Find sinusoidal lines via RANSAC

Question

I have a set of points that I need to group using their vicinity to the respective sinusoidal lines. I tried to determine the lines using a standard Hough transform, but that doesn't solve the problem (only a few lines are detected).

I'd like to test if RANSAC would work better to detect the various sin curves. Do you have an example for a similar algorithm?

I know that RANSAC is not the best tool to find multiple lines, so what I would do is a) find the function fitting most points; b) iterate the search, considering only the remaining ones.

Answer 1

RANSAC

The algorithm

Until an inlier percentage threshold is reached or N sample combinations are tested.

• It randomly selects the smallest sample as possible to build or fit a model.
• The other data points are classified as inliers or outliers
• The model is accepted or rejected

Inputs:

• error tolerance for determining inliers and outliers
• Threshold inlier percentage
• Maximum sample combinations tested

Possible improvements

• Make sure that no combination is tested more than once
• If a better way is possible to select combinations, use that.
• Once a lot of inliers are found, use a new set of inliers for the further search

Source: Fischler and Bolles - Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography

Your aplication

Your model is a sine defined as f(x) = amplitude * sin(period * x) + bias. Fitting this model will not be as easy as it is dependent on three parameters. I think that it will risk in long runs and a possibility of overfitting. A possible solution might be to run the algorithm multiple times for different periods and keep the bias and amplitude fixed.

iterationThreshold = 10000;
iterationCount = 0
errorthreshold = 0.05;

while(numel(inliers(:,1)) > inlierThreshold)

   samples = extractMinimumSamples(points);
   [sineX, sineY] = fitSine(samples);
   inliers = determineInliers(points, SineX, SineY)

   iterationCount = iterationCount + 1;

   if(iterationCount => iterationThreshold)
      break;
   end

end  

See also the possible improvements for modifications to this code