Parameterization of point-cloud freeform surfaces using adaptive sequential learning RBFnetworks

We propose a self-organizing Radial Basis Function (RBF) neural network method for parameterization of freeform surfaces from larger, noisy and unoriented point clouds. In particular, an adaptive sequential learning algorithm is presented for network construction from a single instance of point set. The adaptive learning allows neurons to be dynamically inserted and fully adjusted (e.g. their locations, widths and weights), according to mapping residuals and data point novelty associated to underlying geometry. Pseudo-neurons, exhibiting very limited contributions, can be removed through a pruning procedure. Additionally, a neighborhood extended Kalman filter (NEKF) was developed to significantly accelerate parameterization. Experimental results show that this adaptive learning enables effective capture of global low-frequency variations while preserving sharp local details, ultimately leading to accurate and compact parameterization, as characterized by a small number of neurons. Parameterization using the proposed RBF network provides simple, low cost and low storage solutions to many problems such as surface construction, re-sampling, hole filling, multiple level-of-detail meshing and data compression from unstructured and incomplete range data. Performance results are also presented for comparison

ONLINE HIERARCHICAL MODELS FOR SURFACE RECONSTRUCTION

Applications based on three-dimensional object models are today very common, and can be found in many fields as design, archeology, medicine, and entertainment. A digital 3D model can be obtained by means of physical object measurements performed by using a 3D scanner. In this approach, an important step of the 3D model building process consists of creating the object's surface representation from a cloud of noisy points sampled on the object itself. This process can be viewed as the estimation of a function from a finite subset of its points. Both in statistics and machine learning this is known as a regression problem. Machine learning views the function estimation as a learning problem to be addressed by using computational intelligence techniques: the points represent a set of examples and the surface to be reconstructed represents the law that has generated them. On the other hand, in many applications the cloud of sampled points may become available only progressively during system operation. The conventional approaches to regression are therefore not suited to deal efficiently with this operating condition. The aim of the thesis is to introduce innovative approaches to the regression problem suited for achieving high reconstruction accuracy, while limiting the computational complexity, and appropriate for online operation. Two classical computational intelligence paradigms have been considered as basic tools to address the regression problem: namely the Radial Basis Functions and the Support Vector Machines. The original and innovative aspect introduced by this thesis is the extension of these tools toward a multi-scale incremental structure, based on hierarchical schemes and suited for online operation. This allows for obtaining modular, scalable, accurate and efficient modeling procedures with training algorithms appropriate for dealing with online learning. Radial Basis Function Networks have a fast configuration procedure that, operating locally, does not require iterative algorithms. On the other side, the computational complexity of the configuration procedure of Support Vector Machines is independent from the number of input variables. These two approaches have been considered in order to analyze advantages and limits of each of them due to the differences in their intrinsic nature

Automatic multiscale meshing through HRBF networks

A procedure for the real-time construction of three-dimensional (3-D) multiscale meshes from not evenly sampled 3-D points is described and discussed in this paper. The process is based on the connectionist model named hierarchical radial basis functions network (HRBF), which has been proved effective in the reconstruction of smooth surfaces from sparse noisy data points. The network goal is to achieve a uniform reconstruction error, equal to measurement error, by stacking noncomplete grids of Gaussians at decreasing scales. It is shown here how the HRBF properties can be used to develop a configuration algorithm, which produces a continuous surface in real time. In addition, the model is extended to automatically convert the continuous surface into a 3-D mesh according to an adequate error measure