Video coding based on fractals and sparse representations

Orientador: Hélio PedriniDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Vídeos são sequências de imagens estáticas representando cenas em movimento. Transmitir e armazenar essas imagens sem nenhum tipo de pré-processamento necessitaria de enormes larguras de banda nos canais de comunicação e uma quantidade massiva de espaço de armazenamento. A fim de reduzir o número de bits necessários para tais dados, foram criados métodos de compressão com perda. Esses métodos geralmente consistem em um codificador e um decodificador, tal que o codificador gera uma sequência de bits que representa uma aproximação razoável do vídeo através de um formato pré-especificado e o decodificador lê essa sequência, convertendo-a novamente em uma série de imagens. A transmissão de vídeos sob restrições extremas de largura de banda tem aplicações importantes como videoconferências e circuitos fechados de televisão. Neste trabalho são abordados dois métodos destinados a essa aplicação, decomposição usando representações esparsas e compressão fractal. A ampla maioria dos codificadores tem como mecanismo principal o uso de transformações inversíveis capazes de representar imagens espacialmente suaves com poucos coeficientes não-nulos. Representações esparsas são uma generalização dessa ideia, em que a transformação tem como base um conjunto cujo número de elementos excede a dimensão do espaço vetorial onde ela opera. A projeção dos dados pode ser feita a partir de uma heurística rápida chamada Matching Pursuit. Uma abordagem combinando essa heurística com um algoritmo para gerar a base sobrecompleta por aprendizado de máquina é apresentada. Codificadores fractais representam uma aproximação da imagem como um sistema de funções iterativas. Para isso, criam e transmitem uma sequência de comandos, chamada colagem, capazes de obter uma representação da imagem na escala original dada a mesma imagem em uma escala reduzida. A colagem é criada de tal forma que, se aplicada a uma imagem inicial qualquer repetidas vezes, reduzindo sua escala antes de toda iteração, converge em uma aproximação da imagem codificada. Métodos simplificados e rápidos para a criação da colagem e uma generalização desses métodos para a compressão de vídeos são apresentados. Ao invés de construir a colagem tentando mapear qualquer bloco da escala reduzida na escala original, apenas um conjunto pequeno de blocos é considerado. O método de compressão proposto para vídeos agrupa um conjunto de quadros consecutivos do vídeo em um fractal volumétrico. A colagem mapeia blocos tridimensionais entre as escalas, considerando uma escala menor tanto no tempo quanto no espaço. Uma adaptação desse método para canais de comunicação cuja largura de banda é instável também é propostaAbstract: 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 presentedMestradoCiência da ComputaçãoMestre em Ciência da Computaçã

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Evidence of Embodied Social Competence During Conversation in High Functioning Children with Autism Spectrum Disorder

Even high functioning children with Autism Spectrum Disorder (ASD) exhibit impairments that affect their ability to carry out and maintain effective social interactions in multiple contexts. One aspect of subtle nonverbal communication that might play a role in this impairment is the whole-body motor coordination that naturally arises between people during conversation. The current study aimed to measure the time-dependent, coordinated whole-body movements between children with ASD and a clinician during a conversational exchange using tools of nonlinear dynamics. Given the influence that subtle interpersonal coordination has on social interaction feelings, we expected there to be important associations between the dynamic motor movement measures introduced in the current study and the measures used traditionally to categorize ASD impairment (ADOS-2, joint attention and theory of mind). The study found that children with ASD coordinated their bodily movements with a clinician, that these movements were complex and that the complexity of the children’s movements matched that of the clinician’s movements. Importantly, the degree of this bodily coordination was related to higher social cognitive ability. This suggests children with ASD are embodying some degree of social competence during conversations. This study demonstrates the importance of further investigating the subtle but important bodily movement coordination that occurs during social interaction in children with ASD