Presentation

POSTER PRESENTER

Abstract1: Geographic Point Clouds: RBF Approximation & Compression

Approximation of scattered data is often task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n‑dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to a solution of an overdetermined linear system of equation.

This poster presents a new incremental approach for meshless RBF approximation which respects the features of the given geographic data such as ridges, peaks, valleys, etc.  The mentioned factor has the main influence on the quality of approximation and allows to attain significant compression of the data. Moreover, the analytical description of the data is obtained using RBF techniques.

For purposes of determining significant features of the given geographic dataset, stationary points have an important role. However, the determination of stationary points without knowledge the analytical description for the given data is not easy. Therefore, it is described a new approach for finding the stationary points for the given dataset which is based on the piecewise RBF interpolation. Further, the experimental results for different geographic datasets are presented with respect to the quality of approximation in terms of error and the compression ratios are discussed.

Abstract2: Vector Field RBF Approximation: Multilevel & Critical Points Reduction

Vector field simplification aims to reduce the complexity of the flow by removing features according to their relevance and importance. Our goal is to preserve only the important critical points in the vector field and thus simplify the vector field for the visualization purposes. We use Radial Basis Functions (RBF) approximation with Lagrange multipliers for vector field approximation.

Next we propose a new approach for the multi-level radial basis function (RBF) approximation of vector fields. The vector field is approximated in several levels of details, where each additional level of details adds flow patterns at smaller and smaller spatial scales.  It provides the user with a mechanism to visualize a vector field without excessive cluttering while maintaining the global structure of the flow. The proposed approach uses RBF approximation with variable shape parameters and a Gaussian low-pass filter to filter data in order to suppress flow patterns at small spatial scales.

A significant contribution of the proposed method is an analytical form of the vector field which can be used in further processing of the vector field.