Connecting dots with spline or polinomial on an image to process it later

I want to connect the blue dots using splines, polinomial or a smooth line. I have already their coordinates of the pixel matrix.

Can anyone help me?

[Image Analyst]

What does "connect" mean to you. Do you mean like plot a line between them like

plot(x, y, 'b-', 'LineWidth', 2);

?

[Luis de Juan]

yes, i mean plot a smooth line between them, but in that image, not in a white plot. I don't know if I'm explaining myself.. Like this:

[Bruno Luong]

can you provide the coordinates of the points?

[Luis de Juan]

190.500000000000 285.500000000000

224.059860054750 153.192111578190

232.581399572552 420.540399229369

402.508419392691 213.445258896098

451.535515792237 324.819236098713

337.277297466815 113.811071623683

[Image Analyst]

When you say "in the image" do you mean in the graphical overlay above the image, or actually burned into the image pixels themselves (so the underlying image pixels are changed)?

[Luis de Juan]

I want to use that curve to measure lenghts of differents sections of the curve. I understand what you mean, but I don't really know the answer. I would say whatever option with which I could do measurements later

Answer 1

[Karim]

There are multiple ways to do this, here is one example using a file exchange function to subsaple the spline and make a smooth plot.

% grid given by the OP
Grid = [190.500000000000	285.500000000000
    224.059860054750	153.192111578190
    232.581399572552	420.540399229369
    402.508419392691	213.445258896098
    451.535515792237	324.819236098713
    337.277297466815	113.811071623683];

% figure to find the ordering of the grid
figure
scatter(Grid(:,1),Grid(:,2))
hold on
for i = 1:size(Grid,1)
    text(Grid(i,1),Grid(i,2),['  ',num2str(i)])
end
hold off 
grid on

% set up the order, add the first point at the end to close the loop
Order = [2 1 3 5 4 6 2];
% get the new grid
Grid = Grid(Order,:);

% create a spline trough the grid and evaluate it at 100 equal subpoints
% note the 'csape' option is used to indicate that the curve is a closed
% loop and the interpolation is spline based
GridFine = interparc(100,Grid(:,1),Grid(:,2),'csape');

% plot the fine grid
figure
hold on
plot(GridFine(:,1),GridFine(:,2),'r','linewidth',2)
scatter(Grid(:,1),Grid(:,2),'b','filled')
grid on

Note: this answer makes use of the following file exchange submission: interparc - File Exchange - MATLAB Central (mathworks.com)

Answer 2

[Bruno Luong]

Using Free knot spline available here

https://uk.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation

P = [ ...
190.500000000000	285.500000000000;
224.059860054750	153.192111578190;
232.581399572552	420.540399229369;
402.508419392691	213.445258896098;
451.535515792237	324.819236098713;
337.277297466815	113.811071623683 ]

% This is to reorder the point and make them wrap around
K = convhull(P);
P = P(K,:);
% Find the distance between point and cumulate them as as free parameters
d = cumsum([0; sqrt(sum(diff(P,1,1).^2,2))]);

% Spline interpolation with periodic to make a close curve
X = P(:,1);
Y = P(:,2);
options = struct('periodic', true, 'lambda', 1e-6);
ppx = BSFK(d, X, 4, 10, [], options);
ppy = BSFK(d, Y, 4, 10, [], options);

% Graphical check
di = linspace(min(d),max(d), 500);
xi = ppval(ppx, di);
yi = ppval(ppy, di);

close all
plot(xi,yi,'b',X,Y,'or')
axis equal
set('Ydir','reverse')

[Luis de Juan]

Wow, thank you very much. So now how can I do to take that polinomial to my image (480x648 pixels)?

[Bruno Luong]

IA @Image Analyst will guide you on this.

[Luis de Juan]

Thanks Bruno

[Bruno Luong]

Here is one way to burn the contour to an image (all back here)

P = [ ...
190.500000000000	285.500000000000;
224.059860054750	153.192111578190;
232.581399572552	420.540399229369;
402.508419392691	213.445258896098;
451.535515792237	324.819236098713;
337.277297466815	113.811071623683 ]


K = convhull(P);
P = P(K,:);
d = cumsum([0; sqrt(sum(diff(P,1,1).^2,2))]);

X = P(:,1);
Y = P(:,2);
options = struct('periodic', true, 'lambda', 1e-6);
ppx = BSFK(d, X, 4, 10, [], options);
ppy = BSFK(d, Y, 4, 10, [], options);

di = [min(d):0.5:max(d), max(d)]; % Make sur we don't jump more than 1 pixel
xi = round(ppval(ppx, di));
yi = round(ppval(ppy, di));

x = 1:500;
y = 1:500;
Im = zeros(length(y),length(x));
Im(sub2ind(size(Im),yi,xi)) = 1;

close all
imagesc(x,y,Im)
hold on
plot(X,Y,'or')
axis equal

[Luis de Juan]

That's it! But how I use BSFK? unrecognized function!

[Bruno Luong]

BSFK is on File exchange https://uk.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation