Pattern modelling and pattern processing in image and speech signals

Aplicar teoria de patrons a senyals de veu i imatge. [ANGLÈS] In the context of signal processing, the aim of this memoir is to explore the pattern theory (PT) of Grenander and Mumford by focussing on two proof-of-concept applications, one dealing with images and the other with voice. The image application not only classifies the symmetry type of mosaics given a digital picture, but also can generate mosaic images with virtually any pattern decoration. The voice application classifies the phonemes in a digital voice recording and also can generate virtually unlimited variations on its pronunciation. These applications illustrate, in ways that are described in detail in the memoir, some of the key advantages of PT over and beyond the more familiar approaches known as pattern recognition and pattern classification. One important advantage is a sort of "division of labor": the construction of pattern models, which takes into account the data and is eminently theoretical, is separate from the pattern processing work (implementation, algorithms, programs). A second advantage is that pattern analysis (recognition, classification) and pattern synthesis (generating random instances that "look and feel" just as the world signals being modeled) become two sides of the same coin, in the sense that the same approach provides both. Actually, analysis is done via synthesis, because the inspiration for the proposed models comes from the data and recognition is resolved by using suitable plausibility rules in order to find the best pattern parameters fitting the data. Another advantage of the approach is its resilience in front of noisy and ambiguous samples. Finally, it is important to remark that pattern models can often be reused on data that are totally unrelated to the data that led to those models. [CASTELLÀ] En el contexto del procesamiento de la señal, el objetivo de esta memoria es la de explorar la teoría de patrones (PT) de Grenander y Mumford, centrándose en dos aplicaciones, uno relativa a las imágenes y la otra a la voz. La aplicación de imagen no sólo clasifica el tipo de simetría de los mosaicos dada una imagen digital, sino también puede generar imágenes de mosaico con prácticamente cualquier decoración. La aplicación clasifica los fonemas de voz de una grabación digital de voz y también puede generar variaciones prácticamente ilimitadas en su pronunciación. Estas aplicaciones ilustran, de manera que se describen en detalle en la memoria, algunas de las p