Los invariantes generados a partir de momentos extra¿ıdos de una imagen aparecen recurrentemente en la bibliograf¿ıa como uno de los me¿todos ma¿s potentes para la descripcio¿n de ima¿genes, y ma¿s concretamente de formas. En este art¿ıculo se propone el uso de funciones de base continuas a intervalos (PCBF) como alternativa a las bases que se vienen utilizando tradicionalmente en la aplicacio¿n de este me¿todo, todas ellas continas como puedan ser las muy conocidas de Zernike, Legendre o Tchebichev. El uso de funciones discontinuas se justifica en la naturaleza discontinua de los objetos analizados, en este caso las ima¿genes: es de sobra conocido que los contornos de los objetos visibles en ellas se caracterizan como discontinuidades en la serie de valores de luminancia cuando nos desplazamos de un lado a otro de dichos contornos. El ana¿lisis de tales sen¿ales con funciones continuas produce resultados no deseados, como el feno¿meno de Gibbs, que pueden ser evitados mediante el uso de funciones como las propuestas, generando mejores aproximaciones a la forma analizada. Adicionalmente, las bases propuestas permiten fa¿cilmente, como se demuestra, la generacio¿n de invariantes a rotacio¿n, caracter¿ıstica altamente deseable para un descriptor de forma, puesto que a priori no se conoce con que¿ orientacio¿n aparecera¿ esta en la imagen objeto del ana¿lisis. La invarianza a traslacio¿n y escala se consigue mediante un sencillo proceso de normalizacio¿n. Se presentan los test que confirman esta hipo¿tesis, comenzando por un ana¿lisis del comportamiento de los invariantes ante el ruido en la imagen que permitira¿ determinar en que¿ nu¿mero deben ser extra¿ıdos. A continuacio¿n, y una vez definida esta longitud de descripcio¿n, se realizan sendos experimentos para determinar el comportamiento de los invariantes propuestos en una tarea de recuperacio¿n de ima¿genes, tanto libres de ruido como corrompidas con distintos grados de ruido gaussiano. Los resultados avalan la hipo¿tesis de idoneidad para la tarea, demostrando que se pueden alcanzar resultados similares a los de la base de referencia, Zernike, utilizando descripciones hasta un 40% ma¿s cortas.
Invariants generated departing from moments, previously extracted from an image, appear frequently in the bibliography as one of the most powerful means of describing images, and more precisely shapes. In this paper, the use of Piecewise Continuous Basis Functions (PCBF) is proposed as an alternative to those basis which have been used traditionally in the method of moments, all of them continuous as the well known Zernike, Legendre or Tchebichev basis. The use of discontinuous basis can be justified by the own discontinuous nature of the object of such analysis, namely images: it is thoroughly known that the contours of visible objects are modeled as discontinuities in the series of luminance values as we go from one side of the border to the other. Analyzing such discontinuous objects by means of continuous functions can lead to undesired results, as the Gibbs phenomenon, that can be avoided by simply shifting to discontinuous basis for the analysis, getting better approximations to the described object. Additionally, the proposed basis can easily generate, as shown in this paper, rotation invariants, which is a very desirable feature for a shape descriptor, given that the orientation that the shape will have in an image is not known in advance. Translation and scale invariance is obtained by means of a simple normalization process. Test confirming this hypothesis are presented as well, starting with an analysis of the behavior of the proposed invariantes in noisy environments, which allow to fix the number of invariants that have to be extracted. Next, once this description length has been determined, new experiments are carried out to assess the performance of the proposed invariants in a content based retrieval task, both in a noise free and in noisy environments, having images corrupted with different gaussian noise intensities. Results confirm our hypothesis that these descriptors are very well suited for this task, showing that they can achieve results similar to those obtained using the continuous reference basis, which is Zernike's, but with a description which is roughly a 40% shorter.
Bovik, 2009, Chen and Xie, 2011, Dominguez, 2013, Fisher, 2011, Flusser, 2000, Flusser et al., 2009, Hamood and Boussakta, 2011, Hewitt and Hewitt, 1979, Hu, 1962, Khotanzad and Hong, 1990, Krommweh, 2009, Lee and Tarng, 1999, Mukundan, 2004, Rao, 1983, Reiss, 1991, Rudin, 1991, Sasikala and Neevelani, 2010, Sharvit et al., 1998, Teague, 1980, Teh and Chin, 1988, Walsh, 1923 and Xu and Li, 2008.