_x = mean(x);
% centroid_y = mean(y);
centroid_x = median(x);
centroid_y = median(y);
[theta,r] = cart2pol(x-centroid_x,y-centroid_y);
% closing the circle
r(end+1) = r(1);
theta(end+1) = theta(1);
% sort theta in ascending order
[theta,ind] = sort(theta);
r = r(ind);
% remove duplicates 
[theta,IA,IC] = unique(theta);
r = r(IA);
% theta_new = linspace(min(theta),max(theta),360);
theta_new = linspace(-pi,pi,500);
r = interp1(theta,r,theta_new);
theta = theta_new;
% smoothing
r = smoothdata(r,'gaussian',10);
% convert to cartesian
[xn,yn] = pol2cart(theta,r);
% add back centroid info
xn = xn + centroid_x;
yn = yn + centroid_y;
%% XY plot
figure(2), hold on
plot(centroid_x, centroid_y, 'r+', 'MarkerSize', 40, 'LineWidth',2);
plot(x,y,'b*',xn,yn,'rd');
legend('raw','smoothed');
  

Image Analyst 2022-12-15

Since your data are integers, you could write them into an image and then use bwboundaries to get them in a sorted manner, then use movmean or sgloayfilt to smooth them. Try that.

Alberto Acri 2022-12-16

编辑：Alberto Acri 2022-12-16

Thanks for the advice @Image Analyst. I posted a separate question about the "bwboundaries" function (link) because the function generates a curve (red) inside compared to the black curve (black pixels) shown in the image, while I would need the creation of the red curve inside (overlapping) the black curve (shown in the image). Once I understand this part I could use the functions you mentioned.

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