<p>Главни задатак истраживања приказаног у дисертацији је развој модела,<br />заснованог на алгоритмима машинског учења, који описује сложени<br />утицај мерног система на користан, експериментални сигнал са циљем<br />његове елиминације. Студија случаја је широко распрострањена<br />фотоакустична, трансмисиона мерна метода са ћелијом минималне<br />запремине. Мултидисциплинарност и комплексност проблема одредили<br />су следеће кораке у методологији решења: 1) развој софтвера за<br />генерисање симулираних експерименталних података, 2) развој<br />регресионог модела заснованог на трослојној неуронској мрежи, за<br />прецизну и поуздану карактеризацију детектора која се извршава у<br />реалном времену, 3) развој класификационог модела заснованог на<br />неуронској мрежи једноставне структуре за прецизну и поуздану<br />предикцију типа коришћеног детектора која се извршава у реалном<br />времену, 4) спрезање регресионог и класификационог модела уз развој<br />додатног софтвера за прилагођење модела стварном експерименту. На<br />овај начин заокружен је програмски оквир који извршава сложени задатак<br />издвајања &ldquo;правог&rdquo; сигнала oд изобличеног експерименталног сигнала<br />без ангажовања истраживача, односно извршава аутокорекцију.<br />Тестирање је извршено на више различитих детектора и више<br />различитих материјала у фотоаксустичном експерименту. Применом<br />развијеног програмског оквира конкурентност експерименталне технике<br />је знатно порасла: повећана је тачност и поузданост, проширен је мерни<br />опсег и смањено време обраде резултата мерења.</p> / <p>Glavni zadatak istraživanja prikazanog u disertaciji je razvoj modela,<br />zasnovanog na algoritmima mašinskog učenja, koji opisuje složeni<br />uticaj mernog sistema na koristan, eksperimentalni signal sa ciljem<br />njegove eliminacije. Studija slučaja je široko rasprostranjena<br />fotoakustična, transmisiona merna metoda sa ćelijom minimalne<br />zapremine. Multidisciplinarnost i kompleksnost problema odredili<br />su sledeće korake u metodologiji rešenja: 1) razvoj softvera za<br />generisanje simuliranih eksperimentalnih podataka, 2) razvoj<br />regresionog modela zasnovanog na troslojnoj neuronskoj mreži, za<br />preciznu i pouzdanu karakterizaciju detektora koja se izvršava u<br />realnom vremenu, 3) razvoj klasifikacionog modela zasnovanog na<br />neuronskoj mreži jednostavne strukture za preciznu i pouzdanu<br />predikciju tipa korišćenog detektora koja se izvršava u realnom<br />vremenu, 4) sprezanje regresionog i klasifikacionog modela uz razvoj<br />dodatnog softvera za prilagođenje modela stvarnom eksperimentu. Na<br />ovaj način zaokružen je programski okvir koji izvršava složeni zadatak<br />izdvajanja &ldquo;pravog&rdquo; signala od izobličenog eksperimentalnog signala<br />bez angažovanja istraživača, odnosno izvršava autokorekciju.<br />Testiranje je izvršeno na više različitih detektora i više<br />različitih materijala u fotoaksustičnom eksperimentu. Primenom<br />razvijenog programskog okvira konkurentnost eksperimentalne tehnike<br />je znatno porasla: povećana je tačnost i pouzdanost, proširen je merni<br />opseg i smanjeno vreme obrade rezultata merenja.</p> / <p>The main task of the research presented in this dissertation is the development<br />of the model based on machine learning algorithms, which describes the<br />complex influence of the measuring system on a useful, experimental signal,<br />with the aim of the elimination of this influence. The case study is a widespread<br />photoacoustic, transmission measurement method with minimum volume cell<br />configuration. Multidisciplinarity and complexity of the problem determined the<br />following steps in the solution methodology: 1) development of the software for<br />generating simulated experimental data, 2) development of the regression<br />model based on a three-layer neural network, for precise and reliable<br />characterization of detectors, performed in real time, 3) development of the<br />classification model based on a neural network of simple structure for precise<br />and reliable prediction of the type of detector in use, performed in real time, 4)<br />coupling of the regression and the classification model with the development<br />of additional software for adjustment of the model to a real experiment. In this<br />way, the program framework is completed, which performs the complex task<br />of extracting the &quot;true&quot; signal from the distorted experimental signal without the<br />involvement of researchers, performing, thus, the autocorrection. Testing was<br />performed on several different detectors and several different materials in a<br />photoacoustic experiment. With the application of the developed software<br />framework, the competitiveness of the experimental technique has<br />significantly increased: the accuracy and the reliability have been increased,<br />the measurement range has been expanded and the processing time of<br />measurement results has been reduced.</p>

The 1st and 2nd order Lee–Carter methods were compared with the Hyndman–Ullah method in regards to goodness of fit and forecasting ability of mortality rates. Swedish population data was used from the Human Mortality Database. The robust estimation property of the Hyndman–Ullah method was also tested with inclusion of the Spanish flu and a hypothetical scenario of the COVID-19 pandemic. After having presented the three methods and making several comparisons between the methods, it is concluded that the Hyndman–Ullah method is overall superior among the three methods with the implementation of the chosen dataset. Its robust estimation of mortality shocks could also be confirmed.

Ce travail de thèse porte sur l'obtention de bornes de généralisation pour des échantillons statistiques à valeur dans des espaces de Hilbert définis par des noyaux reproduisants. L'approche consiste à obtenir des bornes non asymptotiques indépendantes de la dimension dans des espaces de dimension finie, en utilisant des inégalités PAC-Bayesiennes liées à une perturbation Gaussienne du paramètre et à les étendre ensuite aux espaces de Hilbert séparables. On se pose dans un premier temps la question de l'estimation de l'opérateur de Gram à partir d'un échantillon i. i. d. par un estimateur robuste et on propose des bornes uniformes, sous des hypothèses faibles de moments. Ces résultats permettent de caractériser l'analyse en composantes principales indépendamment de la dimension et d'en proposer des variantes robustes. On propose ensuite un nouvel algorithme de clustering spectral. Au lieu de ne garder que la projection sur les premiers vecteurs propres, on calcule une itérée du Laplacian normalisé. Cette itération, justifiée par l'analyse du clustering en termes de chaînes de Markov, opère comme une version régularisée de la projection sur les premiers vecteurs propres et permet d'obtenir un algorithme dans lequel le nombre de clusters est déterminé automatiquement. On présente des bornes non asymptotiques concernant la convergence de cet algorithme, lorsque les points à classer forment un échantillon i. i. d. d'une loi à support compact dans un espace de Hilbert. Ces bornes sont déduites des bornes obtenues pour l'estimation d'un opérateur de Gram dans un espace de Hilbert. On termine par un aperçu de l'intérêt du clustering spectral dans le cadre de l'analyse d'images. / This thesis focuses on obtaining generalization bounds for random samples in reproducing kernel Hilbert spaces. The approach consists in first obtaining non-asymptotic dimension-free bounds in finite-dimensional spaces using some PAC-Bayesian inequalities related to Gaussian perturbations and then in generalizing the results in a separable Hilbert space. We first investigate the question of estimating the Gram operator by a robust estimator from an i. i. d. sample and we present uniform bounds that hold under weak moment assumptions. These results allow us to qualify principal component analysis independently of the dimension of the ambient space and to propose stable versions of it. In the last part of the thesis we present a new algorithm for spectral clustering. It consists in replacing the projection on the eigenvectors associated with the largest eigenvalues of the Laplacian matrix by a power of the normalized Laplacian. This iteration, justified by the analysis of clustering in terms of Markov chains, performs a smooth truncation. We prove nonasymptotic bounds for the convergence of our spectral clustering algorithm applied to a random sample of points in a Hilbert space that are deduced from the bounds for the Gram operator in a Hilbert space. Experiments are done in the context of image analysis.

The present Ph.D. thesis, primarily conceived to support and reinforce the relation between academic and industrial worlds, was developed in collaboration with Shell Global Solutions (Amsterdam, The Netherlands) in the endeavour of applying and possibly extending well-established latent variable-based approaches (i.e. Principal Component Analysis - PCA - Partial Least Squares regression - PLS - or Partial Least Squares Discriminant Analysis - PLSDA) for complex problem solving not only in the fields of manufacturing troubleshooting and optimisation, but also in the wider environment of multivariate data analysis. To this end, novel efficient algorithmic solutions are proposed throughout all chapters to address very disparate tasks, from calibration transfer in spectroscopy to real-time modelling of streaming flows of data. The manuscript is divided into the following six parts, focused on various topics of interest: Part I - Preface, where an overview of this research work, its main aims and justification is given together with a brief introduction on PCA, PLS and PLSDA; Part II - On kernel-based extensions of PCA, PLS and PLSDA, where the potential of kernel techniques, possibly coupled to specific variants of the recently rediscovered pseudo-sample projection, formulated by the English statistician John C. Gower, is explored and their performance compared to that of more classical methodologies in four different applications scenarios: segmentation of Red-Green-Blue (RGB) images, discrimination of on-/off-specification batch runs, monitoring of batch processes and analysis of mixture designs of experiments; Part III - On the selection of the number of factors in PCA by permutation testing, where an extensive guideline on how to accomplish the selection of PCA components by permutation testing is provided through the comprehensive illustration of an original algorithmic procedure implemented for such a purpose; Part IV - On modelling common and distinctive sources of variability in multi-set data analysis, where several practical aspects of two-block common and distinctive component analysis (carried out by methods like Simultaneous Component Analysis - SCA - DIStinctive and COmmon Simultaneous Component Analysis - DISCO-SCA - Adapted Generalised Singular Value Decomposition - Adapted GSVD - ECO-POWER, Canonical Correlation Analysis - CCA - and 2-block Orthogonal Projections to Latent Structures - O2PLS) are discussed, a new computational strategy for determining the number of common factors underlying two data matrices sharing the same row- or column-dimension is described, and two innovative approaches for calibration transfer between near-infrared spectrometers are presented; Part V - On the on-the-fly processing and modelling of continuous high-dimensional data streams, where a novel software system for rational handling of multi-channel measurements recorded in real time, the On-The-Fly Processing (OTFP) tool, is designed; Part VI - Epilogue, where final conclusions are drawn, future perspectives are delineated, and annexes are included. / La presente tesis doctoral, concebida principalmente para apoyar y reforzar la relación entre la academia y la industria, se desarrolló en colaboración con Shell Global Solutions (Amsterdam, Países Bajos) en el esfuerzo de aplicar y posiblemente extender los enfoques ya consolidados basados en variables latentes (es decir, Análisis de Componentes Principales - PCA - Regresión en Mínimos Cuadrados Parciales - PLS - o PLS discriminante - PLSDA) para la resolución de problemas complejos no sólo en los campos de mejora y optimización de procesos, sino también en el entorno más amplio del análisis de datos multivariados. Con este fin, en todos los capítulos proponemos nuevas soluciones algorítmicas eficientes para abordar tareas dispares, desde la transferencia de calibración en espectroscopia hasta el modelado en tiempo real de flujos de datos. El manuscrito se divide en las seis partes siguientes, centradas en diversos temas de interés: Parte I - Prefacio, donde presentamos un resumen de este trabajo de investigación, damos sus principales objetivos y justificaciones junto con una breve introducción sobre PCA, PLS y PLSDA; Parte II - Sobre las extensiones basadas en kernels de PCA, PLS y PLSDA, donde presentamos el potencial de las técnicas de kernel, eventualmente acopladas a variantes específicas de la recién redescubierta proyección de pseudo-muestras, formulada por el estadista inglés John C. Gower, y comparamos su rendimiento respecto a metodologías más clásicas en cuatro aplicaciones a escenarios diferentes: segmentación de imágenes Rojo-Verde-Azul (RGB), discriminación y monitorización de procesos por lotes y análisis de diseños de experimentos de mezclas; Parte III - Sobre la selección del número de factores en el PCA por pruebas de permutación, donde aportamos una guía extensa sobre cómo conseguir la selección de componentes de PCA mediante pruebas de permutación y una ilustración completa de un procedimiento algorítmico original implementado para tal fin; Parte IV - Sobre la modelización de fuentes de variabilidad común y distintiva en el análisis de datos multi-conjunto, donde discutimos varios aspectos prácticos del análisis de componentes comunes y distintivos de dos bloques de datos (realizado por métodos como el Análisis Simultáneo de Componentes - SCA - Análisis Simultáneo de Componentes Distintivos y Comunes - DISCO-SCA - Descomposición Adaptada Generalizada de Valores Singulares - Adapted GSVD - ECO-POWER, Análisis de Correlaciones Canónicas - CCA - y Proyecciones Ortogonales de 2 conjuntos a Estructuras Latentes - O2PLS). Presentamos a su vez una nueva estrategia computacional para determinar el número de factores comunes subyacentes a dos matrices de datos que comparten la misma dimensión de fila o columna y dos planteamientos novedosos para la transferencia de calibración entre espectrómetros de infrarrojo cercano; Parte V - Sobre el procesamiento y la modelización en tiempo real de flujos de datos de alta dimensión, donde diseñamos la herramienta de Procesamiento en Tiempo Real (OTFP), un nuevo sistema de manejo racional de mediciones multi-canal registradas en tiempo real; Parte VI - Epílogo, donde presentamos las conclusiones finales, delimitamos las perspectivas futuras, e incluimos los anexos. / La present tesi doctoral, concebuda principalment per a recolzar i reforçar la relació entre l'acadèmia i la indústria, es va desenvolupar en col·laboració amb Shell Global Solutions (Amsterdam, Països Baixos) amb l'esforç d'aplicar i possiblement estendre els enfocaments ja consolidats basats en variables latents (és a dir, Anàlisi de Components Principals - PCA - Regressió en Mínims Quadrats Parcials - PLS - o PLS discriminant - PLSDA) per a la resolució de problemes complexos no solament en els camps de la millora i optimització de processos, sinó també en l'entorn més ampli de l'anàlisi de dades multivariades. A aquest efecte, en tots els capítols proposem noves solucions algorítmiques eficients per a abordar tasques dispars, des de la transferència de calibratge en espectroscopia fins al modelatge en temps real de fluxos de dades. El manuscrit es divideix en les sis parts següents, centrades en diversos temes d'interès: Part I - Prefaci, on presentem un resum d'aquest treball de recerca, es donen els seus principals objectius i justificacions juntament amb una breu introducció sobre PCA, PLS i PLSDA; Part II - Sobre les extensions basades en kernels de PCA, PLS i PLSDA, on presentem el potencial de les tècniques de kernel, eventualment acoblades a variants específiques de la recentment redescoberta projecció de pseudo-mostres, formulada per l'estadista anglés John C. Gower, i comparem el seu rendiment respecte a metodologies més clàssiques en quatre aplicacions a escenaris diferents: segmentació d'imatges Roig-Verd-Blau (RGB), discriminació i monitorització de processos per lots i anàlisi de dissenys d'experiments de mescles; Part III - Sobre la selecció del nombre de factors en el PCA per proves de permutació, on aportem una guia extensa sobre com aconseguir la selecció de components de PCA a través de proves de permutació i una il·lustració completa d'un procediment algorítmic original implementat per a la finalitat esmentada; Part IV - Sobre la modelització de fonts de variabilitat comuna i distintiva en l'anàlisi de dades multi-conjunt, on discutim diversos aspectes pràctics de l'anàlisis de components comuns i distintius de dos blocs de dades (realitzat per mètodes com l'Anàlisi Simultània de Components - SCA - Anàlisi Simultània de Components Distintius i Comuns - DISCO-SCA - Descomposició Adaptada Generalitzada en Valors Singulars - Adapted GSVD - ECO-POWER, Anàlisi de Correlacions Canòniques - CCA - i Projeccions Ortogonals de 2 blocs a Estructures Latents - O2PLS). Presentem al mateix temps una nova estratègia computacional per a determinar el nombre de factors comuns subjacents a dues matrius de dades que comparteixen la mateixa dimensió de fila o columna, i dos plantejaments nous per a la transferència de calibratge entre espectròmetres d'infraroig proper; Part V - Sobre el processament i la modelització en temps real de fluxos de dades d'alta dimensió, on dissenyem l'eina de Processament en Temps Real (OTFP), un nou sistema de tractament racional de mesures multi-canal registrades en temps real; Part VI - Epíleg, on presentem les conclusions finals, delimitem les perspectives futures, i incloem annexos. / Vitale, R. (2017). Novel chemometric proposals for advanced multivariate data analysis, processing and interpretation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90442 / TESIS

Tato práce se zabývá vývojem nezávislého elektrického zdroje pro moderní nízkopříkonové elektrické aplikace. Protože tradiční řešení napájení drobných spotřebičů s využitím baterií či akumulátorů snižuje uživatelský komfort kvůli potřebě pravidelné údržby, navrhovaný zdroj využívá principu energy harvesting. Tento princip spočívá v získávání energie přímo z okolního prostředí napájené aplikace a její přeměně na energii elektrickou, která je dále využita pro na-pájení moderních MEMS (mikroelektromechanických) zařízení. Potenciální aplikací vyvíjeného zdroje je především moderní nositelná elektronika a biomedicínské senzory. Tato oblast využití ovšem klade zvýšené nároky na parametry generátoru, který musí zajistit dostatečný generovaný výkon z energie, dostupné v okolí lidského těla, a to při zachování prakticky využitelné velikosti a hmotnosti. Po stanovení předběžných požadavků a provedení analýz vhodnosti dostupných zdrojů energie ke konverzi byla k využití vybrána kinetická energie lidských aktivit. Byla provedena série měření zrychlení na lidském těle, především v místě předpokládaného umístění generátoru, aby bylo možno analyzovat a generalizovat hodnoty energie dostupné ke konverzi v daném umístění. V návaznosti na tato měření a analýzy byl vyvinut inovativní kinetický energy harvester, který byl následně vyroben jako funkční vzorek. Tento vzorek byl pak testován v reálných podmínkách pro verifikaci simulačního modelu a vyhodnocení reálné použitelnosti takového zařízení. Kromě samotného vývoje generátoru je v práci popsán i originální způsob zvýšení generovaného výkonu pro kinetické energy harvestery a jsou prezentována statistická data a modely pro predikci využitelnosti kinetických harvesterů pro získávání energie z lidské aktivity.

Since the introduction of economic reforms in the late 1970s, China has experienced phenomenal economic growth along with rapid urbanization. The accelerated urbanization coincides with remarkable social-economic transformations and urban landscape changes. A city, as an urban system, is composed of social and physical subsystems that interact with each other. Equally assessing each component is necessary for a comprehensive understanding of the urbanization process. The goal of this thesis research is to deconstruct the urbanization process through a social-ecological perspective. More specifically, this study examines social transformations, physical evolutions, and their relationships. Four research questions are proposed as (1) How does urban social landscape transform in time and space? (2) What trends are apparent in the urban land growth process and spatial heterogeneity? (3) How does social transformation relate to urban land growth, within a spatio-temporal perspective? and (4) How do social-demographic features relate to residents’ use and perception of urban green open spaces, focusing on the ecological services provided by and the need to improve those spaces? Given the lack of research on second-tier cities’ growth processes, this study selects Wuhan, a megacity in central China, as a case study, with a focus on its urban development zone (UDZ). A social-ecological approach is applied to study the multi-dimensional features of an urban system. The thesis is in paper format, containing five chapters. Besides the Introduction (Chapter 1) and Conclusion (Chapter 5), the main body consists of three articles. These three articles correspond to the four research questions proposed. Chapter 2 responds to the first research question by addressing how the urban social landscape transforms. Chapter 3 seeks to answer the second and third questions by evaluating urban land growth and its links with social factors from a spatio-temporal perspective. Chapter 4 matches the fourth question by seeking to understand residents’ preferences and feelings toward the urban green open space. Chapter 1 introduces the research context, reviews the urban ecology theory and relevant empirical research, as well as assesses the social-ecological approach related to studying the urban system. In this chapter, we also propose an improved social-ecological system (ISES) framework which guides the equally weighted study of both social and physical subsystems in an urban area. Chapter 2 (the first paper) seeks to investigate progressive transformations in the social dimensions of Wuhan UDZ while also focusing on their spatial transformations, using national census data in 1990, 2000, and 2010. We used varimax rotated principal component analysis (PCA) for the extraction of social dimensions and ArcMap for spatial visualization. This allows us to further analyze the spatial distribution of social clusters. The results suggest that industrial relocation, educational attainment increase, population aging, and migration are the main characteristics of social transformation during 1990 and 2010. Industrial relocation along with the spatial separation appeared as principal social dimensions in the 1990s but became more prominent in the 2000s, accompanied by the improvement of workers’ education levels. Aging population presented spatial movement outward from the city center. Population mobility increased significantly, and immigration became an important social dimension and presented spatial expansion in the 2000s. The socio-spatial patterns transform with a combination of concentric rings and sectoral clusters in different stages. These transformations are formed by the regional push-pull forces and the centripetal-centrifugal forces inside the city. We conclude that the social landscape transforms in a way with diversity and inclusion. Government dominates socio-spatial transformations in the initial stages, while market plays an increasing role in the later stages. To build a more inclusive society requires continuous and systematic improvement of relevant policies. Chapter 3 (the second paper) discusses urban land growth patterns and answers how social factors are associated with the evolution patterns between 1990 and 2010. We extract land cover information based on Landsat images with the vegetation area – impervious surface –water area (V-I-W) model and examine the urban growth patterns during various stages using landscape metrics of the area, aggregation, and shape. Then, we apply geographically weighted regression (GWR) to depict the link between urban land metrics and social factors. The results show that urban land coalescence and diffusion simultaneously exist; the city center is dominated by redevelopment, infilling, edge expansion; and the peripheral areas by outlying expansion. GWR coefficient surfaces show little differences in the models between social factors and urban land area metrics PLAND while remarkable differences are present in the coefficients of GWR models for the urban land patch shape irregularities and social factors. Urban land growth patterns relate to the government-led land supply system, the functional zoning of urban space planning, and the agglomeration and dispersion of social space under the market orientation. The authors conclude that urban management should consider the coexistence of different spatial growth modes and introduce factors such as social preferences in the urban land layout. This may apply to rapidly urbanizing areas. Chapter 4 (the third paper) aims to understand social-natural relationships, with a focus on how socio-demographic features can shape residents’ preference toward green open spaces and their perceptions of ecological services and improvements. Data is collected through online questionnaire surveys and interviews. The results indicate that preferences toward green open spaces vary among different social groups. Demands for improvement to green open spaces are rooted in residents’ appreciation for daily relaxation and health benefits, and link with their preference for visiting. However, how residents perceive green open spaces’ benefits does not rely only on an in-person visit. Interaction experience with nature and knowledge of natural development affect perception of daily use and health-related services. Residents’ perceptions of green open space’s ecological functions are associated with the changes in nature reported by those respondents. Responses to improving green open space reflect the residents’ pursuit of the aesthetics and practicality of such spaces. Though respondents are commonly aware of the ecological importance of green open space, there are differences in their willingness to voluntarily participate in its management. We conclude that to encourage the public to participate in configuration and improvement of green open spaces through a variety of ways, including considering residents’ opinions, is an efficient way in order to better social-ecological relationships. Chapter 5 reviews the main findings and conclusions, research limitations as well as future possibilities. This study establishes a dialogue between urban social and physical subsystems, with an integrated quantitative study of the urbanization process, emphasizing the relationships between two urban subsystems. It provides a comprehensive social-ecological view on a second-tier city based on the social and physical transformations that occurred in Wuhan during a transitional period of a socialist market economy. We conclude that the development of China's second-tier cities between 1990 and 2010 is characterized by the transformations of social dimensions and landscape, the coexistence of multiple urban spatial development modes, and the spatial differentiation between the center and the periphery of the city. The GWR models present spatial non-stationary relationships between social factors and the urban patch shape regularities. The further examination of social-natural relationships finds that residents’ social-demographic features and environmental experience affect their perceptions toward green open space, especially ecological services and improvement necessity. The evolution of urban social and physical systems and their relationships has brought increased attention to inclusive urban social management, public participatory planning, and people-centered social and ecological interactions. This research provides a constructive rethinking of second-tier cities’ growth in China and may serve as a reference for other rapidly urbanizing areas.

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This thesis considers the problematic of the object recognition in a digital picture, particularly about the human face recognition and its components. There are described the basics of the computer vision, the object detector Viola-Jones, its computer realization with help of the OpenCV libraries and the test results. This thesis also describes the accurate system of the facial features detection per the algorithm of the Active Shape Models and also related mechanism of the classifier training, including the software implementation.

This master‘s thesis deals with biometric fingerprint liveness detection. The theoretical part of the work describes fingerprint recognition biometric systems, fingerprint liveness detection issues and methods for fingerprint liveness detection. The practical part of the work describes proposed set of discriminant features and preprocessing of fingerprint image. Proposed approach using neural network to detect a liveness. The algorithm is tested on LivDet database comprising real and fake images acquired with tree sensors. Classification performance approximately 93% was obtained.