title: RANSAC variation: does an inlier membership probability distribution makes sense?
body: <p>I'm using RANSAC to fit a geometric model to a point cloud with outliers. I know, because of the generation process of the point cloud, that 99.9% of the inlier distances to my model are distributed following a gaussian probability density function with known μ and σ, in the interval [−3σ,−3σ].</p>
  
  <p>The first question is whether do you think that it is reasonable to evaluate the total number of inliers for a certain model adding the inlier membership probability instead of adding 1 for each inlier. That is, the traditional RANSAC assumes that everything that is in an interval delimited by a threshold is an inlier; I would like to know if I can bend that, giving to some inliers more weight than others, following a probability distribution for this purpose. </p>
  
  <p>In case this is reasonable, the second question is, how do you think it affects the number of samples N:</p>
  
  <p>1−(1−(1−e)^s)^N=p</p>
  
  <p>being e the probability that a point is an outlier, s the number of points used in a sample, N the number of samples (RANSAC iterations), p the desired probability that we get a good sample.</p>
  
  <p>If none of that is reasonable, how do you suggest I may introduce my prior information of the inlier distribution?</p>
  
  <p>Thanks in advance,</p>
  
  <p>Federico</p>