About lacunarity, some links between fractal and integral geometry, and an application to texture segmentation

International audienceIn this work, we apply two techniques for segmentation of different states of one texture (e.g. deformations of an homogeneous texture) : - fractal geometry, that deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry - integral geometry, that treats sets globally and allows to introduce robust measures. We focus on the study of two parameters, lacunarity and Favard length, and proove a theoretical link between them. As an application, we are able to achieve automatic classification of lung diseases on the basis on SPECT images

About lacunarity, some links between fractal and integral geometry, and an application to texture segmentation

In this work, we apply two techniques for segmentation of different states of one texture (e.g. deformations of an homogeneous texture) : - fractal geometry, that deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry - integral geometry, that treats sets globally and allows to introduce robust measures. We focus on the study of two parameters, lacunarity and Favard length, and proove a theoretical link between them. As an application, we are able to achieve automatic classification of lung diseases on the basis on SPECT images

Multifractal Segmentation of Images

International audienceIn this work, we propose a multifractal approach to the problem of image analysis. We show that an alternative description of images, based on a multifractal characterization of the signal, can be used instead of the classical approach that involves smoothing of the discrete data in order to compute local extrema. We classify each point of the image according to two parameters, its type of singularity and its relative height, by computing the spectra associated with different kinds of capacities defined from the grey levels. All these informations are then used together through a Bayesian approach

Transformée en ondelettes, tortuosité et lacunarité fractale pour la caractérisation de surfaces rugueuses : application à la mesure de rugosité du pavage

Profils de chaussée et données lasers -- Systèmes d'information géographique -- Normalisation des signaux lasers -- Normalisation par la moyenne locale : approximation et limitation -- Caractérisation de la rugosité -- Segmentation de texture -- Caractérisation de la rugosité -- Segmentation de texture -- Caractérisation de chaque profil -- Caractérisation locale -- Classification -- Séparation des classes et méthode de Fisher -- Données spatialement distribuées et systèmes d'information géographique -- Introduction : système SIG -- Système de gestion de l'information du pavage -- Architecture du système -- Représentation des mesures et analyse

Digital Image Processing

Newspapers and the popular scientific press today publish many examples of highly impressive images. These images range, for example, from those showing regions of star birth in the distant Universe to the extent of the stratospheric ozone depletion over Antarctica in springtime, and to those regions of the human brain affected by Alzheimer’s disease. Processed digitally to generate spectacular images, often in false colour, they all make an immediate and deep impact on the viewer’s imagination and understanding. Professor Jonathan Blackledge’s erudite but very useful new treatise Digital Image Processing: Mathematical and Computational Methods explains both the underlying theory and the techniques used to produce such images in considerable detail. It also provides many valuable example problems - and their solutions - so that the reader can test his/her grasp of the physical, mathematical and numerical aspects of the particular topics and methods discussed. As such, this magnum opus complements the author’s earlier work Digital Signal Processing. Both books are a wonderful resource for students who wish to make their careers in this fascinating and rapidly developing field which has an ever increasing number of areas of application. The strengths of this large book lie in: • excellent explanatory introduction to the subject; • thorough treatment of the theoretical foundations, dealing with both electromagnetic and acoustic wave scattering and allied techniques; • comprehensive discussion of all the basic principles, the mathematical transforms (e.g. the Fourier and Radon transforms), their interrelationships and, in particular, Born scattering theory and its application to imaging systems modelling; discussion in detail - including the assumptions and limitations - of optical imaging, seismic imaging, medical imaging (using ultrasound), X-ray computer aided tomography, tomography when the wavelength of the probing radiation is of the same order as the dimensions of the scatterer, Synthetic Aperture Radar (airborne or spaceborne), digital watermarking and holography; detail devoted to the methods of implementation of the analytical schemes in various case studies and also as numerical packages (especially in C/C++); • coverage of deconvolution, de-blurring (or sharpening) an image, maximum entropy techniques, Bayesian estimators, techniques for enhancing the dynamic range of an image, methods of filtering images and techniques for noise reduction; • discussion of thresholding, techniques for detecting edges in an image and for contrast stretching, stochastic scattering (random walk models) and models for characterizing an image statistically; • investigation of fractal images, fractal dimension segmentation, image texture, the coding and storing of large quantities of data, and image compression such as JPEG; • valuable summary of the important results obtained in each Chapter given at its end; • suggestions for further reading at the end of each Chapter. I warmly commend this text to all readers, and trust that they will find it to be invaluable. Professor Michael J Rycroft Visiting Professor at the International Space University, Strasbourg, France, and at Cranfield University, England

Caracterización de productos del cerdo ibérico mediante el análisis multifractal de imágenes

La presente tesis doctoral se presenta como compendio de publicaciones en las que se propone una metodología no destructiva para la obtención de indicadores que pueden ser usados en métodos predictivos de la calidad de productos cárnicos derivados del cerdo ibérico. Para ello se ha aplicado el análisis multifractal de imágenes digitales de esos productos. Dada la importancia del sector porcino en nuestro país resulta necesario la investigación de nuevas metodologías para el estudio de las características intrínsecas de la raza ibérica como es la infiltración grasa intramuscular que viene determinada por factores genéticos y de alimentación. A su vez, los competitivos precios sumados a la existencia de fraudes en las denominaciones comerciales hacen necesario que en este sector se desarrollen métodos de predicción que de manera rápida y barata ayuden a afrontar estos problemas. El análisis multifractal de imágenes cumple con estas dos características y actualmente está surgiendo como un método innovador en estudios relacionados con la determinación de la calidad y características de diferentes alimentos. Con esta premisa, en una primera publicación se aborda la naturaleza multifractal de la infiltración grasa de solomillo de cerdo blanco y solomillo de cerdo ibérico. Así, se diseñó y se desarrolló el sistema y condicionantes técnicos de obtención de imágenes, el sistema informático de procesado de las imágenes y la metodología del análisis multifractal. El procedimiento general consiste en la obtención de imágenes a color en condiciones homogéneas, tratamiento de las imágenes para obtener una muestra de la región de interés y posterior transformación a blanco (tejido grasoconectivo) y negro (magro), binarización de la imagen a un archivo txt y tratamiento mediante algoritmos para determinar los parámetros multifractales. Mediante este procedimiento, se determinaron los parámetros multifractales comprobando la existencia de autosemejanza en la distribución del tejido graso-conectivo y logrando, gracias a este hecho, la distinción de muestras de ambas razas. El contenido de la segunda publicación se centró en constatar la naturaleza multifractal de la infiltración grasa muestras de jamón de las cuatro denominaciones de cerdo ibérico cortadas a mano y a máquina. Se comprobó la naturaleza multifractal del tejido graso-conectivo de las muestras y la capacidad de distinción entre denominaciones para ambos tipos de corte. En la tercera publicación se propone una optimización en el procesado de las imágenes. Para ello se hace uso de un filtrado homomórfico de paso alto en las regiones de interés de los cortes de jamón ibérico cortado a mano mediante el uso de dos radios de filtro distintos, comparando los resultados del análisis multifractal de estas imágenes con los resultados de las imágenes sin filtro. El estudio llevado a cabo permite apreciar una notable mejora de los resultados para los cortes a mano de las cuatro denominaciones de jamón de cerdo ibérico. Los resultados obtenidos sugieren la idoneidad de la metodología propuesta para generar parámetros descriptores de la distribución caótica del tejido graso-conectivo que pueden ser usados para la predicción de la calidad de la carne del cerdo ibérico.This doctoral thesis is presented as a compendium of publications in which a non-destructive methodology is proposed to obtain indicators that can be used in predictive methods of the quality of meat products derived from Iberian pigs. For this aim, the use of multifractal analysis of images has been applied. Due to the importance of the Iberian pig sector in our country, it is necessary to investigate new methodologies for the study of the intrinsic characteristics of the Iberian breed such as intramuscular fat infiltration that is determined by genetic and feeding factors. At the same time, the competitive prices added to the existence of fraud in the commercial denominations make it necessary for this sector to develop prediction methods that quickly and cheaply help to face these problems. Multifractal image analysis meets these two characteristics and is currently emerging as an innovative method in studies related to the determination of the quality and characteristics of different foods. With this premise, the first study faces the multifractal nature of fatty infiltration of white pork tenderloin and Iberian pork tenderloin. In this study, the system and technical conditions for obtaining images, the computer system for image processing and the methodology of multifractal analysis were designed and developed. The general procedure consists in obtaining color images in homogeneous conditions, treatment of the images to obtain a sample of the region of interest and subsequent transformation to white (fatty-connective tissue) and black (lean), binarization of the image in a txt file and processing using algorithms to determine multifractal parameters. Through this procedure, the multifractal parameters for both pieces were determined by checking the existence of self-similarity in the distribution of fatty-connective tissue and achieving, thanks to this fact, the distinction of samples of both races. The content of the second publication focused on verifying the multifractal nature of the fatty infiltration of ham samples of the four denominations of Iberian pigs cut by hand and by machine. The multifractal nature and the ability to classify between denominations for both types of cut were checked. The third article discusses an optimization in image processing. For this purpose, a high-pass homomorphic filtering is used in the regions of interest of the Iberian ham cuts cut by hand using two different filter radii, comparing the results of the multifractal analysis of these images with the results of the unfiltered images The study results in a remarkable improvement of the results for the hand cuts of the four designations of Iberian pork ham. The results obtained suggest the suitability of the proposed methodology to generate parameters that describe the chaotic distribution of fatty-connective tissue that can be used to predict the quality of Iberian pig meat

Fractals in Geoscience and Remote Sensing

Abstract not availableNA-NOT AVAILABL

Forest disturbance and recovery: A general review in the context of spaceborne remote sensing of impacts on aboveground biomass and canopy structure

Abrupt forest disturbances generating gaps \u3e0.001 km2 impact roughly 0.4–0.7 million km2a−1. Fire, windstorms, logging, and shifting cultivation are dominant disturbances; minor contributors are land conversion, flooding, landslides, and avalanches. All can have substantial impacts on canopy biomass and structure. Quantifying disturbance location, extent, severity, and the fate of disturbed biomass will improve carbon budget estimates and lead to better initialization, parameterization, and/or testing of forest carbon cycle models. Spaceborne remote sensing maps large-scale forest disturbance occurrence, location, and extent, particularly with moderate- and fine-scale resolution passive optical/near-infrared (NIR) instruments. High-resolution remote sensing (e.g., ∼1 m passive optical/NIR, or small footprint lidar) can map crown geometry and gaps, but has rarely been systematically applied to study small-scale disturbance and natural mortality gap dynamics over large regions. Reducing uncertainty in disturbance and recovery impacts on global forest carbon balance requires quantification of (1) predisturbance forest biomass; (2) disturbance impact on standing biomass and its fate; and (3) rate of biomass accumulation during recovery. Active remote sensing data (e.g., lidar, radar) are more directly indicative of canopy biomass and many structural properties than passive instrument data; a new generation of instruments designed to generate global coverage/sampling of canopy biomass and structure can improve our ability to quantify the carbon balance of Earth\u27s forests. Generating a high-quality quantitative assessment of disturbance impacts on canopy biomass and structure with spaceborne remote sensing requires comprehensive, well designed, and well coordinated field programs collecting high-quality ground-based data and linkages to dynamical models that can use this information