Cleaning large correlation matrices: tools from random matrix theory

This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free Probability, with an emphasis on the Marchenko-Pastur equation that provides information on the resolvent of multiplicatively corrupted noisy matrices. Special care is devoted to the statistics of the eigenvectors of the empirical correlation matrix, which turn out to be crucial for many applications. We show in particular how these results can be used to build consistent "Rotationally Invariant" estimators (RIE) for large correlation matrices when there is no prior on the structure of the underlying process. The last part of this review is dedicated to some real-world applications within financial markets as a case in point. We establish empirically the efficacy of the RIE framework, which is found to be superior in this case to all previously proposed methods. The case of additively (rather than multiplicatively) corrupted noisy matrices is also dealt with in a special Appendix. Several open problems and interesting technical developments are discussed throughout the paper.Comment: 165 pages, article submitted to Physics Report

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Quaternion Matrices : Statistical Properties and Applications to Signal Processing and Wavelets

Similarly to how complex numbers provide a possible framework for extending scalar signal processing techniques to 2-channel signals, the 4-dimensional hypercomplex algebra of quaternions can be used to represent signals with 3 or 4 components. For a quaternion random vector to be suited for quaternion linear processing, it must be (second-order) proper. We consider the likelihood ratio test (LRT) for propriety, and compute the exact distribution for statistics of Box type, which include this LRT. Various approximate distributions are compared. The Wishart distribution of a quaternion sample covariance matrix is derived from first principles. Quaternions are isomorphic to an algebra of structured 4x4 real matrices. This mapping is our main tool, and suggests considering more general real matrix problems as a way of investigating quaternion linear algorithms. A quaternion vector autoregressive (VAR) time-series model is equivalent to a structured real VAR model. We show that generalised least squares (and Gaussian maximum likelihood) estimation of the parameters reduces to ordinary least squares, but only if the innovations are proper. A LRT is suggested to simultaneously test for quaternion structure in the regression coefficients and innovation covariance. Matrix-valued wavelets (MVWs) are generalised (multi)wavelets for vector-valued signals. Quaternion wavelets are equivalent to structured MVWs. Taking into account orthogonal similarity, all MVWs can be constructed from non-trivial MVWs. We show that there are no non-scalar non-trivial MVWs with short support [0,3]. Through symbolic computation we construct the families of shortest non-trivial 2x2 Daubechies MVWs and quaternion Daubechies wavelets.Open Acces

Morphometric Otolith Analysis

Abstract Fish otoliths have long played an important role in sustainable �sheries management. Stock assessment models currently used rely on species speci�c age pro�les obtained from the seasonal patterns of growth marks that otoliths exhibit. We compare methods widely used in �sheries science (elliptical Fourier) with an industry standardised encoding method (MPEG7 - Curvature-Scale-Space) and with a recent addition to shape modelling techniques (time-series shapelets) to determine which performs best. An investigation is carried out into transform methods that retain size-information, and whether the boundary encoding method is impacted be otolith age, performing tests over three 2-class otolith datasets across six discrete and concurrent age groups. Impact of segmentation methods are assessed to determine whether automated or expert segmented methods of boundary extraction are more advantageous, and whether constructed classi�ers can be used at di�erent institutions. Tests show that neither time-series shaplets nor Curvature-Scale-Space methods o�er any real advantage over Fourier transform methods given mixed age datasets. However, we show that size indices are most indicative of �sheries stock in younger single-age datasets, with shape holding more discriminatory potential in older samples. Whilst commonly used Fourier transform methods generally return best results; we show that classi�cation of otolith boundaries is impacted by the method of boundary segmentation. Hand traced boundaries produce classi�ers more robust to test data segmentation methods and are more suited to distributed classi�ers. Additionally we present a proof of concept study showing that high energy synchrotron scans are a new, non-invasive method of modelling internal otolith structure, allowing comparison of slices along near in�nite numbers of virtual complex planes

Context-aware home monitoring system for Parkinson's disease patients : ambient and wearable sensing for freezing of gait detection

Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i Technische Universiteit Eindhoven. This PhD Thesis has been developed in the framework of, and according to, the rules of the Erasmus Mundus Joint Doctorate on Interactive and Cognitive Environments EMJD ICE [FPA no. 2010-0012]Parkinson’s disease (PD). It is characterized by brief episodes of inability to step, or by extremely short steps that typically occur on gait initiation or on turning while walking. The consequences of FOG are aggravated mobility and higher affinity to falls, which have a direct effect on the quality of life of the individual. There does not exist completely effective pharmacological treatment for the FOG phenomena. However, external stimuli, such as lines on the floor or rhythmic sounds, can focus the attention of a person who experiences a FOG episode and help her initiate gait. The optimal effectiveness in such approach, known as cueing, is achieved through timely activation of a cueing device upon the accurate detection of a FOG episode. Therefore, a robust and accurate FOG detection is the main problem that needs to be solved when developing a suitable assistive technology solution for this specific user group. This thesis proposes the use of activity and spatial context of a person as the means to improve the detection of FOG episodes during monitoring at home. The thesis describes design, algorithm implementation and evaluation of a distributed home system for FOG detection based on multiple cameras and a single inertial gait sensor worn at the waist of the patient. Through detailed observation of collected home data of 17 PD patients, we realized that a novel solution for FOG detection could be achieved by using contextual information of the patient’s position, orientation, basic posture and movement on a semantically annotated two-dimensional (2D) map of the indoor environment. We envisioned the future context-aware system as a network of Microsoft Kinect cameras placed in the patient’s home that interacts with a wearable inertial sensor on the patient (smartphone). Since the hardware platform of the system constitutes from the commercial of-the-shelf hardware, the majority of the system development efforts involved the production of software modules (for position tracking, orientation tracking, activity recognition) that run on top of the middle-ware operating system in the home gateway server. The main component of the system that had to be developed is the Kinect application for tracking the position and height of multiple people, based on the input in the form of 3D point cloud data. Besides position tracking, this software module also provides mapping and semantic annotation of FOG specific zones on the scene in front of the Kinect. One instance of vision tracking application is supposed to run for every Kinect sensor in the system, yielding potentially high number of simultaneous tracks. At any moment, the system has to track one specific person - the patient. To enable tracking of the patient between different non-overlapped cameras in the distributed system, a new re-identification approach based on appearance model learning with one-class Support Vector Machine (SVM) was developed. Evaluation of the re-identification method was conducted on a 16 people dataset in a laboratory environment. Since the patient orientation in the indoor space was recognized as an important part of the context, the system necessitated the ability to estimate the orientation of the person, expressed in the frame of the 2D scene on which the patient is tracked by the camera. We devised method to fuse position tracking information from the vision system and inertial data from the smartphone in order to obtain patient’s 2D pose estimation on the scene map. Additionally, a method for the estimation of the position of the smartphone on the waist of the patient was proposed. Position and orientation estimation accuracy were evaluated on a 12 people dataset. Finally, having available positional, orientation and height information, a new seven-class activity classification was realized using a hierarchical classifier that combines height-based posture classifier with translational and rotational SVM movement classifiers. Each of the SVM movement classifiers and the joint hierarchical classifier were evaluated in the laboratory experiment with 8 healthy persons. The final context-based FOG detection algorithm uses activity information and spatial context information in order to confirm or disprove FOG detected by the current state-of-the-art FOG detection algorithm (which uses only wearable sensor data). A dataset with home data of 3 PD patients was produced using two Kinect cameras and a smartphone in synchronized recording. The new context-based FOG detection algorithm and the wearable-only FOG detection algorithm were both evaluated with the home dataset and their results were compared. The context-based algorithm very positively influences the reduction of false positive detections, which is expressed through achieved higher specificity. In some cases, context-based algorithm also eliminates true positive detections, reducing sensitivity to the lesser extent. The final comparison of the two algorithms on the basis of their sensitivity and specificity, shows the improvement in the overall FOG detection achieved with the new context-aware home system.Esta tesis propone el uso de la actividad y el contexto espacial de una persona como medio para mejorar la detección de episodios de FOG (Freezing of gait) durante el seguimiento en el domicilio. La tesis describe el diseño, implementación de algoritmos y evaluación de un sistema doméstico distribuido para detección de FOG basado en varias cámaras y un único sensor de marcha inercial en la cintura del paciente. Mediante de la observación detallada de los datos caseros recopilados de 17 pacientes con EP, nos dimos cuenta de que se puede lograr una solución novedosa para la detección de FOG mediante el uso de información contextual de la posición del paciente, orientación, postura básica y movimiento anotada semánticamente en un mapa bidimensional (2D) del entorno interior. Imaginamos el futuro sistema de consciencia del contexto como una red de cámaras Microsoft Kinect colocadas en el hogar del paciente, que interactúa con un sensor de inercia portátil en el paciente (teléfono inteligente). Al constituirse la plataforma del sistema a partir de hardware comercial disponible, los esfuerzos de desarrollo consistieron en la producción de módulos de software (para el seguimiento de la posición, orientación seguimiento, reconocimiento de actividad) que se ejecutan en la parte superior del sistema operativo del servidor de puerta de enlace de casa. El componente principal del sistema que tuvo que desarrollarse es la aplicación Kinect para seguimiento de la posición y la altura de varias personas, según la entrada en forma de punto 3D de datos en la nube. Además del seguimiento de posición, este módulo de software también proporciona mapeo y semántica. anotación de zonas específicas de FOG en la escena frente al Kinect. Se supone que una instancia de la aplicación de seguimiento de visión se ejecuta para cada sensor Kinect en el sistema, produciendo un número potencialmente alto de pistas simultáneas. En cualquier momento, el sistema tiene que rastrear a una persona específica - el paciente. Para habilitar el seguimiento del paciente entre diferentes cámaras no superpuestas en el sistema distribuido, se desarrolló un nuevo enfoque de re-identificación basado en el aprendizaje de modelos de apariencia con one-class Suport Vector Machine (SVM). La evaluación del método de re-identificación se realizó con un conjunto de datos de 16 personas en un entorno de laboratorio. Dado que la orientación del paciente en el espacio interior fue reconocida como una parte importante del contexto, el sistema necesitaba la capacidad de estimar la orientación de la persona, expresada en el marco de la escena 2D en la que la cámara sigue al paciente. Diseñamos un método para fusionar la información de seguimiento de posición del sistema de visión y los datos de inercia del smartphone para obtener la estimación de postura 2D del paciente en el mapa de la escena. Además, se propuso un método para la estimación de la posición del Smartphone en la cintura del paciente. La precisión de la estimación de la posición y la orientación se evaluó en un conjunto de datos de 12 personas. Finalmente, al tener disponible información de posición, orientación y altura, se realizó una nueva clasificación de actividad de seven-class utilizando un clasificador jerárquico que combina un clasificador de postura basado en la altura con clasificadores de movimiento SVM traslacional y rotacional. Cada uno de los clasificadores de movimiento SVM y el clasificador jerárquico conjunto se evaluaron en el experimento de laboratorio con 8 personas sanas. El último algoritmo de detección de FOG basado en el contexto utiliza información de actividad e información de texto espacial para confirmar o refutar el FOG detectado por el algoritmo de detección de FOG actual. El algoritmo basado en el contexto influye muy positivamente en la reducción de las detecciones de falsos positivos, que se expresa a través de una mayor especificida

Context-aware home monitoring system for Parkinson's disease patietns : ambient and werable sensing for freezing of gait detection

Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i Technische Universiteit Eindhoven. This PhD Thesis has been developed in the framework of, and according to, the rules of the Erasmus Mundus Joint Doctorate on Interactive and Cognitive Environments EMJD ICE [FPA no. 2010-0012]Parkinson’s disease (PD). It is characterized by brief episodes of inability to step, or by extremely short steps that typically occur on gait initiation or on turning while walking. The consequences of FOG are aggravated mobility and higher affinity to falls, which have a direct effect on the quality of life of the individual. There does not exist completely effective pharmacological treatment for the FOG phenomena. However, external stimuli, such as lines on the floor or rhythmic sounds, can focus the attention of a person who experiences a FOG episode and help her initiate gait. The optimal effectiveness in such approach, known as cueing, is achieved through timely activation of a cueing device upon the accurate detection of a FOG episode. Therefore, a robust and accurate FOG detection is the main problem that needs to be solved when developing a suitable assistive technology solution for this specific user group. This thesis proposes the use of activity and spatial context of a person as the means to improve the detection of FOG episodes during monitoring at home. The thesis describes design, algorithm implementation and evaluation of a distributed home system for FOG detection based on multiple cameras and a single inertial gait sensor worn at the waist of the patient. Through detailed observation of collected home data of 17 PD patients, we realized that a novel solution for FOG detection could be achieved by using contextual information of the patient’s position, orientation, basic posture and movement on a semantically annotated two-dimensional (2D) map of the indoor environment. We envisioned the future context-aware system as a network of Microsoft Kinect cameras placed in the patient’s home that interacts with a wearable inertial sensor on the patient (smartphone). Since the hardware platform of the system constitutes from the commercial of-the-shelf hardware, the majority of the system development efforts involved the production of software modules (for position tracking, orientation tracking, activity recognition) that run on top of the middle-ware operating system in the home gateway server. The main component of the system that had to be developed is the Kinect application for tracking the position and height of multiple people, based on the input in the form of 3D point cloud data. Besides position tracking, this software module also provides mapping and semantic annotation of FOG specific zones on the scene in front of the Kinect. One instance of vision tracking application is supposed to run for every Kinect sensor in the system, yielding potentially high number of simultaneous tracks. At any moment, the system has to track one specific person - the patient. To enable tracking of the patient between different non-overlapped cameras in the distributed system, a new re-identification approach based on appearance model learning with one-class Support Vector Machine (SVM) was developed. Evaluation of the re-identification method was conducted on a 16 people dataset in a laboratory environment. Since the patient orientation in the indoor space was recognized as an important part of the context, the system necessitated the ability to estimate the orientation of the person, expressed in the frame of the 2D scene on which the patient is tracked by the camera. We devised method to fuse position tracking information from the vision system and inertial data from the smartphone in order to obtain patient’s 2D pose estimation on the scene map. Additionally, a method for the estimation of the position of the smartphone on the waist of the patient was proposed. Position and orientation estimation accuracy were evaluated on a 12 people dataset. Finally, having available positional, orientation and height information, a new seven-class activity classification was realized using a hierarchical classifier that combines height-based posture classifier with translational and rotational SVM movement classifiers. Each of the SVM movement classifiers and the joint hierarchical classifier were evaluated in the laboratory experiment with 8 healthy persons. The final context-based FOG detection algorithm uses activity information and spatial context information in order to confirm or disprove FOG detected by the current state-of-the-art FOG detection algorithm (which uses only wearable sensor data). A dataset with home data of 3 PD patients was produced using two Kinect cameras and a smartphone in synchronized recording. The new context-based FOG detection algorithm and the wearable-only FOG detection algorithm were both evaluated with the home dataset and their results were compared. The context-based algorithm very positively influences the reduction of false positive detections, which is expressed through achieved higher specificity. In some cases, context-based algorithm also eliminates true positive detections, reducing sensitivity to the lesser extent. The final comparison of the two algorithms on the basis of their sensitivity and specificity, shows the improvement in the overall FOG detection achieved with the new context-aware home system.Esta tesis propone el uso de la actividad y el contexto espacial de una persona como medio para mejorar la detección de episodios de FOG (Freezing of gait) durante el seguimiento en el domicilio. La tesis describe el diseño, implementación de algoritmos y evaluación de un sistema doméstico distribuido para detección de FOG basado en varias cámaras y un único sensor de marcha inercial en la cintura del paciente. Mediante de la observación detallada de los datos caseros recopilados de 17 pacientes con EP, nos dimos cuenta de que se puede lograr una solución novedosa para la detección de FOG mediante el uso de información contextual de la posición del paciente, orientación, postura básica y movimiento anotada semánticamente en un mapa bidimensional (2D) del entorno interior. Imaginamos el futuro sistema de consciencia del contexto como una red de cámaras Microsoft Kinect colocadas en el hogar del paciente, que interactúa con un sensor de inercia portátil en el paciente (teléfono inteligente). Al constituirse la plataforma del sistema a partir de hardware comercial disponible, los esfuerzos de desarrollo consistieron en la producción de módulos de software (para el seguimiento de la posición, orientación seguimiento, reconocimiento de actividad) que se ejecutan en la parte superior del sistema operativo del servidor de puerta de enlace de casa. El componente principal del sistema que tuvo que desarrollarse es la aplicación Kinect para seguimiento de la posición y la altura de varias personas, según la entrada en forma de punto 3D de datos en la nube. Además del seguimiento de posición, este módulo de software también proporciona mapeo y semántica. anotación de zonas específicas de FOG en la escena frente al Kinect. Se supone que una instancia de la aplicación de seguimiento de visión se ejecuta para cada sensor Kinect en el sistema, produciendo un número potencialmente alto de pistas simultáneas. En cualquier momento, el sistema tiene que rastrear a una persona específica - el paciente. Para habilitar el seguimiento del paciente entre diferentes cámaras no superpuestas en el sistema distribuido, se desarrolló un nuevo enfoque de re-identificación basado en el aprendizaje de modelos de apariencia con one-class Suport Vector Machine (SVM). La evaluación del método de re-identificación se realizó con un conjunto de datos de 16 personas en un entorno de laboratorio. Dado que la orientación del paciente en el espacio interior fue reconocida como una parte importante del contexto, el sistema necesitaba la capacidad de estimar la orientación de la persona, expresada en el marco de la escena 2D en la que la cámara sigue al paciente. Diseñamos un método para fusionar la información de seguimiento de posición del sistema de visión y los datos de inercia del smartphone para obtener la estimación de postura 2D del paciente en el mapa de la escena. Además, se propuso un método para la estimación de la posición del Smartphone en la cintura del paciente. La precisión de la estimación de la posición y la orientación se evaluó en un conjunto de datos de 12 personas. Finalmente, al tener disponible información de posición, orientación y altura, se realizó una nueva clasificación de actividad de seven-class utilizando un clasificador jerárquico que combina un clasificador de postura basado en la altura con clasificadores de movimiento SVM traslacional y rotacional. Cada uno de los clasificadores de movimiento SVM y el clasificador jerárquico conjunto se evaluaron en el experimento de laboratorio con 8 personas sanas. El último algoritmo de detección de FOG basado en el contexto utiliza información de actividad e información de texto espacial para confirmar o refutar el FOG detectado por el algoritmo de detección de FOG actual. El algoritmo basado en el contexto influye muy positivamente en la reducción de las detecciones de falsos positivos, que se expresa a través de una mayor especificidadPostprint (published version

Context-aware home monitoring system for Parkinson's disease patietns : ambient and werable sensing for freezing of gait detection

Parkinson’s disease (PD). It is characterized by brief episodes of inability to step, or by extremely short steps that typically occur on gait initiation or on turning while walking. The consequences of FOG are aggravated mobility and higher affinity to falls, which have a direct effect on the quality of life of the individual. There does not exist completely effective pharmacological treatment for the FOG phenomena. However, external stimuli, such as lines on the floor or rhythmic sounds, can focus the attention of a person who experiences a FOG episode and help her initiate gait. The optimal effectiveness in such approach, known as cueing, is achieved through timely activation of a cueing device upon the accurate detection of a FOG episode. Therefore, a robust and accurate FOG detection is the main problem that needs to be solved when developing a suitable assistive technology solution for this specific user group. This thesis proposes the use of activity and spatial context of a person as the means to improve the detection of FOG episodes during monitoring at home. The thesis describes design, algorithm implementation and evaluation of a distributed home system for FOG detection based on multiple cameras and a single inertial gait sensor worn at the waist of the patient. Through detailed observation of collected home data of 17 PD patients, we realized that a novel solution for FOG detection could be achieved by using contextual information of the patient’s position, orientation, basic posture and movement on a semantically annotated two-dimensional (2D) map of the indoor environment. We envisioned the future context-aware system as a network of Microsoft Kinect cameras placed in the patient’s home that interacts with a wearable inertial sensor on the patient (smartphone). Since the hardware platform of the system constitutes from the commercial of-the-shelf hardware, the majority of the system development efforts involved the production of software modules (for position tracking, orientation tracking, activity recognition) that run on top of the middle-ware operating system in the home gateway server. The main component of the system that had to be developed is the Kinect application for tracking the position and height of multiple people, based on the input in the form of 3D point cloud data. Besides position tracking, this software module also provides mapping and semantic annotation of FOG specific zones on the scene in front of the Kinect. One instance of vision tracking application is supposed to run for every Kinect sensor in the system, yielding potentially high number of simultaneous tracks. At any moment, the system has to track one specific person - the patient. To enable tracking of the patient between different non-overlapped cameras in the distributed system, a new re-identification approach based on appearance model learning with one-class Support Vector Machine (SVM) was developed. Evaluation of the re-identification method was conducted on a 16 people dataset in a laboratory environment. Since the patient orientation in the indoor space was recognized as an important part of the context, the system necessitated the ability to estimate the orientation of the person, expressed in the frame of the 2D scene on which the patient is tracked by the camera. We devised method to fuse position tracking information from the vision system and inertial data from the smartphone in order to obtain patient’s 2D pose estimation on the scene map. Additionally, a method for the estimation of the position of the smartphone on the waist of the patient was proposed. Position and orientation estimation accuracy were evaluated on a 12 people dataset. Finally, having available positional, orientation and height information, a new seven-class activity classification was realized using a hierarchical classifier that combines height-based posture classifier with translational and rotational SVM movement classifiers. Each of the SVM movement classifiers and the joint hierarchical classifier were evaluated in the laboratory experiment with 8 healthy persons. The final context-based FOG detection algorithm uses activity information and spatial context information in order to confirm or disprove FOG detected by the current state-of-the-art FOG detection algorithm (which uses only wearable sensor data). A dataset with home data of 3 PD patients was produced using two Kinect cameras and a smartphone in synchronized recording. The new context-based FOG detection algorithm and the wearable-only FOG detection algorithm were both evaluated with the home dataset and their results were compared. The context-based algorithm very positively influences the reduction of false positive detections, which is expressed through achieved higher specificity. In some cases, context-based algorithm also eliminates true positive detections, reducing sensitivity to the lesser extent. The final comparison of the two algorithms on the basis of their sensitivity and specificity, shows the improvement in the overall FOG detection achieved with the new context-aware home system.Esta tesis propone el uso de la actividad y el contexto espacial de una persona como medio para mejorar la detección de episodios de FOG (Freezing of gait) durante el seguimiento en el domicilio. La tesis describe el diseño, implementación de algoritmos y evaluación de un sistema doméstico distribuido para detección de FOG basado en varias cámaras y un único sensor de marcha inercial en la cintura del paciente. Mediante de la observación detallada de los datos caseros recopilados de 17 pacientes con EP, nos dimos cuenta de que se puede lograr una solución novedosa para la detección de FOG mediante el uso de información contextual de la posición del paciente, orientación, postura básica y movimiento anotada semánticamente en un mapa bidimensional (2D) del entorno interior. Imaginamos el futuro sistema de consciencia del contexto como una red de cámaras Microsoft Kinect colocadas en el hogar del paciente, que interactúa con un sensor de inercia portátil en el paciente (teléfono inteligente). Al constituirse la plataforma del sistema a partir de hardware comercial disponible, los esfuerzos de desarrollo consistieron en la producción de módulos de software (para el seguimiento de la posición, orientación seguimiento, reconocimiento de actividad) que se ejecutan en la parte superior del sistema operativo del servidor de puerta de enlace de casa. El componente principal del sistema que tuvo que desarrollarse es la aplicación Kinect para seguimiento de la posición y la altura de varias personas, según la entrada en forma de punto 3D de datos en la nube. Además del seguimiento de posición, este módulo de software también proporciona mapeo y semántica. anotación de zonas específicas de FOG en la escena frente al Kinect. Se supone que una instancia de la aplicación de seguimiento de visión se ejecuta para cada sensor Kinect en el sistema, produciendo un número potencialmente alto de pistas simultáneas. En cualquier momento, el sistema tiene que rastrear a una persona específica - el paciente. Para habilitar el seguimiento del paciente entre diferentes cámaras no superpuestas en el sistema distribuido, se desarrolló un nuevo enfoque de re-identificación basado en el aprendizaje de modelos de apariencia con one-class Suport Vector Machine (SVM). La evaluación del método de re-identificación se realizó con un conjunto de datos de 16 personas en un entorno de laboratorio. Dado que la orientación del paciente en el espacio interior fue reconocida como una parte importante del contexto, el sistema necesitaba la capacidad de estimar la orientación de la persona, expresada en el marco de la escena 2D en la que la cámara sigue al paciente. Diseñamos un método para fusionar la información de seguimiento de posición del sistema de visión y los datos de inercia del smartphone para obtener la estimación de postura 2D del paciente en el mapa de la escena. Además, se propuso un método para la estimación de la posición del Smartphone en la cintura del paciente. La precisión de la estimación de la posición y la orientación se evaluó en un conjunto de datos de 12 personas. Finalmente, al tener disponible información de posición, orientación y altura, se realizó una nueva clasificación de actividad de seven-class utilizando un clasificador jerárquico que combina un clasificador de postura basado en la altura con clasificadores de movimiento SVM traslacional y rotacional. Cada uno de los clasificadores de movimiento SVM y el clasificador jerárquico conjunto se evaluaron en el experimento de laboratorio con 8 personas sanas. El último algoritmo de detección de FOG basado en el contexto utiliza información de actividad e información de texto espacial para confirmar o refutar el FOG detectado por el algoritmo de detección de FOG actual. El algoritmo basado en el contexto influye muy positivamente en la reducción de las detecciones de falsos positivos, que se expresa a través de una mayor especificida