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

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.

Answer 1

[Image Analyst]

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)

[Alberto Acri]

Thank you for your reply @Image Analyst. No, I don't have the data sorted. I may try to create it.

I would like to point out that the improvement I asked for is for the curve on the left but I would like the most generic code possible because I want to apply it to both curves in the coordinate_A.txt file, but also to other .txt files that have different curves. I am telling you this because I saw this line of code "leftIndexes = x < 250;"

[Image Analyst]

Yeah, but you have to smooth each shape independently. So after you smooth the left, you can extract the right and smooth that. But once sorted, the algorithm I used should work. The problem is your shape is not convex so the sorting by angle didn't work. I could sort them by picking one point to begin with and then taking the closest other point, as long as that point has no longer been used. But I thought I'd check with you first before I code that up.

Another way would be if the coordinates were points on a digital image. In that case you could do it very easily by calling bwboundaries

boundaries = bwboundaries(binaryImage);

[Alberto Acri]

I thank you for the suggestion. These are curves that are not derived from an image.

[Image Analyst]

Do you have the stats toolbox so you can use pdist2? That could make it easier to sort.

[Alberto Acri]

yes

[Mathieu NOE]

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');


  

[Alberto Acri]

Thank you for your reply @Mathieu NOE. It might be useful but, for example, for the right curve it is not good. Is there any other more effective method?

[Image Analyst]

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]

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.