On the Mahalanobis Distance Classification Criterion for Multidimensional Normal Distributions

Many existing engineering works model the statistical characteristics of the entities under study as normal distributions. These models are eventually used for decision making, requiring in practice the definition of the classification region corresponding to the desired confidence level. Surprisingly enough, however, a great amount of computer vision works using multidimensional normal models leave unspecified or fail to establish correct confidence regions due to misconceptions on the features of Gaussian functions or to wrong analogies with the unidimensional case. The resulting regions incur in deviations that can be unacceptable in high-dimensional models. Here we provide a comprehensive derivation of the optimal confidence regions for multivariate normal distributions of arbitrary dimensionality. To this end, firstly we derive the condition for region optimality of general continuous multidimensional distributions, and then we apply it to the widespread case of the normal probability density function. The obtained results are used to analyze the confidence error incurred by previous works related to vision research, showing that deviations caused by wrong regions may turn into unacceptable as dimensionality increases. To support the theoretical analysis, a quantitative example in the context of moving object detection by means of background modeling is given.

Expressive power of binary relevance and chain classifiers based on Bayesian Networks for multi-label classification

Bayesian network classifiers are widely used in machine learning because they intuitively represent causal relations. Multi-label classification problems require each instance to be assigned a subset of a defined set of h labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of h binary classes. In this paper we obtain the decision boundaries of two widely used Bayesian network approaches for building multi-label classifiers: Multi-label Bayesian network classifiers built using the binary relevance method and Bayesian network chain classifiers. We extend our previous single-label results to multi-label chain classifiers, and we prove that, as expected, chain classifiers provide a more expressive model than the binary relevance method.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Autonomous classification models in ubiquitous environments

Stream-mining approach is defined as a set of cutting-edge techniques designed to process streams of data in real time, in order to extract knowledge. In the particular case of classification, stream-mining has to adapt its behaviour to the volatile underlying data distributions, what has been called concept drift. Moreover, it is important to note that concept drift may lead to situations where predictive models become invalid and have therefore to be updated to represent the actual concepts that data poses. In this context, there is a specific type of concept drift, known as recurrent concept drift, where the concepts represented by data have already appeared in the past. In those cases the learning process could be saved or at least minimized by applying a previously trained model. This could be extremely useful in ubiquitous environments that are characterized by the existence of resource constrained devices. To deal with the aforementioned scenario, meta-models can be used in the process of enhancing the drift detection mechanisms used by data stream algorithms, by representing and predicting when the change will occur. There are some real-world situations where a concept reappears, as in the case of intrusion detection systems (IDS), where the same incidents or an adaptation of them usually reappear over time. In these environments the early prediction of drift by means of a better knowledge of past models can help to anticipate to the change, thus improving efficiency of the model regarding the training instances needed. By means of using meta-models as a recurrent drift detection mechanism, the ability to share concepts representations among different data mining processes is open. That kind of exchanges could improve the accuracy of the resultant local model as such model may benefit from patterns similar to the local concept that were observed in other scenarios, but not yet locally. This would also improve the efficiency of training instances used during the classification process, as long as the exchange of models would aid in the application of already trained recurrent models, that have been previously seen by any of the collaborative devices. Which it is to say that the scope of recurrence detection and representation is broaden. In fact the detection, representation and exchange of concept drift patterns would be extremely useful for the law enforcement activities fighting against cyber crime. Being the information exchange one of the main pillars of cooperation, national units would benefit from the experience and knowledge gained by third parties. Moreover, in the specific scope of critical infrastructures protection it is crucial to count with information exchange mechanisms, both from a strategical and technical scope. The exchange of concept drift detection schemes in cyber security environments would aid in the process of preventing, detecting and effectively responding to threads in cyber space. Furthermore, as a complement of meta-models, a mechanism to assess the similarity between classification models is also needed when dealing with recurrent concepts. In this context, when reusing a previously trained model a rough comparison between concepts is usually made, applying boolean logic. The introduction of fuzzy logic comparisons between models could lead to a better efficient reuse of previously seen concepts, by applying not just equal models, but also similar ones. This work faces the aforementioned open issues by means of: the MMPRec system, that integrates a meta-model mechanism and a fuzzy similarity function; a collaborative environment to share meta-models between different devices; a recurrent drift generator that allows to test the usefulness of recurrent drift systems, as it is the case of MMPRec. Moreover, this thesis presents an experimental validation of the proposed contributions using synthetic and real datasets.

Automated detection and classification of brain injury lesions on structural magnetic resonance imaging

El daño cerebral adquirido (DCA) es un problema social y sanitario grave, de magnitud creciente y de una gran complejidad diagnóstica y terapéutica. Su elevada incidencia, junto con el aumento de la supervivencia de los pacientes, una vez superada la fase aguda, lo convierten también en un problema de alta prevalencia. En concreto, según la Organización Mundial de la Salud (OMS) el DCA estará entre las 10 causas más comunes de discapacidad en el año 2020. La neurorrehabilitación permite mejorar el déficit tanto cognitivo como funcional y aumentar la autonomía de las personas con DCA. Con la incorporación de nuevas soluciones tecnológicas al proceso de neurorrehabilitación se pretende alcanzar un nuevo paradigma donde se puedan diseñar tratamientos que sean intensivos, personalizados, monitorizados y basados en la evidencia. Ya que son estas cuatro características las que aseguran que los tratamientos son eficaces. A diferencia de la mayor parte de las disciplinas médicas, no existen asociaciones de síntomas y signos de la alteración cognitiva que faciliten la orientación terapéutica. Actualmente, los tratamientos de neurorrehabilitación se diseñan en base a los resultados obtenidos en una batería de evaluación neuropsicológica que evalúa el nivel de afectación de cada una de las funciones cognitivas (memoria, atención, funciones ejecutivas, etc.). La línea de investigación en la que se enmarca este trabajo de investigación pretende diseñar y desarrollar un perfil cognitivo basado no sólo en el resultado obtenido en esa batería de test, sino también en información teórica que engloba tanto estructuras anatómicas como relaciones funcionales e información anatómica obtenida de los estudios de imagen. De esta forma, el perfil cognitivo utilizado para diseñar los tratamientos integra información personalizada y basada en la evidencia. Las técnicas de neuroimagen representan una herramienta fundamental en la identificación de lesiones para la generación de estos perfiles cognitivos. La aproximación clásica utilizada en la identificación de lesiones consiste en delinear manualmente regiones anatómicas cerebrales. Esta aproximación presenta diversos problemas relacionados con inconsistencias de criterio entre distintos clínicos, reproducibilidad y tiempo. Por tanto, la automatización de este procedimiento es fundamental para asegurar una extracción objetiva de información. La delineación automática de regiones anatómicas se realiza mediante el registro tanto contra atlas como contra otros estudios de imagen de distintos sujetos. Sin embargo, los cambios patológicos asociados al DCA están siempre asociados a anormalidades de intensidad y/o cambios en la localización de las estructuras. Este hecho provoca que los algoritmos de registro tradicionales basados en intensidad no funcionen correctamente y requieran la intervención del clínico para seleccionar ciertos puntos (que en esta tesis hemos denominado puntos singulares). Además estos algoritmos tampoco permiten que se produzcan deformaciones grandes deslocalizadas. Hecho que también puede ocurrir ante la presencia de lesiones provocadas por un accidente cerebrovascular (ACV) o un traumatismo craneoencefálico (TCE). Esta tesis se centra en el diseño, desarrollo e implementación de una metodología para la detección automática de estructuras lesionadas que integra algoritmos cuyo objetivo principal es generar resultados que puedan ser reproducibles y objetivos. Esta metodología se divide en cuatro etapas: pre-procesado, identificación de puntos singulares, registro y detección de lesiones. Los trabajos y resultados alcanzados en esta tesis son los siguientes: Pre-procesado. En esta primera etapa el objetivo es homogeneizar todos los datos de entrada con el objetivo de poder extraer conclusiones válidas de los resultados obtenidos. Esta etapa, por tanto, tiene un gran impacto en los resultados finales. Se compone de tres operaciones: eliminación del cráneo, normalización en intensidad y normalización espacial. Identificación de puntos singulares. El objetivo de esta etapa es automatizar la identificación de puntos anatómicos (puntos singulares). Esta etapa equivale a la identificación manual de puntos anatómicos por parte del clínico, permitiendo: identificar un mayor número de puntos lo que se traduce en mayor información; eliminar el factor asociado a la variabilidad inter-sujeto, por tanto, los resultados son reproducibles y objetivos; y elimina el tiempo invertido en el marcado manual de puntos. Este trabajo de investigación propone un algoritmo de identificación de puntos singulares (descriptor) basado en una solución multi-detector y que contiene información multi-paramétrica: espacial y asociada a la intensidad. Este algoritmo ha sido contrastado con otros algoritmos similares encontrados en el estado del arte. Registro. En esta etapa se pretenden poner en concordancia espacial dos estudios de imagen de sujetos/pacientes distintos. El algoritmo propuesto en este trabajo de investigación está basado en descriptores y su principal objetivo es el cálculo de un campo vectorial que permita introducir deformaciones deslocalizadas en la imagen (en distintas regiones de la imagen) y tan grandes como indique el vector de deformación asociado. El algoritmo propuesto ha sido comparado con otros algoritmos de registro utilizados en aplicaciones de neuroimagen que se utilizan con estudios de sujetos control. Los resultados obtenidos son prometedores y representan un nuevo contexto para la identificación automática de estructuras. Identificación de lesiones. En esta última etapa se identifican aquellas estructuras cuyas características asociadas a la localización espacial y al área o volumen han sido modificadas con respecto a una situación de normalidad. Para ello se realiza un estudio estadístico del atlas que se vaya a utilizar y se establecen los parámetros estadísticos de normalidad asociados a la localización y al área. En función de las estructuras delineadas en el atlas, se podrán identificar más o menos estructuras anatómicas, siendo nuestra metodología independiente del atlas seleccionado. En general, esta tesis doctoral corrobora las hipótesis de investigación postuladas relativas a la identificación automática de lesiones utilizando estudios de imagen médica estructural, concretamente estudios de resonancia magnética. Basándose en estos cimientos, se han abrir nuevos campos de investigación que contribuyan a la mejora en la detección de lesiones. ABSTRACT Brain injury constitutes a serious social and health problem of increasing magnitude and of great diagnostic and therapeutic complexity. Its high incidence and survival rate, after the initial critical phases, makes it a prevalent problem that needs to be addressed. In particular, according to the World Health Organization (WHO), brain injury will be among the 10 most common causes of disability by 2020. Neurorehabilitation improves both cognitive and functional deficits and increases the autonomy of brain injury patients. The incorporation of new technologies to the neurorehabilitation tries to reach a new paradigm focused on designing intensive, personalized, monitored and evidence-based treatments. Since these four characteristics ensure the effectivity of treatments. Contrary to most medical disciplines, it is not possible to link symptoms and cognitive disorder syndromes, to assist the therapist. Currently, neurorehabilitation treatments are planned considering the results obtained from a neuropsychological assessment battery, which evaluates the functional impairment of each cognitive function (memory, attention, executive functions, etc.). The research line, on which this PhD falls under, aims to design and develop a cognitive profile based not only on the results obtained in the assessment battery, but also on theoretical information that includes both anatomical structures and functional relationships and anatomical information obtained from medical imaging studies, such as magnetic resonance. Therefore, the cognitive profile used to design these treatments integrates information personalized and evidence-based. Neuroimaging techniques represent an essential tool to identify lesions and generate this type of cognitive dysfunctional profiles. Manual delineation of brain anatomical regions is the classical approach to identify brain anatomical regions. Manual approaches present several problems related to inconsistencies across different clinicians, time and repeatability. Automated delineation is done by registering brains to one another or to a template. However, when imaging studies contain lesions, there are several intensity abnormalities and location alterations that reduce the performance of most of the registration algorithms based on intensity parameters. Thus, specialists may have to manually interact with imaging studies to select landmarks (called singular points in this PhD) or identify regions of interest. These two solutions have the same inconvenient than manual approaches, mentioned before. Moreover, these registration algorithms do not allow large and distributed deformations. This type of deformations may also appear when a stroke or a traumatic brain injury (TBI) occur. This PhD is focused on the design, development and implementation of a new methodology to automatically identify lesions in anatomical structures. This methodology integrates algorithms whose main objective is to generate objective and reproducible results. It is divided into four stages: pre-processing, singular points identification, registration and lesion detection. Pre-processing stage. In this first stage, the aim is to standardize all input data in order to be able to draw valid conclusions from the results. Therefore, this stage has a direct impact on the final results. It consists of three steps: skull-stripping, spatial and intensity normalization. Singular points identification. This stage aims to automatize the identification of anatomical points (singular points). It involves the manual identification of anatomical points by the clinician. This automatic identification allows to identify a greater number of points which results in more information; to remove the factor associated to inter-subject variability and thus, the results are reproducible and objective; and to eliminate the time spent on manual marking. This PhD proposed an algorithm to automatically identify singular points (descriptor) based on a multi-detector approach. This algorithm contains multi-parametric (spatial and intensity) information. This algorithm has been compared with other similar algorithms found on the state of the art. Registration. The goal of this stage is to put in spatial correspondence two imaging studies of different subjects/patients. The algorithm proposed in this PhD is based on descriptors. Its main objective is to compute a vector field to introduce distributed deformations (changes in different imaging regions), as large as the deformation vector indicates. The proposed algorithm has been compared with other registration algorithms used on different neuroimaging applications which are used with control subjects. The obtained results are promising and they represent a new context for the automatic identification of anatomical structures. Lesion identification. This final stage aims to identify those anatomical structures whose characteristics associated to spatial location and area or volume has been modified with respect to a normal state. A statistical study of the atlas to be used is performed to establish which are the statistical parameters associated to the normal state. The anatomical structures that may be identified depend on the selected anatomical structures identified on the atlas. The proposed methodology is independent from the selected atlas. Overall, this PhD corroborates the investigated research hypotheses regarding the automatic identification of lesions based on structural medical imaging studies (resonance magnetic studies). Based on these foundations, new research fields to improve the automatic identification of lesions in brain injury can be proposed.