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

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!

[Hannah]

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));

Answer 1

[Kothuri]

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