Hierarchical Modeling of Multidimensional Data in Regularly Decomposed Spaces: Implementation on Computer

TL;DR

This paper presents new hierarchical modeling techniques for multidimensional data, along with algorithms and software implementations on parallel computers to handle large databases efficiently.

Contribution

It introduces novel algorithms for multidimensional hierarchical modeling and details their implementation on parallel architectures, enhancing processing of large numerical databases.

Findings

Development of new algorithms for geometric and integral transformations

Successful porting of modeling software on parallel computers

Enhanced processing capabilities for large multidimensional data sets

Abstract

The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in the aim to develop new techniques for multidimensional hierarchical modeling and to port them on parallel architecture computers for satisfying the future needs in processing huge numerical data bases. Following the first tome describing the modeling principles, the second tome details the way used for developing the modeling software and for porting it on different computers, especially on parallel architecture computers. In addition to these works, it is gone through new algorithms that have been developed after those that have been presented in the former tome and that are described in pseudo-code in annex of the present document: - operators for constructive geometry (building simple shapes, Boolean operators, slice handling); - integral transformations (epigraph, hypograph, convex hull) ; - homotopic transformations (boundary, erosion, dilation, opening, closing) ; - median transformations (median filtering, thinning, median set, intrinsic dimension) ; - transformations of (hyper-)surface manifolds (median filtering, extension, polynomial fitting of a simple function). The present publication is ending with the software porting on two distributed memory parallel computers: - a thin-grained synchronous computer ; - a coarse-grained asynchronous computer.