Implicit model fitting to an unorganized set of points

Constructing a computer model from a mass of unorganized coordinate data acquired of a physical object is a frequent problem in engineering. Unfortunately, data are usually observed with noise due to surface attributes of the physical object, impact of the environment and uncertainty of the measuring device. The aim is thus to reconstruct the physical model in a way as to minimize the misfit between the reconstructed model and the true object. We present an approach that alloys clustering and generalized total least squares regression to detect groups in observations and estimate local parameters over naturally delineated domains in a noisy context. The global model is an aggregate of local models, each of which is described by a primitive, which evolves during an iterative refinement process. A resampling step with random initial assignment is added to minimize the probability that the method converges to a suboptimal solution.