How to smooth the curve indicated on the image?

Hi, Can anyone help me in smoothing this data ?

I have included the coordinates of the left and right side in txt.

I´d really appreciate,

Thanks

Answer 1

[Mathieu NOE]

hello

you can try this

adjust the amount of smoothing (and window type ) in this line :

rs = smoothdata(r_new,'gaussian',61);

full code :

xL = readmatrix('left.txt');
yL = (1:numel(xL))';

xR = readmatrix('right.txt');
yR = (1:numel(xR))';
xR = xR(end:-1:1); % flip upside down 
yR = yR(end:-1:1); % flip upside down 

% remove NaN's and concatenate left and right coordinates
x= [xL;xR];
idx = isnan(x);
x(idx) = [];
y= [yL;yR];
y(idx) = [];

% %% method 1 using smoothn  (https://fr.mathworks.com/matlabcentral/fileexchange/25634-smoothn/?requestedDomain=)
%  z = smoothn({x,y},1e3);
%   figure(1),plot(x,y,'r.',z{1},z{2},'k','linewidth',2)

%% method 2 
centroid_x = mean(x);
centroid_y = mean(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),1000);
r_new = interp1(theta,r,theta_new);

% smoothing
rs = smoothdata(r_new,'gaussian',61);

% convert to cartesian
[xn,yn] = pol2cart(theta_new,rs);

% add back centroid info
xn = xn + centroid_x;
yn = yn + centroid_y;


%% XY plot
figure(2),plot(x,y,'b*',xn,yn,'r');
legend('raw','smoothed');


  

[Rhandrey Maestri]

Hi, thanks for your answer.

Is it possible to not smooth the down part with the wave? Those waves are important.

I want to smooth the lateral parts, as they should be more linear.

Thanks very much

[Mathieu NOE]

can you make a simple (handmade) sketch of how it should look like ?

[Mathieu NOE]

maybe this ?

clc
clearvars

xL = readmatrix('left.txt');
yL = (1:numel(xL))';
% remove NaN for left data
idx = isnan(xL);
xL(idx) = [];
yL(idx) = [];


xR = readmatrix('right.txt');
yR = (1:numel(xR))';

% remove NaN for left data
idx = isnan(xR);
xR(idx) = [];
yR(idx) = [];

% smooth the X data with "smart" function below 
outL = smart_smooth(xL);
outR = smart_smooth(xR);

plot(xL,yL,'b',outL,yL,'r',xR,yR,'b',outR,yR,'r');

%%%%%%%%%%%%%%%%function%%%%%%%%%%%%%%%%
function out = smart_smooth(in)
% "smart filter" : simple first order low pass filter (2 stages in series = 2nd order filter), 
% the smoothing factor varies with time (low at the beginning and end , then
% increases in the middle section 

%% main loop 
out = zeros(size(in));
out(1) = in(1);
alpha_max = 0.995;
samples = numel(in);

for ci = 2:samples
   
    if ci <250  % start time to modify (increase alpha)
        alpha = alpha_max*ci/250;
    elseif ci > samples-40
        alpha = 0;
    else
        alpha = alpha_max;
    end
    
    % first order low pass IIR filter recursion
    out(ci) = alpha.*out(ci-1)  + (1-alpha).*in(ci);
    
end

end

[Rhandrey Maestri]

Hi, your second solution is very good.

In this image I show in black line what I would like even more if possible (but with the curves more soft as in your solution). There is also a small wave on the top before getting continuous.

[Mathieu NOE]

hello again

so I tweaked a bit the code

for the small waves at the top I cannot make them bigger are they are , hope it's good enough now

xL = readmatrix('left.txt');
yL = (1:numel(xL))';
% remove NaN for left data
idx = isnan(xL);
xL(idx) = [];
yL(idx) = [];


xR = readmatrix('right.txt');
yR = (1:numel(xR))';

% remove NaN for left data
idx = isnan(xR);
xR(idx) = [];
yR(idx) = [];

% smooth the X data with "smart" function below 
alpha_max = 0.999;
para1 = 220; % samples
para2 = 55; % samples

outL = smart_smooth(xL,para1,para2,alpha_max);
outR = smart_smooth(xR,para1,para2,alpha_max);

% concatenate left and right coordinates
xR = xR(end:-1:1); % flip upside down 
yR = yR(end:-1:1); % flip upside down 
outR = outR(end:-1:1); % flip upside down 

x= [xL;xR;xL(1)]; % close the curve
y= [yL;yR;yL(1)]; % close the curve
xs= [outL;outR;outL(1)]; % close the curve

plot(x,y,'b',xs,y,'r');

%%%%%%%%%%%%%%%%function%%%%%%%%%%%%%%%%
function out = smart_smooth(in,para1,para2,alpha_max)
% "smart filter" : simple first order low pass filter (2 stages in series = 2nd order filter), 
% the smoothing factor varies with time (low at the beginning and end , then
% increases in the middle section 

%% main loop 
out = zeros(size(in));
out(1) = in(1);
samples = numel(in);

for ci = 2:samples
   
    if ci <= para1  % start time to increase alpha
        alpha = alpha_max*ci/para1;
    elseif ci >= samples-para2   % start time to decrease alpha
        alpha = alpha_max*(1-ci/samples);
    else
        alpha = alpha_max;
    end
    
    % first order low pass IIR filter recursion
    out(ci) = alpha.*out(ci-1)  + (1-alpha).*in(ci);
    
end

end

Answer 2

[Image Analyst]

You can use a Savitzky-Golay filter, like the attached demo.