Utilização da técnica de preenchimento de espaço em texturas - GREGORIIS, Giordanna de (2020)
Texture is one of the main visual attributes for describing patterns found in nature. Several methods of texture analysis have been used as a powerful tool for real applications involving image analysis and computational vision. However, existing methods can not successfully discriminate the complexity of texture patterns. Such methods disregard the possibility of describing image structures through measures such as the fractal dimension. Measures based on fractality allow a non-integer geometric interpretation that has applications in areas such as Mathematics, Physics, Biology, etc. In recent years, fractal analysis has emerged as a promising approach to capturing self-similarities in textures. Based on the fractal analysis, many successful approaches to texture classification were proposed. The basic idea of these methods is to use fractal dimension to summarize the spatial distribution of image patterns. In this paper the algorithm proposed by Shier and Bourke which uses, in an empirical way, ideas and some procedures of Fractal Geometry, was analyzed and implemented. Besides the application in the generation of textures for computer graphics in general, it has been investigated the use of the algorithm in two special situations: space filling and artistic texture. This algorithm that aims to fill a specific region using shapes whose distribution obeys a Power Law ruled by the Hurwitz zeta function, in this way these shapes are inserted ad infinitum. As a final result images with self-similar textures that resembles the Apollonian fractal (when using circles) are displayed. As a final product of the monograph it was developed a tool, called Mosaico Fractal, which is able to fill a two-dimensional region with geometric figures and generate artistic textures. An important feature of this paper is the interactions between Computer Science, Mathematics and Art, allowing an interdisciplinary view of the subject.