Computational intelligence for surface modeling

The surface reconstruction problem, which consists in the search of the surface that best describes a given set of points, is of interest in many application fields (e.g., design, archeology, medicine, and entertainment). This can be viewed as a supervised learning problem, where the vector coordinates (or other features) of each point is an input instance, while a further coordinate is an output label. The approximation function provides a law to obtain labels from instances. Several effective computational intelligence paradigms have been developed for solving the surface reconstruction problem, e.g., Multi-layer Perceptron Networks, Radial Basis Function (RBF) Networks, Self-Organizing Maps (SOM), and Support Vector Machines (SVM). However, other paradigms such as Genetic Algorithms has been used to improve the performances of traditional approaches of surface reconstruction. In general, the performance of a single paradigm depends on the application context. Since the real objects has generally a complex structure, that can be described at different levels of detail, a hierarchical multi-scale representation allows for a more accurate tuning of the reconstruction, with a lower complexity of the final model. In this paper, the basic concepts of surface reconstruction will be introduced and the approaches based on computational intelligence paradigms will be presented. In particular, the approaches based on some hierarchical techniques (namely, HRBF and HSVR) will be analyzed and discussed in detail.