Finding surrounding contour from 2D meaasurements is a quite complicated problem. It seems easy at first, but one can easily find out that it is not a trivial regression problem, i.e., input output problem. For example, let's say we are given sensory measurements below.
I believe finding the appropriate contour surrounding the measurement must be done in 3-dimensional space. Currently, I am trying to use thin plate spline (TPS) like method to model 3D surface and find the contour using level curve.
Above is the result of the estimated contour using TPS-like method. One hueristics involved is estimating the smoothness of the mapping. When the measurements are noisy, smoothness tends to increase to make a best-matching contour estimation as belows.
Below is the estimated contour. One can easily see that the smoothness increases from 1 to 4.5 and the resulting contour looses some measurements as following all given measurements will produce bizare contour (not smooth!).
find_optimal_smoothness.m
