Uma abordagem de compressão de imagens através de sistemas de funções iteradas

• Autor(a) principal: Reis, Glauco dos Santos
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do Mackenzie
• Texto Completo: http://dspace.mackenzie.br/handle/10899/24324
• topic: fractal; IFS (Iterated Function System); compressão de imagem; problema inverso; sistema de funções iteradas; transformação afim; fractal, IFS (Iterated Function System); image compression; inverse problem; iterated function systems; affine transformation; CNPQ::ENGENHARIAS::ENGENHARIA ELETRICA

A new image compression technique is proposed, based on the affine transformations (ATs) that define an iterated function system (IFS). Previous related research in the field has shown that an image may be approximated by iteratively subjecting a set of sub-regions to a group of ATs. In this case, the original image should be partitioned in regions, and each one of the active pixels are transformed by the AT. The new transformed set should be approximated to other image regions. This iterated execution to find ATs for the best set of areas might result in smaller storage space since the similar areas might be replaced by AT coefficients. Despite this advantage, the technique is computationally intensive, because both the sub-regions and the corresponding ATs that have to be searched for. Here, a new form of similarity is proposed, based on the successive points generated by the iteration of affine transformations. By understanding an AT as a discrete dynamical system, with each image point represented by an iteration of the AT, the method captures similarities between these points, namely, those with the same color in the image; by saving the starting point and the transformations coefficients, the points can be iterated back, to reconstruct the original image. This results in lighter computational effort, since the comparison is made point by point, instead of region by region. Experiments were made on a group of 10 images, representing a broad set of distinct features and resolutions. The proposed algorithm competes in terms of storage size, when compared to JPEG, mainly when the image size is small, and the number of colors are reduced, as currently happens for most images used in the Internet. Although the proposed method is faster than the traditional method for IFS compression, it is slower than common file formats like JPEG.