The Coverage Model and Its Use in Image Processing
The CUDA implementation of the method of lines for the curvature dependent flows
We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs - the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge-Kutta-Merson solver. It is a robust solver with an automatic choice of the...
The Educational Use of Mathematical Software: Techniques and Examples
The formation of a tree leaf
In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...
The Fourier Analysis of Bezier Curves
The Furthest-Site Geodesic Voronoi Diagram.
The Rooted Tree Embedding Problem into Points in the Plane.
The structure-from-motion reconstruction pipeline – a survey with focus on short image sequences
The problem addressed in this paper is the reconstruction of an object in the form of a realistically textured 3D model from images taken with an uncalibrated camera. We especially focus on reconstructions from short image sequences. By means of a description of an easy to use system, which is able to accomplish this in a fast and reliable way, we give a survey of all steps of the reconstruction pipeline. For the purpose of developing a coherent reconstruction system it is necessary to integrate...
The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.
The Upper Envelope of Voronoi Surfaces and Its Applications.
Tight Upper Bounds for the Discrepancy of Half-Spaces.
Tiling Polygons with Parallelograms.
Towards Sub-cellular Modeling with Delaunay Triangulation
In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...
Transformation of Hyperbolic Escher Patterns
Triangle-free planar graphs and segment intersection graphs.
Triangulace s hranovými kritérii - Šípkové Růženky právem nebo neprávem zapomenuté?
Planární triangulace zadané množiny bodů je častým základem aplikací, proto vzniklo mnoho metod, jak triangulaci zkonstruovat. Všechny metody se snaží dospět k trojúhelníkům "co nejrovnostrannějším", což je možné zařídit optimalizací úhlových nebo hranových kritérií. Vzhledem k vynikajícím vlastnostem, všestrannosti a snadné konstrukci Delaunayovy triangulace, nejdůležitější a nejznámější představitelky úhlových kritérií, stojí ostatní typy triangulace, zejména hranově optimalizované, poněkud...
Triangulating a Nonconvex Polytope.
Triangulating a Simple Polygon in Linear Time.
Tubular NURB surfaces with boundary control.