Sample consensus fitting of bivariate polynomials for initializing EM-based modeling of smooth 3D surfaces

This paper presents a method for finding the largest, connected, smooth surface in noisy depth images. The formulation of the fitting in a Sample Consensus approach allows the use of RANSAC (or any other similar estimator), and makes the method tolerant to low percentage of inliers in the input. Therefore it can be used to simultaneously segment and model the surface of interest. This is important in applications like analyzing physical properties of carbon-fiber-reinforced polymer (CFRP) structures using depth cameras. Employing bivariate polynomials for modeling turns out to be advantageous, allowing to capture the variations along the two principle directions on the surface. However, fitting them efficiently using RANSAC is not straightforward. We present the necessary pre- and post-processing, distance and normal direction checks, and degree optimization (lowering the order of the polynomial), and evaluate how these improve results. Finally, to improve the initial estimate provided by RANSAC and to stabilize the results, an Expectation Maximization (EM) strategy is employed to converge to the best solution. The method was tested on high-quality data and as well on real-world scenes captured by a RGB-D camera.