43 resultados para Computer vision system
em Universidad Politécnica de Madrid
Resumo:
This paper outlines an automatic computervision system for the identification of avena sterilis which is a special weed seed growing in cereal crops. The final goal is to reduce the quantity of herbicide to be sprayed as an important and necessary step for precision agriculture. So, only areas where the presence of weeds is important should be sprayed. The main problems for the identification of this kind of weed are its similar spectral signature with respect the crops and also its irregular distribution in the field. It has been designed a new strategy involving two processes: image segmentation and decision making. The image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based attributes measuring the relations among the crops and weeds. The decision making is based on the SupportVectorMachines and determines if a cell must be sprayed. The main findings of this paper are reflected in the combination of the segmentation and the SupportVectorMachines decision processes. Another important contribution of this approach is the minimum requirements of the system in terms of memory and computation power if compared with other previous works. The performance of the method is illustrated by comparative analysis against some existing strategies.
Resumo:
In this paper, we propose a system for authenticating local bee pollen against fraudulent samples using image processing and classification techniques. Our system is based on the colour properties of bee pollen loads and the use of one-class classifiers to reject unknown pollen samples. The latter classification techniques allow us to tackle the major difficulty of the problem, the existence of many possible fraudulent pollen types. Also presented is a multi-classifier model with an ambiguity discovery process to fuse the output of the one-class classifiers. The method is validated by authenticating Spanish bee pollen types, the overall accuracy of the final system of being 94%. Therefore, the system is able to rapidly reject the non-local pollen samples with inexpensive hardware and without the need to send the product to the laboratory.
Resumo:
La evolución de los teléfonos móviles inteligentes, dotados de cámaras digitales, está provocando una creciente demanda de aplicaciones cada vez más complejas que necesitan algoritmos de visión artificial en tiempo real; puesto que el tamaño de las señales de vídeo no hace sino aumentar y en cambio el rendimiento de los procesadores de un solo núcleo se ha estancado, los nuevos algoritmos que se diseñen para visión artificial han de ser paralelos para poder ejecutarse en múltiples procesadores y ser computacionalmente escalables. Una de las clases de procesadores más interesantes en la actualidad se encuentra en las tarjetas gráficas (GPU), que son dispositivos que ofrecen un alto grado de paralelismo, un excelente rendimiento numérico y una creciente versatilidad, lo que los hace interesantes para llevar a cabo computación científica. En esta tesis se exploran dos aplicaciones de visión artificial que revisten una gran complejidad computacional y no pueden ser ejecutadas en tiempo real empleando procesadores tradicionales. En cambio, como se demuestra en esta tesis, la paralelización de las distintas subtareas y su implementación sobre una GPU arrojan los resultados deseados de ejecución con tasas de refresco interactivas. Asimismo, se propone una técnica para la evaluación rápida de funciones de complejidad arbitraria especialmente indicada para su uso en una GPU. En primer lugar se estudia la aplicación de técnicas de síntesis de imágenes virtuales a partir de únicamente dos cámaras lejanas y no paralelas—en contraste con la configuración habitual en TV 3D de cámaras cercanas y paralelas—con información de color y profundidad. Empleando filtros de mediana modificados para la elaboración de un mapa de profundidad virtual y proyecciones inversas, se comprueba que estas técnicas son adecuadas para una libre elección del punto de vista. Además, se demuestra que la codificación de la información de profundidad con respecto a un sistema de referencia global es sumamente perjudicial y debería ser evitada. Por otro lado se propone un sistema de detección de objetos móviles basado en técnicas de estimación de densidad con funciones locales. Este tipo de técnicas es muy adecuada para el modelado de escenas complejas con fondos multimodales, pero ha recibido poco uso debido a su gran complejidad computacional. El sistema propuesto, implementado en tiempo real sobre una GPU, incluye propuestas para la estimación dinámica de los anchos de banda de las funciones locales, actualización selectiva del modelo de fondo, actualización de la posición de las muestras de referencia del modelo de primer plano empleando un filtro de partículas multirregión y selección automática de regiones de interés para reducir el coste computacional. Los resultados, evaluados sobre diversas bases de datos y comparados con otros algoritmos del estado del arte, demuestran la gran versatilidad y calidad de la propuesta. Finalmente se propone un método para la aproximación de funciones arbitrarias empleando funciones continuas lineales a tramos, especialmente indicada para su implementación en una GPU mediante el uso de las unidades de filtraje de texturas, normalmente no utilizadas para cómputo numérico. La propuesta incluye un riguroso análisis matemático del error cometido en la aproximación en función del número de muestras empleadas, así como un método para la obtención de una partición cuasióptima del dominio de la función para minimizar el error. ABSTRACT The evolution of smartphones, all equipped with digital cameras, is driving a growing demand for ever more complex applications that need to rely on real-time computer vision algorithms. However, video signals are only increasing in size, whereas the performance of single-core processors has somewhat stagnated in the past few years. Consequently, new computer vision algorithms will need to be parallel to run on multiple processors and be computationally scalable. One of the most promising classes of processors nowadays can be found in graphics processing units (GPU). These are devices offering a high parallelism degree, excellent numerical performance and increasing versatility, which makes them interesting to run scientific computations. In this thesis, we explore two computer vision applications with a high computational complexity that precludes them from running in real time on traditional uniprocessors. However, we show that by parallelizing subtasks and implementing them on a GPU, both applications attain their goals of running at interactive frame rates. In addition, we propose a technique for fast evaluation of arbitrarily complex functions, specially designed for GPU implementation. First, we explore the application of depth-image–based rendering techniques to the unusual configuration of two convergent, wide baseline cameras, in contrast to the usual configuration used in 3D TV, which are narrow baseline, parallel cameras. By using a backward mapping approach with a depth inpainting scheme based on median filters, we show that these techniques are adequate for free viewpoint video applications. In addition, we show that referring depth information to a global reference system is ill-advised and should be avoided. Then, we propose a background subtraction system based on kernel density estimation techniques. These techniques are very adequate for modelling complex scenes featuring multimodal backgrounds, but have not been so popular due to their huge computational and memory complexity. The proposed system, implemented in real time on a GPU, features novel proposals for dynamic kernel bandwidth estimation for the background model, selective update of the background model, update of the position of reference samples of the foreground model using a multi-region particle filter, and automatic selection of regions of interest to reduce computational cost. The results, evaluated on several databases and compared to other state-of-the-art algorithms, demonstrate the high quality and versatility of our proposal. Finally, we propose a general method for the approximation of arbitrarily complex functions using continuous piecewise linear functions, specially formulated for GPU implementation by leveraging their texture filtering units, normally unused for numerical computation. Our proposal features a rigorous mathematical analysis of the approximation error in function of the number of samples, as well as a method to obtain a suboptimal partition of the domain of the function to minimize approximation error.
Resumo:
This paper presents a computer vision system that successfully discriminates between weed patches and crop rows under uncontrolled lighting in real-time. The system consists of two independent subsystems, a fast image processing delivering results in real-time (Fast Image Processing, FIP), and a slower and more accurate processing (Robust Crop Row Detection, RCRD) that is used to correct the first subsystem's mistakes. This combination produces a system that achieves very good results under a wide variety of conditions. Tested on several maize videos taken of different fields and during different years, the system successfully detects an average of 95% of weeds and 80% of crops under different illumination, soil humidity and weed/crop growth conditions. Moreover, the system has been shown to produce acceptable results even under very difficult conditions, such as in the presence of dramatic sowing errors or abrupt camera movements. The computer vision system has been developed for integration into a treatment system because the ideal setup for any weed sprayer system would include a tool that could provide information on the weeds and crops present at each point in real-time, while the tractor mounting the spraying bar is moving
Resumo:
In this paper we tackle the problem of landing a helicopter autonomously on a ship deck, using as the main sensor, an on-board colour camera. To create a test-bed, we first adequately simulate the movement of a ship landing platform on the Sea, for different Sea States, for different ships, randomly and realistically enough. We use a commercial parallel robot to get this movement. Once we had this, we developed an accurate and robust computer vision system to measure the pose of the helipad with respect to the on-board camera. To deal with the noise and the possible fails of the computer vision, a state estimator was created. With all of this, we are now able to develop and test a controller that closes the loop and finish the autonomous landing task.
Resumo:
Industrial applications of computer vision sometimes require detection of atypical objects that occur as small groups of pixels in digital images. These objects are difficult to single out because they are small and randomly distributed. In this work we propose an image segmentation method using the novel Ant System-based Clustering Algorithm (ASCA). ASCA models the foraging behaviour of ants, which move through the data space searching for high data-density regions, and leave pheromone trails on their path. The pheromone map is used to identify the exact number of clusters, and assign the pixels to these clusters using the pheromone gradient. We applied ASCA to detection of microcalcifications in digital mammograms and compared its performance with state-of-the-art clustering algorithms such as 1D Self-Organizing Map, k-Means, Fuzzy c-Means and Possibilistic Fuzzy c-Means. The main advantage of ASCA is that the number of clusters needs not to be known a priori. The experimental results show that ASCA is more efficient than the other algorithms in detecting small clusters of atypical data.
Resumo:
There is clear evidence that investment in intelligent transportation system technologies brings major social and economic benefits. Technological advances in the area of automatic systems in particular are becoming vital for the reduction of road deaths. We here describe our approach to automation of one the riskiest autonomous manœuvres involving vehicles – overtaking. The approach is based on a stereo vision system responsible for detecting any preceding vehicle and triggering the autonomous overtaking manœuvre. To this end, a fuzzy-logic based controller was developed to emulate how humans overtake. Its input is information from the vision system and from a positioning-based system consisting of a differential global positioning system (DGPS) and an inertial measurement unit (IMU). Its output is the generation of action on the vehicle’s actuators, i.e., the steering wheel and throttle and brake pedals. The system has been incorporated into a commercial Citroën car and tested on the private driving circuit at the facilities of our research center, CAR, with different preceding vehicles – a motorbike, car, and truck – with encouraging results.
Resumo:
A more natural, intuitive, user-friendly, and less intrusive Human–Computer interface for controlling an application by executing hand gestures is presented. For this purpose, a robust vision-based hand-gesture recognition system has been developed, and a new database has been created to test it. The system is divided into three stages: detection, tracking, and recognition. The detection stage searches in every frame of a video sequence potential hand poses using a binary Support Vector Machine classifier and Local Binary Patterns as feature vectors. These detections are employed as input of a tracker to generate a spatio-temporal trajectory of hand poses. Finally, the recognition stage segments a spatio-temporal volume of data using the obtained trajectories, and compute a video descriptor called Volumetric Spatiograms of Local Binary Patterns (VS-LBP), which is delivered to a bank of SVM classifiers to perform the gesture recognition. The VS-LBP is a novel video descriptor that constitutes one of the most important contributions of the paper, which is able to provide much richer spatio-temporal information than other existing approaches in the state of the art with a manageable computational cost. Excellent results have been obtained outperforming other approaches of the state of the art.
Resumo:
En esta tesis se aborda la detección y el seguimiento automático de vehículos mediante técnicas de visión artificial con una cámara monocular embarcada. Este problema ha suscitado un gran interés por parte de la industria automovilística y de la comunidad científica ya que supone el primer paso en aras de la ayuda a la conducción, la prevención de accidentes y, en última instancia, la conducción automática. A pesar de que se le ha dedicado mucho esfuerzo en los últimos años, de momento no se ha encontrado ninguna solución completamente satisfactoria y por lo tanto continúa siendo un tema de investigación abierto. Los principales problemas que plantean la detección y seguimiento mediante visión artificial son la gran variabilidad entre vehículos, un fondo que cambia dinámicamente debido al movimiento de la cámara, y la necesidad de operar en tiempo real. En este contexto, esta tesis propone un marco unificado para la detección y seguimiento de vehículos que afronta los problemas descritos mediante un enfoque estadístico. El marco se compone de tres grandes bloques, i.e., generación de hipótesis, verificación de hipótesis, y seguimiento de vehículos, que se llevan a cabo de manera secuencial. No obstante, se potencia el intercambio de información entre los diferentes bloques con objeto de obtener el máximo grado posible de adaptación a cambios en el entorno y de reducir el coste computacional. Para abordar la primera tarea de generación de hipótesis, se proponen dos métodos complementarios basados respectivamente en el análisis de la apariencia y la geometría de la escena. Para ello resulta especialmente interesante el uso de un dominio transformado en el que se elimina la perspectiva de la imagen original, puesto que este dominio permite una búsqueda rápida dentro de la imagen y por tanto una generación eficiente de hipótesis de localización de los vehículos. Los candidatos finales se obtienen por medio de un marco colaborativo entre el dominio original y el dominio transformado. Para la verificación de hipótesis se adopta un método de aprendizaje supervisado. Así, se evalúan algunos de los métodos de extracción de características más populares y se proponen nuevos descriptores con arreglo al conocimiento de la apariencia de los vehículos. Para evaluar la efectividad en la tarea de clasificación de estos descriptores, y dado que no existen bases de datos públicas que se adapten al problema descrito, se ha generado una nueva base de datos sobre la que se han realizado pruebas masivas. Finalmente, se presenta una metodología para la fusión de los diferentes clasificadores y se plantea una discusión sobre las combinaciones que ofrecen los mejores resultados. El núcleo del marco propuesto está constituido por un método Bayesiano de seguimiento basado en filtros de partículas. Se plantean contribuciones en los tres elementos fundamentales de estos filtros: el algoritmo de inferencia, el modelo dinámico y el modelo de observación. En concreto, se propone el uso de un método de muestreo basado en MCMC que evita el elevado coste computacional de los filtros de partículas tradicionales y por consiguiente permite que el modelado conjunto de múltiples vehículos sea computacionalmente viable. Por otra parte, el dominio transformado mencionado anteriormente permite la definición de un modelo dinámico de velocidad constante ya que se preserva el movimiento suave de los vehículos en autopistas. Por último, se propone un modelo de observación que integra diferentes características. En particular, además de la apariencia de los vehículos, el modelo tiene en cuenta también toda la información recibida de los bloques de procesamiento previos. El método propuesto se ejecuta en tiempo real en un ordenador de propósito general y da unos resultados sobresalientes en comparación con los métodos tradicionales. ABSTRACT This thesis addresses on-road vehicle detection and tracking with a monocular vision system. This problem has attracted the attention of the automotive industry and the research community as it is the first step for driver assistance and collision avoidance systems and for eventual autonomous driving. Although many effort has been devoted to address it in recent years, no satisfactory solution has yet been devised and thus it is an active research issue. The main challenges for vision-based vehicle detection and tracking are the high variability among vehicles, the dynamically changing background due to camera motion and the real-time processing requirement. In this thesis, a unified approach using statistical methods is presented for vehicle detection and tracking that tackles these issues. The approach is divided into three primary tasks, i.e., vehicle hypothesis generation, hypothesis verification, and vehicle tracking, which are performed sequentially. Nevertheless, the exchange of information between processing blocks is fostered so that the maximum degree of adaptation to changes in the environment can be achieved and the computational cost is alleviated. Two complementary strategies are proposed to address the first task, i.e., hypothesis generation, based respectively on appearance and geometry analysis. To this end, the use of a rectified domain in which the perspective is removed from the original image is especially interesting, as it allows for fast image scanning and coarse hypothesis generation. The final vehicle candidates are produced using a collaborative framework between the original and the rectified domains. A supervised classification strategy is adopted for the verification of the hypothesized vehicle locations. In particular, state-of-the-art methods for feature extraction are evaluated and new descriptors are proposed by exploiting the knowledge on vehicle appearance. Due to the lack of appropriate public databases, a new database is generated and the classification performance of the descriptors is extensively tested on it. Finally, a methodology for the fusion of the different classifiers is presented and the best combinations are discussed. The core of the proposed approach is a Bayesian tracking framework using particle filters. Contributions are made on its three key elements: the inference algorithm, the dynamic model and the observation model. In particular, the use of a Markov chain Monte Carlo method is proposed for sampling, which circumvents the exponential complexity increase of traditional particle filters thus making joint multiple vehicle tracking affordable. On the other hand, the aforementioned rectified domain allows for the definition of a constant-velocity dynamic model since it preserves the smooth motion of vehicles in highways. Finally, a multiple-cue observation model is proposed that not only accounts for vehicle appearance but also integrates the available information from the analysis in the previous blocks. The proposed approach is proven to run near real-time in a general purpose PC and to deliver outstanding results compared to traditional methods.
Resumo:
This paper proposes a novel design of a reconfigurable humanoid robot head, based on biological likeness of human being so that the humanoid robot could agreeably interact with people in various everyday tasks. The proposed humanoid head has a modular and adaptive structural design and is equipped with three main components: frame, neck motion system and omnidirectional stereovision system modules. The omnidirectional stereovision system module being the last module, a motivating contribution with regard to other computer vision systems implemented in former humanoids, it opens new research possibilities for achieving human-like behaviour. A proposal for a real-time catadioptric stereovision system is presented, including stereo geometry for rectifying the system configuration and depth estimation. The methodology for an initial approach for visual servoing tasks is divided into two phases, first related to the robust detection of moving objects, their depth estimation and position calculation, and second the development of attention-based control strategies. Perception capabilities provided allow the extraction of 3D information from a wide range of visions from uncontrolled dynamic environments, and work results are illustrated through a number of experiments.
Resumo:
The genus Diplotaxis, comprising 32 or 34 species, plus several additional infraspecific taxa, displays a considerable degree of heterogeneity in the morphology, molecular markers, chromosome numbers and geographical amplitude of the species. The taxonomic relationships within the genus Diplotaxis were investigated by phenetic characterisation of germplasm belonging to 27 taxa of the genus, because there is an increasing interest in Diplotaxis, since some of its species (D. tenuifolia, D. muralis) are gathered or cultivated for human consumption, whereas others are frequent arable weeds (D. erucoides) in many European vineyards. Using a computer-aided vision system, 33 morpho-colorimetric features of seeds were electronically measured. The data were used to implement a statistical classifier, which is able to discriminate the taxa within the genus Diplotaxis, in order to compare the resulting species grouping with the current infrageneric systematics of this genus. Despite the high heterogeneity of the samples, due to the great intra-population variability, the stepwise Linear Discriminant Analysis method, applied to distinguish the groups, was able to reach over 80% correct identification. The results obtained allowed us to confirm the current taxonomic position of most taxa and suggested the taxonomic position of others for reconsideration.
Resumo:
El principal objetivo de esta tesis es dotar a los vehículos aéreos no tripulados (UAVs, por sus siglas en inglés) de una fuente de información adicional basada en visión. Esta fuente de información proviene de cámaras ubicadas a bordo de los vehículos o en el suelo. Con ella se busca que los UAVs realicen tareas de aterrizaje o inspección guiados por visión, especialmente en aquellas situaciones en las que no haya disponibilidad de estimar la posición del vehículo con base en GPS, cuando las estimaciones de GPS no tengan la suficiente precisión requerida por las tareas a realizar, o cuando restricciones de carga de pago impidan añadir sensores a bordo de los vehículos. Esta tesis trata con tres de las principales áreas de la visión por computador: seguimiento visual y estimación visual de la pose (posición y orientación), que a su vez constituyen la base de la tercera, denominada control servo visual, que en nuestra aplicación se enfoca en el empleo de información visual para controlar los UAVs. Al respecto, esta tesis se ocupa de presentar propuestas novedosas que permitan solucionar problemas relativos al seguimiento de objetos mediante cámaras ubicadas a bordo de los UAVs, se ocupa de la estimación de la pose de los UAVs basada en información visual obtenida por cámaras ubicadas en el suelo o a bordo, y también se ocupa de la aplicación de las técnicas propuestas para solucionar diferentes problemas, como aquellos concernientes al seguimiento visual para tareas de reabastecimiento autónomo en vuelo o al aterrizaje basado en visión, entre otros. Las diversas técnicas de visión por computador presentadas en esta tesis se proponen con el fin de solucionar dificultades que suelen presentarse cuando se realizan tareas basadas en visión con UAVs, como las relativas a la obtención, en tiempo real, de estimaciones robustas, o como problemas generados por vibraciones. Los algoritmos propuestos en esta tesis han sido probados con información de imágenes reales obtenidas realizando pruebas on-line y off-line. Diversos mecanismos de evaluación han sido empleados con el propósito de analizar el desempeño de los algoritmos propuestos, entre los que se incluyen datos simulados, imágenes de vuelos reales, estimaciones precisas de posición empleando el sistema VICON y comparaciones con algoritmos del estado del arte. Los resultados obtenidos indican que los algoritmos de visión por computador propuestos tienen un desempeño que es comparable e incluso mejor al de algoritmos que se encuentran en el estado del arte. Los algoritmos propuestos permiten la obtención de estimaciones robustas en tiempo real, lo cual permite su uso en tareas de control visual. El desempeño de estos algoritmos es apropiado para las exigencias de las distintas aplicaciones examinadas: reabastecimiento autónomo en vuelo, aterrizaje y estimación del estado del UAV. Abstract The main objective of this thesis is to provide Unmanned Aerial Vehicles (UAVs) with an additional vision-based source of information extracted by cameras located either on-board or on the ground, in order to allow UAVs to develop visually guided tasks, such as landing or inspection, especially in situations where GPS information is not available, where GPS-based position estimation is not accurate enough for the task to develop, or where payload restrictions do not allow the incorporation of additional sensors on-board. This thesis covers three of the main computer vision areas: visual tracking and visual pose estimation, which are the bases the third one called visual servoing, which, in this work, focuses on using visual information to control UAVs. In this sense, the thesis focuses on presenting novel solutions for solving the tracking problem of objects when using cameras on-board UAVs, on estimating the pose of the UAVs based on the visual information collected by cameras located either on the ground or on-board, and also focuses on applying these proposed techniques for solving different problems, such as visual tracking for aerial refuelling or vision-based landing, among others. The different computer vision techniques presented in this thesis are proposed to solve some of the frequently problems found when addressing vision-based tasks in UAVs, such as obtaining robust vision-based estimations at real-time frame rates, and problems caused by vibrations, or 3D motion. All the proposed algorithms have been tested with real-image data in on-line and off-line tests. Different evaluation mechanisms have been used to analyze the performance of the proposed algorithms, such as simulated data, images from real-flight tests, publicly available datasets, manually generated ground truth data, accurate position estimations using a VICON system and a robotic cell, and comparison with state of the art algorithms. Results show that the proposed computer vision algorithms obtain performances that are comparable to, or even better than, state of the art algorithms, obtaining robust estimations at real-time frame rates. This proves that the proposed techniques are fast enough for vision-based control tasks. Therefore, the performance of the proposed vision algorithms has shown to be of a standard appropriate to the different explored applications: aerial refuelling and landing, and state estimation. It is noteworthy that they have low computational overheads for vision systems.
Resumo:
In this paper, an intelligent control approach based on neuro-fuzzy systems performance is presented, with the objective of counteracting the vibrations that affect the low-cost vision platform onboard an unmanned aerial system of rotating nature. A scaled dynamical model of a helicopter is used to simulate vibrations on its fuselage. The impact of these vibrations on the low-cost vision system will be assessed and an intelligent control approach will be derived in order to reduce its detrimental influence. Different trials that consider a neuro-fuzzy approach as a fundamental part of an intelligent semi-active control strategy have been carried out. Satisfactory results have been achieved compared to those obtained by means of vibration reduction passive techniques.
Resumo:
We propose a new method to automatically refine a facial disparity map obtained with standard cameras and under conventional illumination conditions by using a smart combination of traditional computer vision and 3D graphics techniques. Our system inputs two stereo images acquired with standard (calibrated) cameras and uses dense disparity estimation strategies to obtain a coarse initial disparity map, and SIFT to detect and match several feature points in the subjects face. We then use these points as anchors to modify the disparity in the facial area by building a Delaunay triangulation of their convex hull and interpolating their disparity values inside each triangle. We thus obtain a refined disparity map providing a much more accurate representation of the the subjects facial features. This refined facial disparity map may be easily transformed, through the camera calibration parameters, into a depth map to be used, also automatically, to improve the facial mesh of a 3D avatar to match the subjects real human features.
Resumo:
This paper proposes an automatic expert system for accuracy crop row detection in maize fields based on images acquired from a vision system. Different applications in maize, particularly those based on site specific treatments, require the identification of the crop rows. The vision system is designed with a defined geometry and installed onboard a mobile agricultural vehicle, i.e. submitted to vibrations, gyros or uncontrolled movements. Crop rows can be estimated by applying geometrical parameters under image perspective projection. Because of the above undesired effects, most often, the estimation results inaccurate as compared to the real crop rows. The proposed expert system exploits the human knowledge which is mapped into two modules based on image processing techniques. The first one is intended for separating green plants (crops and weeds) from the rest (soil, stones and others). The second one is based on the system geometry where the expected crop lines are mapped onto the image and then a correction is applied through the well-tested and robust Theil–Sen estimator in order to adjust them to the real ones. Its performance is favorably compared against the classical Pearson product–moment correlation coefficient.