Watermarking applications of Krawtchouk-Sobolev type orthogonal moments

In this contribution, we consider the sequence {Hn(x; q)}n≥0 of monic polynomials orthogonal with respect to a Sobolev-type inner product involving forward difference operators For the first time in the literature, we apply the non-standard properties of {Hn(x; q)}n≥0 in a watermarking problem. Several differences are found in this watermarking application for the non-standard cases (when j > 0) with respect to the standard classical Krawtchouk case λ = µ = 0.Universidad de Alcal

On The Potential of Image Moments for Medical Diagnosis

Medical imaging is widely used for diagnosis and postoperative or post-therapy monitoring. The ever-increasing number of images produced has encouraged the introduction of automated methods to assist doctors or pathologists. In recent years, especially after the advent of convolutional neural networks, many researchers have focused on this approach, considering it to be the only method for diagnosis since it can perform a direct classification of images. However, many diagnostic systems still rely on handcrafted features to improve interpretability and limit resource consumption. In this work, we focused our efforts on orthogonal moments, first by providing an overview and taxonomy of their macrocategories and then by analysing their classification performance on very different medical tasks represented by four public benchmark data sets. The results confirmed that convolutional neural networks achieved excellent performance on all tasks. Despite being composed of much fewer features than those extracted by the networks, orthogonal moments proved to be competitive with them, showing comparable and, in some cases, better performance. In addition, Cartesian and harmonic categories provided a very low standard deviation, proving their robustness in medical diagnostic tasks. We strongly believe that the integration of the studied orthogonal moments can lead to more robust and reliable diagnostic systems, considering the performance obtained and the low variation of the results. Finally, since they have been shown to be effective on both magnetic resonance and computed tomography images, they can be easily extended to other imaging techniques

Improved Feature Extraction, Feature Selection, and Identification Techniques That Create a Fast Unsupervised Hyperspectral Target Detection Algorithm

This research extends the emerging field of hyperspectral image (HSI) target detectors that assume a global linear mixture model (LMM) of HSI and employ independent component analysis (ICA) to unmix HSI images. Via new techniques to fully automate feature extraction, feature selection, and target pixel identification, an autonomous global anomaly detector, AutoGAD, has been developed for potential employment in an operational environment for real-time processing of HSI targets. For dimensionality reduction (initial feature extraction prior to ICA), a geometric solution that effectively approximates the number of distinct spectral signals is presented. The solution is based on the theory of the shape of the eigenvalue curve of the covariance matrix of spectral data containing noise. For feature selection, previously a subjective definition called significant kurtosis change was used to denote the separation between targets classes and non-target classes. This research presents two new measures, potential target signal to noise ratio (PT SNR) and max pixel score which computed for each of the ICA features to create a new two dimensional feature space where the overlap between target and non-target classes is reduced compared to the one dimensional kurtosis value feature space. Finally, after target feature selection, adaptive noise filtering, but with an iterative approach, is applied to the signals. The effect is a reduction in the power of the noise while preserving the power of the target signal prior to target identification to reduce false positive detections. A zero-detection histogram method is applied to the smoothed signals to identify target locations to the user. MATLAB code for the AutoGAD algorithm is provided

Iterated integrals of orthogonal polynomials and applications

Mención Internacional en el título de doctorLa presente tesis doctoral tiene por objeto el estudio de familias de polinomios que son soluciones del siguiente problema con valores iniciales donde tanto f como g son polinomios y L en los capítulos 2 y 3 es el operador derivada m-ésima de f. La diferencia en los dos casos anteriores es que mientras en el capítulo 2 se considera que g es un polinomio ortogonal clásico sobre la recta real, en el capítulo 3 denotamos por g al polinomio ortogonal con respecto a una cierta medida soportada sobre un arco de la circunferencia unidad y [omega]k es constante para cada k = 0 ,..., m. El capítulo 4, se dedica a las aplicaciones al procesamiento digital de imágenes, de las soluciones del problema (1) cuando f = g. Como puede apreciarse más adelante, este último caso corresponde a los conocidos polinomios de Krawtchouk. Acerca de la localización de los puntos críticos de polinomios en términos de sus ceros existe una teoría amplia (vea [72, Part I] y [81]), cuyas bases fundamentales son los teoremas de Rolle, Gauss-Lucas y sus refinamientos. Sin embargo, no existen recíprocos generales de estos resultados. Es obvio, que dado un cero de un polinomio y sus puntos críticos, los restantes ceros están unívocamente determinados. No obstante, solo existen unos pocos resultados sobre localización de ceros en función de sus puntos críticos y uno de sus ceros, la mayoría de los cuales se pueden ver en [72, x4.5]. En general, estos resultados son corolarios del Teorema de Composición de Schur-Szego (vea [72, Th.3.4.1d]. Quizás, los resultados más significativos en este sentido sean los Teoremas de Walsh [72, Th. 4.5.1] y Biernacki [72, Th. 4.5.2]. Hasta donde conocemos, sobre la localización de ceros de integrales iteradas de polinomios, normalizados con la condicin de anularse en el origen, solo existe el trabajo [16]. El mencionado artículo estudia varios casos particulares de familias de polinomios, entre ellos los polinomios de Legendre, y plantea una serie de conjeturas, algunas de las cuales se responden en los Capítulos 2 y 3 de esta memoria. El Capítulo 2 de esta memoria está dedicado a las integrales iteradas de polinomios ortogonales clásicos sobre la recta real, con énfasis en el caso Jacobi. Los trabajos [9, 10] muestran el interés de este tipo de polinomios para las aplicaciones a los métodos numéricos de elementos finitos. Es bien conocido que el polinomio mónico de Hermite Hn+m de grado (n + m) 2 Z+, donde tanto n como m son enteros no negativos. Como se mencionó anteriormente, el tercer capítulo se dedica al estudio del comportamientos asintótico los polinomios obtenidos mediante la integración iterada de los polinomios ortogonales con respecto a medias soportadas en un arco de la circunferencia unidad y el conjunto de acumulación de sus ceros. Se encuentra el comportamiento asintótico relativo entre las familias de polinomios ortogonales y sus respectivas familias de polinomios obtenidos por integración iterada. Se muestra la representación gráfica de regiones cerradas que contienen los ceros de las nuevas familias de polinomios y de curvas donde se acumulan los mismos en varios casos particulares. El tema central del Capítulo 4 es la implementación de un algoritmo eficiente para la detección de bordes de imágenes digitales basado en las propiedades de los polinomios ortogonales de Krawtchouk en dos variables. La primera parte del capítulo se dedica a estudiar las propiedades de esta familia de polinomios ortogonales en dos variables, que son de interés para el algoritmo propuesto. Las novedades de este algoritmo que fundamentan la calificación de eficiente son las siguientes: La aproximación de las diferencias parciales (derivadas parciales discretas) se realiza mediante una combinación lineal de polinomios de Krawtchouk en dos variables, los cuales son ortogonales con respecto a un producto interior discreto que involucra a la distribución binomial. En consecuencia, ya no es necesario suavizar la imagen mediante un filtro Gaussiano en dos dimensiones antes de realizar la diferenciación numérica, con el fin de regularizar la naturaleza mal condicionada de la diferenciación (ver [91]) y por lo tanto mejorar la localización de los bordes. En [11, 36] los autores describen un procedimiento para la detección de bordes utilizando los polinomios discretos de Chebyshev y un único umbral de discriminación de bordes para toda la imagen. Aquí, el algoritmo propuesto utiliza dos niveles de umbrales adaptativos, lo que reduce la presencia de falsos positivos o negativos en la selección de pixels-bordes. El operador gradiente para submatrices bloques de 5x5, en lugar del tradicional 3x3, proporciona una mejor localización de los pixels-bordes, ya que los bordes tienden a ser más gruesos cuando el tamaño del bloque incrementa [36, 69]. Para evitar el efecto de bordes gruesos y mejorar el resultado final en el algoritmo se aplican operaciones morfológicas (estrechar, erosionar y adelgazar) a la imagen de borde obtenida después del segundo paso de procesamiento del algoritmo. Para demostrar la efectividad del algoritmo propuesto se utilizaron imágenes tomadas de dos campos de aplicación muy diferentes: imágenes naturales utilizadas para la detección de objetos, vigilancia, etc; así como mapas de profundidad utilizados actualmente en aplicaciones y servicios multimedia de video 3D. Los contornos de objetos superpuestos, como la identificación de objetos de primer plano en mapas de profundidad, se obtienen con bastante buena precisión.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Francisco José Marcellán Español.- Secretario: Ramón Ángel Orive Rodríguez.- Vocal: Wilfredo Óscar Urbina Romer

Physical Realization of a Supervised Learning System Built with Organic Memristive Synapses

International audienceMultiple modern applications of electronics call for inexpensive chips that can perform complex operations on natural data with limited energy. A vision for accomplishing this is implementing hardware neural networks, which fuse computation and memory, with low cost organic electronics. A challenge, however, is the implementation of synapses (analog memories) composed of such materials. In this work, we introduce robust, fastly programmable, nonvolatile organic memristive nanodevices based on electrografted redox complexes that implement synapses thanks to a wide range of accessible intermediate conductivity states. We demonstrate experimentally an elementary neural network, capable of learning functions, which combines four pairs of organic memristors as synapses and conventional electronics as neurons. Our architecture is highly resilient to issues caused by imperfect devices. It tolerates inter-device variability and an adaptable learning rule offers immunity against asymmetries in device switching. Highly compliant with conventional fabrication processes, the system can be extended to larger computing systems capable of complex cognitive tasks, as demonstrated in complementary simulations

Development of a reflective stereo slope gauge for the measurement of ocean surface wave slope statistics

An optical instrument for the measurement of surface ocean wave statistics has been developed and is presented in this thesis. Based on the reflective stereo slope gauge (RSSG) principle, it can simultaneously measure wave slope and height statistics. The instrument comprises a stereo camera setup and two light sources built from infrared LEDs (940 nm). Slope statistics are derived from the statistical distribution of the positions of specular reflections in images of the water surface. The parallax of the reflections in the stereo images gives the distance of the camera to the water surface which can be used to infer wave height statistics. A laboratory version of the instrument has been built, calibrated and tested in experiments at the Aeolotron wind wave facility. Two-dimensional slope probability distributions for slopes in the range of -0.05 < s_x,s_y < 0.05 were obtained for a range of wind speeds and clean water as well as surface slick conditions. The mean square slope of the surface was derived and compared to data from simultaneous reference measurements. The two data sets are found to agree well for lower wind speeds, at higher wind speeds significant deviations occur. The causes for these deviations have been identified and taken into account in designing the instrument for field measurements. This ocean version of the instrument is ready to accompany heat exchange measurements aboard a research vessel in the Baltic Sea in June 2010

Optical measurement of short wind waves - from the laboratory to the field

With the Reflective Stereo Slope Gauge and the Medium Angle Slope Gauge, two new imaging instruments for the measurement of short wind waves on the ocean have been developed, validated, and deployed to a four week field experiment. Using active illumination with near-infrared LED light sources they are independent of natural light. Unlike other reflection-based techniques, they can be operated day and night under a wide range of environmental conditions. The instruments' performance was carefully validated in the laboratory and in the field. Their unique capabilities of simultaneously measuring the twodimensional slope probability distribution and the mean square slope (mss) of the waves, as well as wave height and a parameter linked to local surface curvature are demonstrated. Extensive measurements of short wave statistics from an air-sea interaction experiment off the coast of Peru are reported. A large variability of surface conditions due to the changing presence of surfactants on spatial scales smaller than one hundred meters was encountered. In a laboratory experiment, the dependence of gas transfer velocities on the suppression of waves by the soluble artificial surfactant Triton X-100 was investigated. It is shown that mss describes gas transfer velocities better than wind speed or the friction velocity. The new instruments can provide robust routine ship-borne measurements of mss, a key component in the effort of replacing wind speed with mean square slope as the standard parameter for gas transfer velocities