Marek Vanco

Direct segmentation of algebraic models for reverse engineering

In Reverse Engineering a physical object is digitally reconstructed from a set of boundary points. In the segmentation phase these points are grouped into subsets to facilitate consecutive steps as surface fitting. In this paper we present a segmentation method with subsequent classification of simple algebraic surfaces. Our method is direct in the sense that it operates directly on the point set in contrast to other approaches that are based on a triangulation of the data set. The segmentation process involves a fast algorithm for k-nearest neighbors search and an estimation of first and second order surface properties. The first order segmentation, that is based on normal vectors, provides an initial subdivision of the surface and detects sharp edges as well as flat or highly curved areas. One of the main features of our method is to proceed by alternating the steps of segmentation and normal vector estimation. The second order segmentation subdivides the surface according to principal curvatures and provides a sufficient foundation for the classification of simple algebraic surfaces. If the boundary of the original object contains such surfaces the segmentation is optimized based on the result of a surface fitting procedure.

Surface Reconstruction from Unorganized Point Data with Quadrics

We present a reverse engineering method for constructing a surface approximation scheme whose input is a set of unorganized noisy points in space and whose output is a set of quadric patches. The local surface properties, necessary for the subsequent segmentation, are estimated directly from the data using a simple and efficient data structure—the neighborhood graph. Our segmentation scheme, based on principal curvatures, constructs initial point subsets, which may be enlarged or further subdivided based on associated approximation error estimates obtained through approximation of the initial segments by quadric surfaces. Our method is highly efficient and produces a high‐quality piecewise quadric surface approximation of engineering objects, which we demonstrate for several simple and complex example data sets.

Extracting and Visualizing Structural Features in Environmental Point Cloud LiDaR Data Sets

We present a user-assisted approach to extracting and visualizing structural features from point clouds obtained by terrestrial and airborne laser scanning devices. We apply a multi-scale approach to express the membership of local point environments to corresponding geometric shape classes in terms of probability. This information is filtered and combined to establish feature graphs which can be visualized in combination with the color-encoded feature and structural probability estimates of the measured raw point data. Our method can be used, for example, for exploring geological point data scanned from multiple viewpoints.

Geometric preprocessing of noisy point sets: an experimental study

Point based graphics avoids the generation of a polygonal approximation of sampled geometry and uses algorithms that directly work with the point set.Basic ingredients of point based methods are algorithms to compute nearest neighbors, to estimate surface properties as, e.g. normals and to smooth the point set. In this paper we report on the results of an experimental study that compared different methods for the mentioned subtasks.

Direct segmentation for reverse engineering

In reverse engineering a physical object is digitally reconstructed from a set of boundary points. In the segmentation phase these points are grouped into subsets to facilitate consecutive steps as surface fitting. In this paper we present a step segmentation method with subsequent classification of simple algebraic surfaces. Our method is direct in the sense that it operates directly on the point set in contrast to other approaches that are based on a triangulation of the data set. The segmentation process involves a fast algorithm for k-nearest neighbors search and an estimation of first and second order surface properties. First order segmentation, based on normal vectors, provides an initial subdivision of the surface and detects sharp edges as well as flat or highly curved areas. One of the main features of our method is to proceed by alternating the steps of segmentation and normal vector estimation. Second order segmentation subdivides the surface according to principal curvatures and provides a sufficient foundation for the classification of simple algebraic surfaces. If the boundary of the original object contains such surfaces the segmentation is optimized based on the result of a surface fitting procedure.

Distance field computation for geological slab surface data sets

The three-dimensional shapes of tectonic plates that sink into the Earth’s mantle (slabs) are the starting point for a range of geoscience studies, from determining the forces driving the motion of tectonic plates, to potential seismic and tsunami hazards, to the sources of magmas beneath active volcanos. For many of these applications finite element methods are used to model the deformation or fluid flow, and therefore the input model parameters, such as feature geometries, temperature or viscosity, must be defined with respect to a smooth, continuous distance field around the slab. In this paper we present a framework for processing sparse and noisy seismic data (earthquake locations), defining the shape of the slab and computing a continuous distance function on a mesh with variable node spacing. Due to the inhomogeneous volumetric distribution of earthquakes within the slab and significant inaccuracies in the locations of earthquakes occurring hundreds of kilometers below the Earth’s surface, the seismicity data set is extremely noisy and incomplete. Therefore, the preprocessing is the major part of the framework consisting of several steps including a point based smoothing procedure, a powerful method to use other observational constraints on slab location (e.g., seismic tomography or geologic history) to extend of the slab shape beyond earthquake data set and continuous resampling using moving least squares method. For the preprocessed point data we introduce approaches for finding the three-dimensional boundary of the slab and a subdivision of the slab into quadric implicit polynomials. The resulting distance field is then compiled from distances to the piecewise continuous approximation of the slab and distances to slab boundary.