About
15
Publications
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Introduction
Research Experience
January 2017 - present
University of West Bohemia
Position
- Research Assistant
Publications
Publications (15)
Many problems, not only in signal processing, image processing, digital imaging, computer vision and visualization, lead to the Least Square Error (LSE) problem or Total (Orthogonal) Least Square Error (TLSE) problem computation. Usually the standard least square error approximation method is used due to its simplicity, but it is not an optimal sol...
Many Radial Basis Functions (RBFs) contain a shape parameter which has an important role to ensure good quality of the RBF approximation. Determination of the optimal shape parameter is a difficult problem. In the majority of papers dealing with the RBF approximation, the shape parameter is set up experimentally or using some ad-hoc method. Moreove...
In many technical applications, reconstruction of the scattered data is often task. For big scattered dataset in n-dimensional space, the using some meshless method such as the radial basis function (RBF) approximation is appropriate. RBF approximation is based on the distance computation, and therefore, it is dimensionally non-separable. This appr...
Many problems, not only in signal processing, image processing , digital imaging, computer vision and visualization, lead to the Least Square Error (LSE) problem or Total (Orthogonal) Least Square Error (TLSE) problem computation. Usually the standard least square error approximation method is used due to its simplicity, but it is not an optimal so...
Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling function is not known is often given. Therefore, it is necessary to propose an approach for finding the stationary...
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 mult...
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equatio...
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for a higher dimension d>=2, because the other methods require a conversion of a scattered dataset to a semi-regul...
Approximation of scattered data is often a 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 the solution of an overdetermined linear system of...
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher dimension d > 2, because the other methods require the conversion of a scattered dataset to an ordered datase...
A convex hull of points in E2 is used in many applications. In spite of low computational complexity O(h logn) it takes considerable time if large data processing is needed. We present a new algorithm to speed up any planar convex hull calculation. It is based on a polar space subdivision and speed up known convex hull algorithms of 3,7 times and m...
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for a higher dimension d ≥2, because the other methods require a conversion of a scattered dataset to a semi-regul...
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is based on a distance between two points. This method leads to a solution of overdetermined linear system of equatio...
Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This algorithm is based on “spherical” space subdivision. The main idea of the S-CH algorithm is to eliminate as many input...
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum distance of two points in E 2. This algorithm is based on a polar subdivision followed by division of remaining po...
Projects
Projects (2)
Development of new fundamental algorithms and data structures related to Computer Graphics and Visualization reflecting advances in mathematics and technology.
If you wish to join this activity - you are welcome; contact us
http://www.vaclavskala.eu/ or http://www.wscg.eu
(DRAFTs of reports, papers, presentations available also at
http://afrodita.zcu.cz/~skala/publications.htm
Relevant research group publications:
- http://afrodita.zcu.cz/~skala/Publication-RBF.htm
Mission
The research group focuses on development of new methods for spatio-temporal data representation, manipulation and new data structures development using “meshless” approach in the fields of computer graphics and visualization and interpolation techniques.
The main goals of the project are:
meshless surface representations, manipulation, compression/reduction and rendering issues for large data sets
development of new algorithms especially for surface representation of spatio-temporal data, i.e. interpolation, approximation
compression techniques, i.e. how to reduce data representing a surface with regard to a resulting error
research in RBF approximation methods for computer graphics
development of analogue methods to compression of dynamic (t-varying) triangular meshes with a constant connectivity in order to avoid “constant connectivity” issues
Objectives
Objects in computer graphics are usually defined as a surface model using a surface description, e.g. polygonal meshes, parametric patches etc., or as a volumetric model using computer solid geometry etc. Available hardware is optimized actually for triangular meshes. Recently a surface of time varying objects was represented by a triangular mesh with a constant connectivity. It enables to make effective data representation, compression, transmission, decompression and rendering of such models.
In the discrete case, volumetric models are mostly considered, like CT and MRI images, standard techniques like marching cubes or tetrahedra are used and data are represented in regular or adaptive structured meshes.
This project is targeted to exploitation of meshless (meshfree) representations, manipulation, compression/reduction and rendering issues especially for scattered spatio-temporal data. As the meshless techniques are easily scalable to higher dimensions and handle spatial scattered data, research will be targeting also to spatial-temporal data, where quite new methods can be expected and applied also in many engineering computations and GIS systems etc.
