Reconstruction of B-spline curves and surfaces by adaptive group testing

Abstract

Point clouds as measurements of 3D sensors have many applications in various fields such as object modeling, environment mapping and surface representation. Storage and processing of raw point clouds is time consuming and computationally expensive. In addition, their high dimensionality shall be considered, which results in the well known curse of dimensionality. Conventional methods either apply reduction or approximation to the captured point clouds in order to make the data processing tractable. B-spline curves and surfaces can effectively represent 2D data points and 3D point clouds for most applications. Since processing all available data for B-spline curve or surface fitting is not efficient, based on the Group Testing theory an algorithm is developed that finds salient points sequentially. The B-spline curve or surface models are updated by adding a new salient point to the fitting process iteratively until the Akaike Information Criterion (AIC) is met. Also, it has been proved that the proposed method finds a unique solution so as what is defined in the group testing theory. From the experimental results the applicability and performance improvement of the proposed method in relation to some state-of-the-art B-spline curve and surface fitting methods, may be concluded.