How to define the surface line of a wave? Hought Transform on not straight lines and interpolation for mising parts.

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Hannah
Hannah 2024-6-3
回答： Kothuri 2024-6-21
Hi Matlab Friends,
I have following problem that I hope to get help with:
My goal is to film flowing water through a window and detect the water surface line. I attached the original image and the segmented image of the water: As you can see, there is some serious reflection happening, which is segmented as well. Additionally, one party of the sidewall is not see-through resulting in missing parts of the wave.
Ho do I define only the surface as a not-straight line and maybe interpolate the missing part?
  • Is there a method for Hough transformation to fit a curved line?
  • A second idea would be to get the coordinates of the edges by bwboundaries() and use polynomial curvefitting. However, the whole water body gets detected creating a round-ish object and I don't know to extract only the values of the surface line. The data I have so far is the cell array of coordinates of the red line, surrounding the wave:
wave_coordinates = bwboundaries(BW);
xy = cell2mat(wave_coordinates);
waveX = xy(:,1); %20287x1 double
waveY = xy(:,2); %20287x1 double
I am curious for your solution approaches!
  1 个评论
Hannah
Hannah 2024-6-3
A first attempt of mine would be
wave_coordinates = bwboundaries(BW);
xy = cell2mat(wave_coordinates);
%create array with y values
waveY = xy(:,1);
%create array with y values
waveX = xy(:,2);
%find edge points (where x is min and max)
[edge1 idx1] = min(waveX)
[edge2 idx2] = max(waveX)
%find all points that are above the right edge point
idx_upperLine = waveY >= waveY(idx1);
%create array with x and y coordinates of all point above the edge point (which is hopefully the upper Line)
surfaceX = nonzeros(waveX(idx_upperLine));
surfaceY = nonzeros(waveY(idx_upperLine));

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回答（1 个）

Kothuri
Kothuri 2024-6-21
Hi Hannah,
Traditional line detection methods like the Hough transform are typically used for straight line detection, may not be directly applied for curved line detection. Since the water surface is not a straight line, polynomial curve fitting, or spline fitting could be more appropriate.
You can use MATLAB's polyfit function to fit a polynomial to fit the water surface line is within a certain region of the image.
For e.g:
% Assuming waveX and waveY are the coordinates and you have filtered them to focus on the water surface
p = polyfit(waveX, waveY, degree); % Choose an appropriate degree
fitY = polyval(p, waveX);
plot(waveX, fitY, 'r-', 'LineWidth', 2); % This plots the fitted curve
You can refer the below link for more info on polyfit
https://www.mathworks.com/help/matlab/ref/polyfit.html?&s_tid=srchtitle_support_results_1_polyfit#description
You can also try Spline fitting using MATLAB fit function for a more flexible fit that can better adapt to the curvature of the water surface.
For e.g:
fitType = 'smoothingspline'; % This type of spline allows for smoothing which might be necessary for noisy data
fitOptions = fitoptions('Method', 'SmoothingSpline', 'SmoothingParam', 0.5); % Adjust the smoothing parameter as needed
curveFit = fit(waveX, waveY, fitType, fitOptions);
plot(curveFit, waveX, waveY); % This plots the fitted curve along with the original points
You can refer the below link for more info on fitfunctionhttps://www.mathworks.com/help/curvefit/fit.html?&s_tid=srchtitle_support_results_1_fit

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