Resumen (inglés)
Title
ANALYSIS OF DECORATIVE MOTIFS FOR WEAVES AND CERAMIC COATINGS IN THE COMPUTER VISION ENVIRONMENT. APPLICATION TO THE RECONSTRUCTION OF HISTORICAL MOTIFS AND DESIGN.

Abstract
The designs, or patterns, used traditionally in tiles and ceramic coatings, weaves and, in general, the industrial scope of graphical design, are constituted by simple elements that combine, increasing the decorative motifs complexity, by filling up the two-dimensional space of the tile or weave, by means of geometric transformations forming a repetitive pattern.

The different possibilities of mixing these geometric transformations, generating a particular organization, and therefore, all the possible symmetries in the pattern, are limited and they are described by the Plane Symmetry Groups Theory. The different basic elements that contains a repetitive pattern joins to the organizational structure it has in order to constitute the necessary information to know it completely, so that it is possible to simplify to the maximum, without losing information, since the structure itself indicates how they are going to repeat indefinitely.

From the point of view of the design, the knowledge of the structure offers the possibility of modifying its parameters, so that a family of derived patterns can be obtained. This fact takes complete sense when the knowledge of the pattern elements, and their organizational structure, are reached by means of a computer analysis process, that is to say, if the computer is able “to see” in a pattern which are the basic elements and “to understand” how they are organized, that is, obtaining a computerized model of the pattern that reflects its structure, as well as a compact description of its content. The analysis we are going to carry out, due to their complexity, cannot be totally automatic, but that it will need the adjustment of some parameters.

In order to contribute to this purpose, in this doctoral thesis, have been created tools that allow to cover the gap from the shapeless information contained in the pixels of the images (two-dimensional matrix intensities coming from digital photographs or scanner images) until the complex information, classified and hierarchized composed by the visual shapes and their structures. With this aim, apart from using current techniques in image analysis and computer vision, new original techniques have been developed for this specific case that try to take advantage of the patterns structural features.

Due to the complexity of the analysis, it has been divided into various stages, so that in each one it is possible to deepen in the knowledge on the pattern, and the complexity of the treated information is increased. In the initial stages, it works with the pixels of the image in the lower level of abstraction. Next, the basic elements are the objects defined by means of vectorial contours that still are simple entities. Later on, it works with the motifs (object groups), that already constitute organizations with a complete meaning. And finally, in the last stages, we arrive at the greater level of abstraction, with the structure of the pattern.

At the same time that one advances in the analysis of a pattern, the obtained data provides information used for the pattern reconstruction, by replacing wrong elements and fitting all the elements to the structure in the proper way. This reconstruction takes great importance in patterns that come from historical sources, often with centuries of antiquity (which can have deteriorated with the passing time) and characterized, in addition, by its artisan character, with the consequent geometric inaccuracies.

In order to take advantage of the analysis result, we have developed tools that let us use the possibilities for the creation of new patterns or designs:
•	The object shapes are vectorial, that’s why they can use the capacities that incorporate the most habitual tools in graphical design.
•	The structure can be edited like any other element, what influence in how the object and motif distribution on the pattern is.
•	In addition, methods able to generate patterns automatically have been developed, applying to the basic content of a pattern the different structures that are compatible with it.

All this, allows applications in as many fields as:
1.	Analysis and cataloguing tools useful for investigators in fields as the graphical design history, architectonic elements, woven, etc.
2.	Creation of historical archives (databases of patrimony inventories) with complex information, taking advantages of the reconstruction possibilities.
3.	Comparative studies of different periods or regions, thanks to the previous databases.
4.	New high level edition tools for the Design Departments of textile and ceramic industries, that let the inclusion of historical elements.

In order to validate the developed tools, 150 patterns have been analyzed and reconstructed. These patterns come from diverse origins, emphasizing the complete studies of ceramic tiling of the Alcazar of Seville and the Alhambra of Granada, adding to them patterns coming from textiles and, extending the initial scope of different flat elements from the street furniture. In some of the patterns, structural edition possibilities are showed for the analyzed pattern.


Keywords
Plane Symmetry Groups, Patterns, Ceramic coatings, Textile, Visual perception, Image Analysis, Shape recognition, Image reconstruction, Graphical design