  The described works have been carried out in the framework of a mid-term
study initiated by the Centre Electronique de l'Armement and led by ADERSA, a
French company of research under contract. The aim was to study the techniques
of regular dividing of numerical data sets so as to provide tools for problem
solving enabling to model multidimensional numerical objects and to be used in
computer-aided design and manufacturing, in robotics, in image analysis and
synthesis, in pattern recognition, in decision making, in cartography and
numerical data base management. These tools are relying on the principle of
regular hierarchical decomposition and led to the implementation of a
multidimensional generalization of quaternary and octernary trees: the trees of
order 2**k or 2**k-trees mapped in binary trees. This first tome, dedicated to
the hierarchical modeling of multidimensional numerical data, describes the
principles used for building, transforming, analyzing and recognizing patterns
on which is relying the development of the associated algorithms. The whole so
developed algorithms are detailed in pseudo-code at the end of this document.
The present publication especially describes: - a building method adapted
disordered and overcrowded data streams ; - its extension in inductive limits ;
- the computation of the homographic transformation of a tree ; - the attribute
calculus based on generalized moments and the provision of Eigen trees ; -
perception procedures of objects without any covering in affine geometry ; -
several supervised and unsupervised pattern recognition methods.
