Francesco Bellocchio

A Hierarchical RBF Online Learning Algorithm for Real-Time 3-D Scanner

In this paper, a novel real-time online network model is presented. It is derived from the hierarchical radial basis function (HRBF) model and it grows by automatically adding units at smaller scales, where the surface details are located, while data points are being collected. Real-time operation is achieved by exploiting the quasi-local nature of the Gaussian units: through the definition of a quad-tree structure to support their receptive field local network reconfiguration can be obtained. The model has been applied to 3-D scanning, where an updated real-time display of the manifold to the operator is fundamental to drive the acquisition procedure itself. Quantitative results are reported, which show that the accuracy achieved is comparable to that of two batch approaches: batch HRBF and support vector machines (SVMs). However, these two approaches are not suitable to real-time online learning. Moreover, proof of convergence is also given.

Hierarchical Approach for Multiscale Support Vector Regression

Support vector regression (SVR) is based on a linear combination of displaced replicas of the same function, called a kernel. When the function to be approximated is nonstationary, the single kernel approach may be ineffective, as it is not able to follow the variations in the frequency content in the different regions of the input space. The hierarchical support vector regression (HSVR) model presented here aims to provide a good solution also in these cases. HSVR consists of a set of hierarchical layers, each containing a standard SVR with Gaussian kernel at a given scale. Decreasing the scale layer by layer, details are incorporated inside the regression function. HSVR has been widely applied to noisy synthetic and real datasets and it has shown the ability in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by standard SVR. Results also compare favorably with multikernel approaches. Furthermore, tuning the SVR configuration parameters is strongly simplified in the HSVR model.

Illuminance prediction through SVM regression

In a scenario where renewable energies will play a foreground role, a reliable forecast of the energy production of such sources, like solar radiation, is a requirement for managing smart grids. However, the ability to predict the possibility to produce sustainable energy in different climatic conditions can be very useful for many other purposes (e.g., for Climate Sensitive Buildings). This is particularly true when working with climatic data that are, as a matter of fact, highly unsteady. Nevertheless, the use of data collected in the past can help to face the daily and seasonal variability. An algorithm for illuminance prediction based on Support Vector Regression (SVR) is here proposed and the results are presented and discussed.

Multi-scale Support Vector Regression

A multi-kernel Support Vector Machine model, called Hierarchical Support Vector Regression (HSVR), is proposed here. This is a self-organizing (by growing) multiscale version of a Support Vector Regression (SVR) model. It is constituted of hierarchical layers, each containing a standard SVR with Gaussian kernel, at decreasing scales. HSVR have been applied to a noisy synthetic dataset. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by standard SVR. Furthermore with this approach the well known problem of tuning the SVR parameters is strongly simplified.

Kernel regression in HRBF networks for surface reconstruction

The Hierarchical Radial Basis Function (HRBF) Network is a neural model that proved its suitability in the surface reconstruction problem. Its non-iterative configuration algorithm requires an estimate of the surface in the centers of the units of the network. In this paper, we analyze the effect of different estimators in training HRBF networks, in terms of accuracy, required units, and computational time.

Online training of Hierarchical RBF

Efficient multi-scale manifold reconstruction from point clouds can be obtained through the Hierarchical Radial Basis Function (HRBF) network. An online training procedure for HRBF is here presented and applied to real-time surface reconstruction during a 3D scanning session. Results show that the online version compares well with the batch one.

Refining Hierarchical Radial Basis Function Networks

The hierarchical radial basis function (HRBF) Network is a neural model that proved its ability in surface reconstruction problem. The algebraic error is used to drive the HRBF configuration procedure and for evaluating the reconstruction ability of the network. While for function approximation the algebraic distance is the appropriate error metric, for computer graphics applications, such as model reconstruction by 3D scanning, the geometric distance is a more suitable error metric. In this paper, we propose a modified HRBF model which makes use of the geometric error as a measure of the reconstruction accuracy.

Hierarchical Support Vector Regression

In the previous chapter the RBFN model and the advantages of a hierarchical version for surface reconstruction has been presented. In a similar way in this chapter another paradigm, Support Vector Regression (SVR), and its hierarchical version, Hierarchical Support Vector Regression (HSVR) that allows an efficient construction of the approximating surface, are introduced. Thanks to the hierarchical structure, the model can be better applied to 3D surface reconstruction giving a new, more robust and faster configuration procedure.

Surface fitting as a regression problem

A brief overview of the methods for surface reconstruction has been presented in the previous chapters. In this chapter the attention will be focused on a particular class of methods that see surface reconstruction as a multivariate approximation problem. Some of the most popular techniques of this kind will be presented and pros and cons will be discussed. An evolution of two of these techniques, namely Radial Basis Function Neural Networks and Support Vector Machines, will be the topic of the next two chapters.