The use of space filling curves to encode image input blocks in vector quantization (VQ) is proposed. It is based on computing a group of Peano scannings of selected feature vectors for each codeword in the codebook. An ordered list of the Peano scannings and their link to the codebook is stored. Coding is conducted by restricting the search to two windows of codewords with the closest Peano sc...

A graphic processing unit (GPU) implementation of a meshless method for solving compressible flow problems is presented in this paper. Least-square fit is used to discretise the spatial derivatives of Euler equations and an upwind scheme is applied to estimate the flux terms. The compute unified device architecture (CUDA) C programming model is employed to efficiently and flexibly port the mesh...

Inversion of potential-field data involve large and dense coefficient matrices that often exceed the limitations of physical memory in commonly available computers. The repeated multiplications of such matrices to vectors during inversion require an immense amount of CPU power. These two factors pose a significant challenge to solving large-scale problems in practice and can render many realist...

Efficiently parallelizing a whole set of meshing tools, as required by an automated mesh adaptation loop, relies strongly on data localization to avoid memory access contention. In this regard, renumbering mesh items through a space filling curve (SFC), like Hilbert or Peano, is of great help and proved to be quite versatile. This paper briefly introduces the Hilbert SFC renumbering technique a...

In this paper, the global optimization problem miny∈S F (y) with S being a hyperinterval in R and F (y) satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function F (y) can be multiextremal, non-differentiable, and given as a ‘black-box’. To attack the problem, a new global optimization algorithm based on the following two ideas is prop...

A non-linear digital filter is presented in this paper: this filter aims at extending the concept of scalar rank-ordering in the case of multichannel images. The filter is based on two steps: 1) a transformation from a p-dimensional steps to a onedimensional space by means of a space filling curve; 2) a scalar median filtering step. Results which demonstrate the advantages and the good restorat...

In the last decade, nonlinear image processing algorithms have been developed for noise removing. With respect to linear methods, they present the advantage of minimizing distortions of informative characteristics. Morphological filters are a class of nonlinear techniques that have been successfully applied in filtering monochromatic images, but their extension to vectorial -valued images encou...

The paper presents optimization and visualization methods for tool path planning of 5 axis milling machines. The first method is based on the grid generation techniques whereas the second method exploits the space filling curve technologies. Combination of the two techniques is superior with regard to the conventional methods and with regard to the case when the two methods are applied independ...

We describe a method, based on vertex-labeling, to generate algorithms for manipulating the Hilbert space lling curve in the following ways: 1. Computing the image of a point in R. 2. Computing a pre-image of a point in R. 3. Drawing a nite approximation of the curve. 4. Finding neighbor cells in a decomposition ordered according to the curve. Our method is straightforward and exible, resulting...

We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.