Codificação de vídeo baseada em fractais e representações esparsas / Video coding based on fractals and sparse representations


IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia




A video is a sequence of still images representing scenes in motion. A video is a sequence of extremely similar images separated by abrupt changes in their content. If these images were transmitted and stored without any kind of preprocessing, this would require a massive amount of storage space and communication channels with very high bandwidths. Lossy compression methods were created in order to reduce the number of bits used to represent this kind of data. These methods generally consist in an encoder and a decoder, where the encoder generates a sequence of bits that represents an acceptable approximation of the video using a certain predefined format and the decoder reads this sequence, converting it back into a series of images. Transmitting videos under extremely limited bandwidth has important applications in video conferences or closed-circuit television systems. Two different approaches are explored in this work, decomposition based on sparse representations and fractal coding. Most video coders are based on invertible transforms capable of representing spatially smooth images with few non-zero coeficients. Sparse representations are a generalization of this idea using a transform that has an overcomplete dictionary as a basis. Overcomplete dictionaries are sets with more elements in it than the dimension of the vector space in which the transform operates. The data can be projected into this basis using a fast heuristic called Matching Pursuits. A video encoder combining this fast heuristic with a machine learning algorithm capable of constructing the overcomplete dictionary is proposed. Fractal encoders represent an approximation of the image through an iterated function system. In order to do that, a sequence of instructions, called a collage, is created and transmitted. The collage can construct an approximation of the original image given a smaller scale version of it. It is created in such a way that, when applied to any initial image several times, contracting it before each iteration, it converges into an approximation of the encoded image. Simplier and faster methods for creating a collage and a generalization of these methods to video compression are presented. Instead of constructing a collage by matching any block from the smaller scale to the original one, a small subset of possible matches is considered. The proposed video encoding method creates groups of consecutive frames which are used to construct a volumetric fractal. The collage maps tridimensional blocks between the different scales, using a smaller scale in both space and time. An improved version of this algorithm designed for communication channels with variable bandwidth is presented


compressão de imagens fractais método de decomposição image compression fractals decomposition method

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