Generalized Maps

Spaces of generalised sections (also called section-distributions) are introduced, and their fundamental properties are described. Several special cases are considered, with particular attention to the case of semi-densities; when a Hermitian structure on the underlying classical bundle is given, these determine a rigged Hilbert space, which can be regarded as a basic notion in quantum geometry. The essentials of tensor products in distributional spaces, kernels and Fourier transforms are exposed.

Theory of g-Tg-Maps

Several specific types of generalized maps of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

COMPARING IMAGE-BASED METHODS FOR ASSESSING VISUAL CLUTTER IN GENERALIZED MAPS

Map generalization abstracts and simplifies geographic information to derive maps at smaller scales. The automation of map generalization requires techniques to evaluate the global quality of a generalized map. The quality and legibility of a generalized map is related to the complexity of the map, or the amount of clutter in the map, i.e. the excessive amount of information and its disorganization. Computer vision research is highly interested in measuring clutter in images, and this paper proposes to compare some of the existing techniques from computer vision, applied to generalized maps evaluation. Four techniques from the literature are described and tested on a large set of maps, generalized at different scales: edge density, subband entropy, quad tree complexity, and segmentation clutter. The results are analyzed against several criteria related to generalized maps, the identification of cluttered areas, the preservation of the global amount of information, the handling of occlusions and overlaps, foreground vs background, and blank space reduction.

Modeling of Flowers with Inverse Grammar Generation Interface

Flowers belong to one of the natural phenomena that cannot be captured completely, as there is enormous variety of shapes both within and between individuals. The authors propose a procedural modeling of flowering plants using an extension of L-Systems – a model based on three-dimensional generalized maps. Conventionally, in order to build a model the user has to write the grammar, which consists of the description of 3Gmaps and all the production rules. The process of writing a grammar is usually quite laborious and tedious. In order to avoid this the authors propose new interface functionality: the inverse modeling by automatic generation of L-systems. The user describes the flower he wants to model, by assigning the properties of its organs. The algorithm uses this information as an input, which is then analyzed and coded as L-systems grammar.