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Effects Of Apriory Given Homogenouscoordinates Nullspace Constraintson Slam Convergence
Klečka, Jan
The paper aims at the topic of SLAM (Simultaneous Localization and Mapping) algorithms convergence. Standard SLAM algorithms process observations composed of elements which are considered to be independent of each other. Following pages deals with changes that occur on convergence by the apriory assumption that some or all observation elements are bound by some mathematical model. In this case, the considered models are given by nullspace constraints in homogenous coordinates – in other words observed points lies on the same beforehand unknown line or plane. All described experiments are just simulations.
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Training and validation dataset optimization for Earth observation classification accuracy improvement
Potočná, Barbora ; Kupková, Lucie (advisor) ; Potůčková, Markéta (referee)
This thesis deals with training dataset and validation dataset for Earth observation classification accuracy improvement. Experiments with training data and validation data for two classification algorithms (Maximum Likelihood - MLC and Support Vector Machine - SVM) are carried out from the forest-meadow landscape located in the foothill of the Giant Mountains (Podkrkonoší). The thesis is base on the assumption that 1/3 of training data and 2/3 of validation data is an ideal ratio to achieve maximal classification accuracy (Foody, 2009). Another hypothesis was that in a case of SVM classification, a lower number of training point is required to achieve the same or similar accuracy of classification, as in the case of the MLC algorithm (Foody, 2004). The main goal of the thesis was to test the influence of proportion / amount of training and validation data on the classification accuracy of Sentinel - 2A multispectral data using the MLC algorithm. The highest overal accuracy using the MLC classification algorithm was achieved for 375 training and 625 validation points. The overal accuracy for this ratio was 72,88 %. The theory of Foody (2009) that 1/3 of training data and 2/3 of validation data is an ideal ratio to achieve the highest classification accuracy, was confirmed by the overal accuracy and...
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Evaluation of the land cover in the military training area Libavá using Random Forest classifier
Žďánský, Vít ; Štych, Přemysl (advisor) ; Laštovička, Josef (referee)
Data land cover help us understand nature, how it develops, its uses and the influence that human actions have on it. Thanks to new methods in the remote sensing area, we can record these processes faster and at a larger scale than before. This thesis evaluates accuracy of the Random Forest (RF) and Maximum Likelihood (ML) classifiers using satellite data Sentinel-2 from the military training area Libavá. The military area went through a very specific development and the information regarding natural coverage in the region is missing. The classifier documentation contains 8 classes. The classification results from both algorithms are higher than 80 %. As expected, more accurate results were achieved using the Random Forest classifier. The most accurate classifications were of water surfaces and forests. The least accurate classifications were of agricultural land and sparse vegetation. Other classes varied in accuracy levels. This thesis' results are evaluated using error matrices, overall accuracy and the kappa coefficient. Keywords: classification, Random Forest, Maximum Likelihood, military training area, remote sensing, Sentinel 2, land cover, Libavá
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Score tests in contingency tables
Jex, Martin ; Omelka, Marek (advisor) ; Kulich, Michal (referee)
The thesis deals with testing of hypotheses in multinomial distribution. It utilizes two approaches, Pearson's approach known as the of goodness of fit test and the approach stemming from theory of maximum likelihood. The thesis presents derivations of tests based on maximum likelihood. Both approaches are used on the multinomial distribution and for both cases with and without nuisance parameters. The links between both approaches are presented as well. Furthermore both approaches are illustrated on real data to facilitate better understanding of the discussed problems. 1
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Tree species classification using sentinel-2 and Landsat 8 data
Havelka, Ondřej ; Štych, Přemysl (advisor) ; Kupková, Lucie (referee)
The main objectives of this master thesis are to evaluate and compare chosen classification algorithm for the tree species classification. With usage of satellite imagery Sentinel-2 and Landsat 8 is examined whether the better spatial resolution affects the quality of the resulted classification. According to past case studies and literature was chosen supervised algorithms Support Vector Machine, Neural Network and Maximum Likelihood. To achieve the best possible results of classification is necessary to find a suitable choice of parameters and rules. Based on literate was applied different settings which were subsequently evaluated by cross validation. All results are accompanied by tables, charts and maps which comprehensively and clearly summarize the answers to the main objectives of the thesis.
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Incomplete Poisson samples
Zeman, Ondřej ; Dvořák, Jiří (advisor) ; Hlubinka, Daniel (referee)
The topic of my bachelor thesis is studying truncated Poisson sample which is a part of a sample from Poisson distribution, where zero observations are missing. The main goal is estimating the size of the original sample and the parameter λ of the Poisson distribution. In the first chapter I mainly focus on deriving three types of estimators of these parameters and I describe their basic properties. Second chapter contains simulations where the estimators from the first chapter are compared based on the estimates of relative bias and relative mean square error. Eventually in the third chapter I focus on the asymptotic properties of derived estimators with emphasis on consistency of estimators. 1
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Evaluation of methods and input data for land cover classification: case study of the former military areas Ralsko and Brdy
Paluba, Daniel ; Štych, Přemysl (advisor) ; Brom, Jakub (referee)
Taking advantage of Earth Observation (EO) data for monitoring land cover has attracted the attention of a broad spectrum of researchers and end-users in recent decades. The main reason of increased interest in EO can be found mainly in open data of Landsat and Sentinel archive. The main objective of this study is to evaluate the accuracy of the classification algorithms Maximum Likelihood (ML) and Support Vector Machine (SVM) using Landsat 8 and Sentinel-2 data in the case studies of the former military training areas Brdy and Ralsko, which have undergone a very specific land cover development. The study evaluates the land cover in both case studies in 2016 and based on the obtained results discussing a usefulness of the selected data and methods. The results of the land cover classification achieved satisfactory accuracy - the overall accuracy was higher than 85 %. Based on the expectation, the results of accuracy based on SVM algorithm are higher than results obtained by ML algorithm. The highest accuracy has reached in the land cover classes of water bodies and coniferous forests, on the contrary, the lowest accuracy in built-up areas, sparse vegetation and bare soil. Keywords: Earth Observation, Support Vector Machine, Maximum Likelihood, Czechia, Sentinel-2, Landsat 8
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Maximum likelihood methods; selected problems
Chlubnová, Tereza ; Hlubinka, Daniel (advisor) ; Hlávka, Zdeněk (referee)
Maximum likelihood estimation is one of statistical methods for estimating an unknown parameter. It is often used because of a simple calculation of the estimator and also for characteristics of this estimator, which the method provides under some conditions. In the thesis we prove a consistence of the estimator under conditions of regularity and uniqueness of the root of the likelihood equation. If we add other assumptions we show its asymptotic normality and we expand this result from the one-dimensional parameter to the multi-dimensional parameter. The main result of the thesis lies in exercises, in which we cannot express the maximum likelihood estimator in general, but we can show its existence, uniqueness and asymptotic normality. Moreover we demonstrate the utilization of asymptotic normality of the estimator for asymptotic hypothesis tests and confidence intervals of the parameter. Powered by TCPDF (www.tcpdf.org)
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Bayesian and Maximum Likelihood Nonparametric Estimation in Monotone Aalen Model
Timková, Jana ; Volf, Petr (advisor) ; Kraus, David (referee) ; Komárek, Arnošt (referee)
This work is devoted to seeking methods for analysis of survival data with the Aalen model under special circumstances. We supposed, that all regression functions and all covariates of the observed individuals were nonnegative and we named this class of models monotone Aalen models. To find estimators of the unknown regres- sion functions we considered three maximum likelihood based approaches, namely the nonparametric maximum likelihood method, the Bayesian analysis using Beta processes as the priors for the unknown cumulative regression functions and the Bayesian analysis using a correlated prior approach, where the regression functions were supposed to be jump processes with a martingale structure.
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