doc. Ing. Jan Švihlík, Ph.D.

Solar photovoltaic (PV) systems are increasingly recognized as crucial sustainable energy sources with diverse applications. Their implementation leverages rapid advancements in material engineering, communication systems, and computational intelligence tools. This paper focuses on selected mathematical methods for analyzing time series of power generated by PV systems, including numerical methods and algorithms for multichannel signal processing, digital filtering, and signal feature extraction. These methods monitor the characteristics of individual PV panels and identify their feature clusters. Specifically, it examines systems with east/west oriented photovoltaic panels, employing statistical methods and computational tools to analyze power signals, assess time and positioning data, evaluate symmetry coefficients, and apply machine learning tools to detect potential panel failures. Additionally, a general graphical user interface for data analysis is proposed. A detailed case study is presented, analyzing the distribution of selected features over time segments of a PV system comprising seven east-oriented and seven west-oriented panels, with data recorded over a selected set of days at a sampling rate of 15 minutes. The results reveal distinct and well-separated feature clusters for healthy PV panels. General conclusions underscore the effectiveness of signal processing tools in the statistical analysis of PV systems and the potential of feature clustering and symmetry estimation for evaluating disorders of system behaviour using communication technologies, data storage, and remote system monitoring.

Background: Speech dysfunction represents one of the initial motor manifestations to develop in Parkinson's disease (PD) and is measurable through smartphone. Objective: The aim was to develop a fully automated and noise-resistant smartphone-based system that can unobtrusively screen for prodromal parkinsonian speech disorder in subjects with isolated rapid eye movement sleep behavior disorder (iRBD) in a real-world scenario. Methods: This cross-sectional study assessed regular, everyday voice call data from individuals with iRBD compared to early PD patients and healthy controls via a developed smartphone application. The participants also performed an active, regular reading of a short passage on their smartphone. Smartphone data were continuously collected for up to 3 months after the standard in-person assessments at the clinic. Results: A total of 3525 calls that led to 5990 minutes of preprocessed speech were extracted from 72 participants, comprising 21 iRBD patients, 26 PD patients, and 25 controls. With a high area under the curve of 0.85 between iRBD patients and controls, the combination of passive and active smartphone data provided a comparable or even more sensitive evaluation than laboratory examination using a high-quality microphone. The most sensitive features to induce prodromal neurodegeneration in iRBD included imprecise vowel articulation during phone calls (P = 0.03) and monopitch in reading (P = 0.05). Eighteen minutes of speech corresponding to approximately nine calls was sufficient to obtain the best sensitivity for the screening. Conclusion: We consider the developed tool widely applicable to deep longitudinal digital phenotyping data with future applications in neuroprotective trials, deep brain stimulation optimization, neuropsychiatry, speech therapy, population screening, and beyond.

Although long-term averaged spectrum (LTAS) descriptors can detect the change in dysarthria of patients with Parkinson's disease (PD) due to subthalamic nucleus deep brain stimulation (STN-DBS), the relationship between LTAS variables with measures that relate to laryngeal physiology remain unknown. We aimed to find connections between LTAS-based moments and the main acoustic characteristics of hypokinetic dysarthria in PD as the response to STN-DBS stimulation changes. We analyzed reading passages of 23 PD patients in ON and OFF STN-DBS states compared to 23 healthy controls. We found a relation between the stimulation-induced change in several spectral moments and acoustic parameters representing voice quality, articulatory decay, articulation rate, and mean fundamental frequency. While the difference between PD and controls was significant across most acoustic descriptors, only the spectral mean and fundamental frequency variability could differentiate between ON and OFF conditions.

One of the most popular speech parametrizations for dysarthria has been Mel Frequency Cepstral Coefficients (MFCCs). Although the MFCCs ability to capture vocal tract characteristics is known, the reflected dysarthria aspects are primarily undisclosed. Thus, we investigated the relationship between key acoustic variables in Parkinson's disease (PD) and the MFCCs. 23 PD patients were recruited with ON and OFF conditions of Deep Brain Stimulation of the Subthalamic Nucleus (STN-DBS) and examined via a reading passage. The changes in dysarthria aspects were compared to changes in a global MFCC measure and individual MFCCs. A similarity was found in 2nd to 3rd MFCCs changes and voice quality. Changes in 4th to 9th MFCCs reflected articulation clarity. The global MFCC parameter outperformed individual MFCCs and acoustical measures in capturing STN-DBS conditions changes. The findings may assist in interpreting outcomes from clinical trials and improve the monitoring of disease progression.

Purpose: This study aimed to evaluate whether long-term averaged spectrum (LTAS) descriptors for reading and monologue are suitable to detect worsening of dysarthria in patients with Parkinson’s disease (PD) treated with subthalamic nucleus deep brain stimulation (STN-DBS) with potential effect of ON and OFF stimulation conditions and types of connected speech. Method: Four spectral moments based on LTAS were computed for monologue and reading passage collected from 23 individuals with PD treated with bilateral STN-DBS and 23 age-and gender-matched healthy controls. Speech performance of patients with PD was compared in ON and OFF STN-DBS conditions. Results: All LTAS spectral moments including mean, standard deviation, skew-ness, and kurtosis across both monologue and reading passage were able to significantly distinguish between patients with PD in both stimulation conditions and control speakers. The spectral mean was the only LTAS measure sensitive to capture better speech performance in STN-DBS ON, as compared to the STN-DBS OFF stimulation condition (p < .05). Standardized reading passage was more sensitive compared to monologue in detecting dysarthria severity via LTAS descriptors with an area under the curve of up to 0.92 obtained between PD and control groups. Conclusions: Our findings confirmed that LTAS is a suitable approach to objec-tively describe changes in speech impairment severity due to STN-DBS therapy in patients with PD. We envisage these results as an important step toward a continuum development of technological solutions for the automated assessment of stimulation-induced dysarthria.

This paper deals with the modelling of high bit-depth images acquired by astronomical cameras using the discrete wavelet transform and the undecimated discrete wavelet transform for image representation. The probability density function (PDF) model parameters are estimated using the expectation-maximization (EM) algorithm and the method of moments. As proposed in this paper, the task of estimating the overall PDF model parameters can be simplified by so-called mirroring of the initial model which is estimated only for those wavelet coefficients that are greater than or equal to zero. In the case of the EM algorithm, this technique significantly reduces the computational cost of the model fitting algorithm. In our experiments, we achieved a reduction of more than 70%. In the case of the method of moments, this technique simplifies a system of moment equations. Three main PDF models are presented here: firstly, the mirrored mixture of a half-normal distribution and an exponential distribution, secondly, the mirrored mixture of two exponential distributions, and finally, the mirrored mixture of two half-normal distributions. Performance of these models is evaluated on three sets of astronomical images and also on artificial data using the Jeffrey divergence metric. Overall, the mirrored mixture of a half-normal and an exponential distribution overcomes the commonly used GLM (generalized Laplacian model) and also the other studied models.

We read with great interest the recent study by Suppa et al., which performed voice analysis in patients with essential tremor (ET) with (ETVT+) and without (ETVT-) clinically overt voice tremor based on power spectral analysis and machine learning. Traditional spectral analysis showing a prominent oscillatory activity peak at 2–6 Hz in ETVT+ seems to be in agreement with a recent study reporting the occurrence of both low (<4 Hz) and medium (4–7 Hz) vocal tremor in ET.

Hypokinetic dysarthria is a multidimensional impairment affecting all main speech subsystems with variable patterns and severity across individual Parkinson's disease (PD) patients. We can thus assume that inter-individual abnormal speech patterns are related to the various clinical subtypes of PD with different prominent motor symptoms. The aim of this cross-sectional study was to compare speech disorder between patients with the postural instability/gait difficulty (PIGD) and tremor-dominant (TD) motor phenotypes of PD. Speech samples were acquired from a total of 63 participants, including 21 PIGD patients, 21 TD patients, and 21 healthy controls. Quantitative acoustic vocal assessment of 12 unique speech dimensions related to phonation, vocal tremor, oral diadochokinesis, articulation, prosody and speech timing was performed. Speech impairment was more pronounced in the PIGD group than in the TD group, with an area under the curve of 0.76. Patients in the PIGD group manifested abnormalities in pitch breaks, articulatory decay, decreased rate of follow-up speech segments and inappropriate silences, apart from monopitch and irregular AMR that were affected in TD group as well. An abnormal vocal tremor was present in only 10% of PD patients, with no differences between the PD phenotypes. We found a correlation between non-motor symptom severity and speech timing (r = - 0.40,p = 0.009). The present study demonstrates that speech disorder reflects the underlying motor phenotypes. Vocal tremor appeared to be an isolated phenomenon that does not share similar pathophysiology with limb tremor.

In the last decade, several different structured illumination microscopy (SIM) approaches have been developed. Precise determination of the effective spatial resolution in a live cell SIM reconstructed image is essential for reliable interpretation of reconstruction results. Theoretical resolution improvement can be calculated for every SIM method. In practice, the final spatial resolution of the cell structures in the reconstructed image is limited by many different factors. Therefore, assessing the resolution directly from the single image is an inherent part of the live cell imaging. There are several commonly used resolution measurement techniques based on image analysis. These techniques include full-width at half maximum (FWHM) criterion, or Fourier ring correlation (FRC). FWHM measurement requires fluorescence beads or sharp edge/line in the observed image to determine the point spread function (PSF). FRC method requires two stochastically independent images of the same observed sample. Based on our experimental findings, the FRC method does not seem to be well suited for measuring the resolution of SIM live cell video sequences. Here we show a method based on the Fourier transform analysis using power spectral density (PSD). In order to estimate the cut-off frequency from a noisy signal, we use PSD estimation based on Welch’s method. This method is widely used in non-parametric power spectra analysis. Since the PSD-based metric can be computed from a single SIM image (one video frame), without any prior knowledge of the acquiring system, it can become a fundamental tool for imaging in live cell biology.

Signal and image stationarity is the basic assumption for many methods of their analysis. However this assumption is not true in a lot of real cases. The paper is focused on local stationary testing using a small symmetric neighbourhood. The neighbourhood is split into two parts which should have the same statistical properties when the hypothesis of image stationarity is valid. We apply various testing approaches (two-sampled F-test, t-test, WMW, K-S) to obtain adequate p-values for given pixel, mask position, and test type. Finally, using battery of masks and tests, we obtain the series of p-values for every pixel. Applying False Discovery Rate (FDR) methodology, we localize all the pixels when any hypothesis falls. Resulting binary image is an alternative to traditional edge detection but with strong statistical background.

The segmentation of 2D biomedical images is very complex problem which has to be solved interactively. Original MRI, CT, PET, or SPECT image can be enhanced using variational smoother. However, there are Regions of Interest (ROI) which can be exactly localized. The question is how to design human interaction with computer for user friendly biomedical service. Our approach is based on user selected points which determine the ROI border line. The relationship between point positions and image intensity is subject of variational interpolation using thin plate spline model. The general principle of segmentation is demonstrated on biomedical images of human brain.

Super-resolution (SR) microscopy is a powerful technique which enhances the resolution of optical microscopes beyond the diffraction limit. Recent SR methods achieve the resolution of 100 nm. Theoretical resolution enhancement can be mathematically defined. However, the final resolution in the real image can be influenced by technical limitations. Evaluation of resolution in a real sample is essential to assess the performance of an SR technique. Several image based resolution limit evaluation methods exist, but the determination of cutoff frequency is still a challenging task. In order to compare the efficiency of assessing resolution methods, the reference estimation technique is necessary. There exist several conventional methods in digital image processing. In this paper, the most common resolution measurement techniques used in the optical microscopy imaging are presented and their performance compared.

This paper deals with techniques for analysis of perceived color differences in images. Impact of color artifacts in image processing chain is a critical factor in the assessment of overall Quality of Experience (QoE). At first, an overview of color difference measures is presented. The performance of the methods is compared based on the results from subjective studies. Possible utilization of publicly available datasets with associated subjective scores is discussed. Majority of the datasets contain images distorted by various types of distortions not necessarily with controlled color impairments. Dedicated database of images with common color distortions and associated subjective scores is introduced. Performance evaluation and comparison of objective image color difference measures is presented using conventional correlation performance measures and robust receiver operating characteristic (ROC) based analyses.

Traditional median smoother for 2D images is insensitive to impulse noise but generates flat areas as unwanted artifacts. The proposed approach to overcome this issue is based on the minimization of the regularized form of total variation functional. At first the continuous functional is defined for n-dimensional signal in an integral form with regularization term. The continuous functional is converted to the discrete form using equidistant spatial sampling in point grid of pixels, voxels or other elements. This approach is suitable for traditional signal and image processing. The total variance is then converted to the sum of absolute intensity differences as a minimization criterion. The functional convexity guarantees the existence of global minimum and absence of local extremes. Resulting non-linear filter iteratively calculates local medians using red-black method of Successive Over/Under Relaxation (SOR) scheme. The optimal value of the relaxation parameter is also subject to our study. The sensitivity to regularization parameter enables to design high-pass and nonlinear band-pass filters as the difference between the image and low-pass smoother or as the difference between two different low-pass smoothers, respectively. Various median based approaches are compared in the paper.

Modeling of atmospheric turbulence through Kolmogorov theorem belongs to traditional applications of 2D Fourier Transform (2D FT). It is based on Point Spread Function (PSF) in the spatial domain and its frequency domain image known as Optical Transfer Function (OTF). The latter is available in the explicit form. It enables to create an artificial fog effect in traditional image processing using 2D Discrete Fourier Transform (2D DFT). Exact knowledge of the Optical Transfer Function allows performing the image deblurring as deconvolution through Wiener method. The difference between the reference image and the deconvolution outcome can be quantified using SNR in traditional and rank modification. However, the real star image is a result of a stochastic process which is driven by 2D alpha-stable distribution. There is an efficient method how to generate a pseudorandom sample from the alpha-stable distribution. The distribution then enables to simulate the photon distribution following the theoretical PSF, i.e. convergence according to distribution is guaranteed. The comparison of both models and optimal parameter setting of Wiener deconvolution are studied for various exposure times and CCD camera noise levels. Obtained results can be generalized and applied to turbulent noise suppression.

The present paper deals with the problem of volume estimation of individual objects from a single 2D view. Our main application is volume estimation of pancreatic (Langerhans) islets and the single 2D view constraint comes from the time and equipment limitations of the standard clinical procedure. Two main approaches are followed in this paper. First, two regression-based methods are proposed, using a set of simple shape descriptors of the segmented image of the islet. Second, two example-based methods are proposed, based on a database of islets with known volume. For training and evaluation, islet volumes were determined by OPT microscopy and a stereological volume estimation using the so-called Fakir probes. The performance of the single image volume estimation methods is studied on a set of 99 islets from human donors. Further experiments were also performed on a stone dataset and on synthetic 3D shapes, generated using a flexible stochastic particle model. The proposed methods are fast and the experimental results show that in most situations the proposed methods perform significantly better than the methods currently used in clinical practice, which are based on simple spherical or ellipsoidal models.

This paper deals with modeling of astronomical images in the spatial domain. We consider astronomical light images contaminated by the dark current which is modeled by Poisson random process. Dark frame image maps the thermally generated charge of the CCD sensor. In this paper, we solve the problem of an addition of two Poisson random variables. At first, the noise analysis of images obtained from the astronomical camera is performed. It allows estimating parameters of the Poisson probability mass functions in every pixel of the acquired dark frame. Then the resulting distributions of the light image can be found. If the distributions of the light image pixels are identified, then the denoising algorithm can be applied. The performance of the Bayesian approach in the spatial domain is compared with the direct approach based on the method of moments and the dark frame subtraction.

This paper concerns the comparison of automatic volume estimation methods for isolated pancreatic islets. The estimated islet volumes are needed during the process of assessing the islet sample quality prior to the islet transplantation. We study several different methods for automatic volume estimation. For this purpose we acquired a set of projections using optical tomography for a sample of an islet population. Based on these projections we estimated the islet volumes using two stereological methods (the automatic Wulfsohn’s method and the manual fakir method, considered to be the ground truth in this study), together with the filtered back projection followed by 3D segmentation. We have also employed two simple methods, currently used in medical practice, based on fitting a sphere or a prolate ellipsoid to a single binarized 2D islet projections.

Image segmentation is widely used as an initial phase of many image analysis tasks. It is often advantageous to first group pixels into compact, edge-respecting superpixels, because these reduce the size of the segmentation problem and thus the segmentation time by an order of magnitudes. In addition, features calculated from superpixel regions are more robust than features calculated from fixed pixel neighborhoods. We present a fast and general multiclass image segmentation method consisting of the following steps: (i) computation of superpixels; (ii) extraction of superpixel-based descriptors; (iii) calculating image-based class probabilities in a supervised or unsupervised manner; and (iv) regularized superpixel classification using graph cut. We apply this segmentation pipeline to five real-world medical imaging applications and compare the results with three baseline methods: pixelwise graph cut segmentation, supertexton-based segmentation, and classical superpixel-based segmentation. On all datasets, we outperform the baseline results. We also show that unsupervised segmentation is surprisingly efficient in many situations. Unsupervised segmentation provides similar results to the supervised method but does not require manually annotated training data, which is often expensive to obtain.

Detection and localization of astronomical objects are two of the most fundamental topics in astronomical science where localization uses detection results. Object localization is based on modeling of point spread function and estimation of its parameters. Commonly used models as Gauss or Moffat in objects localization provide good approximation of analyzed objects but cannot be sufficient in the case of exact applications such as object energy estimation. Thus the use of sophisticated models is upon the place. One of the key roles plays also the way of the objective function estimation. The least square method is often used, but it expects data with normal distribution, thus there is a question of a maximum likelihood method application. Another important factor of presented problem is choice of the right optimization method. Classical methods for objective function minimization usually require a good initial estimate for all parameters and differentiation of the objective function with respect to model parameters. The results indicated that stochastic methods such as simulated annealing or harmony search achieved better results than the classical optimization methods.

Clinical islet transplantation programs rely on the capacities of individual centers to quantify isolated islets. Current computer-assisted methods require input from human operators. Here we describe two machine learning algorithms for islet quantification: the trainable islet algorithm (TIA) and the nontrainable purity algorithm (NPA). These algorithms automatically segment pancreatic islets and exocrine tissue on microscopic images in order to count individual islets and calculate islet volume and purity. References for islet counts and volumes were generated by the fully manual segmentation (FMS) method, which was validated against the internal DNA standard. References for islet purity were generated via the expert visual assessment (EVA) method, which was validated against the FMS method. The TIA is intended to automatically evaluate micrographs of isolated islets from future donors after being trained on micrographs from a limited number of past donors. Its training ability was first evaluated on 46 images from four donors. The pixel-to-pixel comparison, binary statistics, and islet DNA concentration indicated that the TIA was successfully trained, regardless of the color differences of the original images. Next, the TIA trained on the four donors was validated on an additional 36 images from nine independent donors. The TIA was fast (67 s/image), correlated very well with the FMS method (R 2 = 1.00 and 0.92 for islet volume and islet count, respectively), and had small REs (0.06 and 0.07 for islet volume and islet count, respectively). Validation of the NPA against the EVA method using 70 images from 12 donors revealed that the NPA had a reasonable speed (69 s/image), had an acceptable RE (0.14), and correlated well with the EVA method (R 2 = 0.88). Our results demonstrate that a fully automated analysis of clinical-grade micrographs of isolated pancreatic islets is feasible. The algorithms described herein will be freely available as a Fiji platform plugin.

This paper deals with separation of merged Langerhans islets in segmentations in order to evaluate correct histogram of islet diameters. A distribution of islet diameters is useful for determining the feasibility of islet transplantation in diabetes. First, the merged islets at training segmentations are manually separated by medical experts. Based on the single islets, the merged islets are identified and the SVM classifier is trained on both classes (merged/single islets). The testing segmentations were over-segmented using watershed transform and the most probable back merging of islets were found using trained SVM classifier. Finally, the optimized segmentation is compared with ground truth segmentation (correctly separated islets).

In this contribution we study different methods of automatic volume estimation for pancreatic islets which can be used in the quality control step prior to the islet transplantation. The total islet volume is an important criterion in the quality control. Also, the individual islet volume distribution is interesting it has been indicated that smaller islets can be more effective. A 2D image of a microscopy slice containing the islets is acquired. The input of the volume estimation methods are segmented images of individual islets. The segmentation step is not discussed here. We consider simple methods of volume estimation assuming that the islets have spherical or ellipsoidal shape. We also consider a local stereological method, namely the nucleator. The nucleator does not rely on any shape assumptions and provides unbiased estimates if isotropic sections through the islets are observed. We present a simulation study comparing the performance of the volume estimation methods in different scenarios and an experimental study comparing the methods on a real dataset.

Two classes of linear IIR filters: Laplacian of Gaussian (LoG) and Difference of Gaussians (DoG) are frequently used as high pass filters for contextual vision and edge detection. They are also used for image sharpening when linearly combined with the original image. Resulting sharpening filters are radially symmetric in spatial and frequency domains. Our approach is based on the radial approximation of unknown optimal filter, which is designed as a weighted sum of Gaussian filters with various radii. The novel filter is designed for MRI image enhancement where the image intensity represents anatomical structure plus additive noise. We prefer the gradient norm of Hartley entropy of whole image intensity as a measure which has to be maximized for the best sharpening. The entropy estimation procedure is as fast as FFT included in the filter but this estimate is a continuous function of enhanced image intensities. Physically motivated heuristic is used for optimum sharpening filter design by its parameter tuning. Our approach is compared with Wiener filter on MRI images.

Reliable meteor detection is one of the crucial disciplines in astronomy. A variety of imaging systems is used for meteor path reconstruction. The traditional approach is based on analysis of 2D image sequences obtained from a double station video observation system. Precise localization of meteor path is difficult due to atmospheric turbulence and other factors causing spatio-temporal fluctuations of the image background. The proposed technique performs non-linear preprocessing of image intensity using Box-Cox transform as recommended in our previous work. Both symmetric and asymmetric spatio-temporal differences are designed to be robust in the statistical sense. Resulting local patterns are processed by data whitening technique and obtained vectors are classified via cluster analysis and Self-Organized Map (SOM).

This article deals with modeling of astronomical objects, which is one of the most fundamental topics in astronomical science. Introduction part is focused on problem description and used methods. Point Spread Function Modeling part deals with description of basic models used in astronomical photometry and further on introduction of more sophisticated models such as combinations of interference, turbulence, focusing, etc. This paper also contains a way of objective function definition based on the knowledge of Poisson distributed noise, which is included in astronomical data. The proposed methods are further applied to real astronomical data.

This paper deals with color normalization of microscopy images of Langerhans islets in order to increase robustness of the islet segmentation to illumination changes. The main application is automatic quantitative evaluation of the islet parameters, useful for determining the feasibility of islet transplantation in diabetes. First, background illumination inhomogeneity is compensated and a preliminary foreground/background segmentation is performed. The color normalization itself is done in either $l alpha beta$ or logarithmic RGB color spaces, by comparison with a reference image. The color-normalized images are segmented using color-based features and pixel-wise logistic regression, trained on manually labeled images. Finally, relevant statistics such as the total islet area are evaluated in order to determine the success likelihood of the transplantation. The robustness of the evaluation is increased dramatically by the color normalization, decreasing the image-wise failure rate from 17pct to 0pct and the equal error rate from 30pct to 1pct.

Astronomical instruments located around the world are producing an incredibly large amount of possibly interesting scientific data. Astronomical research is expanding into large and highly sensitive telescopes. Total volume of data rates per night of operations also increases with the quality and resolution of state-of-the-art CCD/CMOS detectors. Since many of the ground-based astronomical experiments are placed in remote locations with limited access to the Internet, it is necessary to solve the problem of the data storage. It mostly means that current data acquistion, processing and analyses algorithm require review. Decision about importance of the data has to be taken in very short time. This work deals with GPU accelerated processing of high frame-rate astronomical video-sequences, mostly originating from experiment MAIA (Meteor Automatic Imager and Analyser), an instrument primarily focused to observing of faint meteoric events with a high time resolution. The instrument with price bellow 2000 euro consists of image intensifier and gigabite ethernet camera running at 61 fps. With resolution better than VGA the system produces up to 2TB of scientifically valuable video data per night. Main goal of the paper is not to optimize any GPU algorithm, but to propose and evaluate parallel GPU algorithms able to process huge amount of video-sequences in order to delete all uninteresting data.

Meteor detection is one of the most important procedures in astronomical imaging. Meteor path in Earth's atmosphere is traditionally reconstructed from double station video observation system generating 2D image sequences. However, the atmospheric turbulence and other factors cause spatially-temporal fluctuations of image background, which makes the localization of meteor path more difficult. Our approach is based on nonlinear preprocessing of image intensity using Box-Cox and logarithmic transform as its particular case. The transformed image sequences are then differentiated along discrete coordinates to obtain statistical description of sky background fluctuations, which can be modeled by multivariate normal distribution. After verification and hypothesis testing, we use the statistical model for outlier detection. Meanwhile the isolated outlier points are ignored, the compact cluster of outliers indicates the presence of meteoroids after ignition.

There are various deconvolution methods for suppression of blur in images. In this paper a survey of image deconvolution techniques is presented with focus on methods designed to handle images acquired with wide-field astronomical imaging systems. Image blur present in such images is space-variant especially due to space-variant point spread function (PSF) of the lens. The imaging system can contain also nonlinear electro-optical elements. Analysis of nonlinear and space-variant imaging systems is usually simplified so that the system is considered as linear and space-invariant (LSI) under specific constraints. Performance analysis of selected image deconvolution methods is presented in this paper, while considering space-variant nature of wide-field astronomical imaging system. Impact of nonlinearity on the overall performance of image deconvolution technique is also analyzed. Test images with characteristics obtained from the real system with space-variant wide-field input lens and nonlinear image intensifier are used for the performance analysis.

Classification of images of Langerhans islet is crucial procedure for optimization of diabetes treatment. Hence, this paper deals with segmentation of microscopy images of Langerhans islets and evaluation of islet parameters such as area, islet diameter, islet equivalent (IE) etc. For all the available images, the ground truth and the islet parameters were independently evaluated by four medical experts in a blinded manner. We utilized linear classifier (perceptron algorithm) and SVM (support vector machine) for image segmentation. All the available image data were segmented and compared with corresponding ground truth. The islet parameters were also evaluated and compared with parameters evaluated by medical experts. The presented fully automatic algorithm analyzes the microscopy images as good as medical experts.

Additional monitoring equipment is commonly used in astronomical imaging. This electro-optical system usually complements the main telescope during acquisition of astronomical phenomena or supports its operation e.g. evaluating the weather conditions. Typically it is a wide-field imaging system, which consists of a digital camera equipped with fish-eye lens. The wide-field imaging system cannot be considered as a space-invariant because of space-variant nature of its input lens. In our previous research efforts we have focused on measurement and analysis of images obtained from the subsidiary all-sky monitor WILLIAM (WIde-field aLL-sky Images Analyzing Monitoring system). Space-variant part of this imaging system consists of input lens with 180 fi angle of view in horizontal and 154 fi in vertical direction. For a precise astronomical measurement over the entire field of view, it is very important to know how the optical aberrations affect characteristics of the imaging system, especially its PSF (Point Spread Function). Two methods were used for characterization of the space-variant PSF, i.e. measurement in the optical laboratory and estimation using acquired images and Zernike polynomials. Analysis of results obtained using these two methods is presented in the paper. Accuracy of astronomical measurements is also discussed while considering the space-variant PSF of the system.

Most of the classical approaches to the measurement and modeling of electro-optical imaging systems rely on the principles of linearity and space invariance (LSI). In our previous research efforts we have focused on measurement and analysis of images obtained from a double station video observation system MAIA (Meteor Automatic Imager and Analyzer). The video acquisition module of this system contains wide-field input lens which contributes to space-variability of the imaging system. For a precise astronomical measurement over the entire field of view, it is very important to comprehend how the characteristics of the imaging system can affect astrometric and photometric outputs. This paper presents an analysis of how the space-variance of the imaging system can affect precision of astrometric and photometric results. This analysis is based on image data acquired in laboratory experiments and astronomical observations with the wide-field system. Methods for efficient calibration of this system to obtain precise astrometric and photometric measurements are also proposed.

Quantization noise is present in all the current digital imaging systems, therefore its understanding and modeling is crucial for optimization of image reconstruction techniques. Hence, this paper deals with modeling of the quantization noise. We exploit the undecimated wavelet transform (UWT) for signal representation. We assume that the quantization noise in the spatial domain can be seen as additive, white and uniformly distributed. Hence, the UWT causes the transform of noise distribution due to weighted sum of noise samples and filter coefficients. From the known quantization step we are able to estimate suitable moments of noise uniform probability density function (PDF). These moments then could be directly evaluated in the undecimated wavelet domain using the derived equations. The presented algorithm gives the a priori information about the quantization noise and can be used for the suppression of it.

We discuss methods for modeling and removal of noise in astronomical images. For its favorable properties, we exploit the undecimated wavelet representation and apply noise suppression in this domain. Usually, the noise analysis of the studied imaging system is carried out in the spatial domain. However, noise in astronomical data is non-Gaussian, and thus the noise model parameters need to be estimated directly in the wavelet domain. We derive equations for estimating the sample moments for non-Gaussian noise in the wavelet domain. We consider that the sample moments in the spatial domain are known from the noise analysis and that the model parameters are estimated by using the method of moments.

We discuss methods for modeling and removal of noise in astronomical images. For its favorable properties, we exploit the undecimated wavelet representation and apply noise suppression in this domain. Usually, the noise analysis of the studied imaging system is carried out in the spatial domain. However, noise in astronomical data is non-Gaussian, and thus the noise model parameters need to be estimated directly in the wavelet domain. We derive equations for estimating the sample moments for non-Gaussian noise in the wavelet domain. We consider that the sample moments in the spatial domain are known from the noise analysis and that the model parameters are estimated by using the method of moments.

This paper is devoted to statistical analysis of noise generated in real imaging systems and noise suppression methods. The introductory part is focused on description of imaging systems, image degradations, and noise types present in them. The noise analysis section includes determination of basic noise characteristics, the probability distribution and dependence on the signal. The described methods are used to compare properties of two digital still cameras: Nikon D70 and Canon EOS 500D and video camera: JAI CM-040GE. The section devoted to noise suppression discusses different methods of wavelet coefficients thresholding and threshold estimation. The wavelet coefficients are produced by two forms of the wavelet transform: the discrete wavelet transform and the dual-tree complex wavelet transform. The described noise suppression methods are applied to the data sets which were acquired by the analyzed systems under poor lighting conditions.

This paper is devoted to the noise analysis and noise suppression in a system for double station observation of the meteors now known as MAIA (Meteor Automatic Imager and Analyzer). The noise analysis is based on acquisition of testing video sequences in different light conditions and their further statistical evaluation. The main goal is to find a suitable noise model and subsequently determine if the noise is signal dependent or not. Noise and image model in the wavelet domain should be based on Gaussian mixture model (GMM) or Generalized Laplacian Model (GLM) and the model parameters should be estimated by moment method. Furthermore, noise should be modeled by GMM or GLM also in the space domain. GMM and GLM allow to model various types of probability density functions. Finally the advanced denoising algorithm using Bayesian estimator is applied and its performance is verified.

This paper deals with advanced methods for elimination of the thermally generated charge in the astronomical images, which were acquired by Charged Coupled Device (CCD) sensor. There exist a number of light images acquired by telescope, which were not corrected by dark frame. The reason is simple the dark frame doesn't exists, because it was not acquired. This situation may for instance come when sufficient memory space is not available. There will be discussed the correction method based on the modeling of the light and dark image in the wavelet domain. As the model for the dark frame image and for the light image the generalized Laplacian was chosen. The models parameters were estimated using moment method, whereas an extensive measurement on astronomical camera were proposed and done. This measurement simplifies estimation of the dark frame model parameters.

This paper deals with advanced method for elimination of the dark current in security images acquired by simple camera with Charged Coupled Device (CCD) sensor. There will be discussed the correction method based on the modeling of the useful security image data and dark current in the wavelet domain. As the model for the dark frame (mapped dark current) image and for the light image the generalized Laplacian was chosen. The models parameters were estimated using moment method, whereas an extensive measurement on camera were proposed and done. This measurement simplifies estimation of the dark frame model parameters. Finally a set of the security image data were corrected and then the objective criteria for an image quality evaluation were applied.

This paper deals with advanced methods for elimination of the thermally generated charge in the astronomical images, which were acquired by Charged Coupled Device (CCD) sensor. There exist a number of light images acquired by telescope, which were not corrected by dark frame. The reason is simple the dark frame doesn't exists, because it was not acquired. This situation may for instance come when sufficient memory space is not available. There will be discussed the correction method based on the modeling of the light and dark image in the wavelet domain. As the model for the dark frame image and for the light image the generalized Laplacian was chosen. The models parameters were estimated using moment method, whereas an extensive measurement on astronomical camera were proposed and done. Finally a set of the astronomical testing images were corrected and then the objective criteria for an image quality evaluation based on the aperture photometry were applied.

This paper is devoted to denoising technique for video noise removal and deals with advanced WT (Wavelet Transform) based method of noise suppression for security purposes. Our goal was to optimize the WT based algorithm to be applicable for the noise suppression in security videos with high computational efficiency. Preprocessing is applied to the output of the sensing system to make the video data more suitable for further denoising. Then a WT based statistical denoising method is applied. The method uses BLSE (Bayesian Least Square Error Estimator) of WT coefficients while utilizing generalized Laplacian PDF modeling and optimized moment method for parameters estimation. Several tests have been done to verify high noise suppression performance, computational efficiency and low distortion of important features.

It is generally known that every astronomical image, which was acquired by CCD sensor, has to be corrected by dark frame. The Dark frame maps the thermally generated charge of the CCD. May become that the dark frame image is not available and it is impossible to correct the astronomical images directly. It is good to note that uncorrected images are not suitable for subsequent investigation. During the recent year the algorithms for the thermally generated charge elimination were proposed. All these algorithms use the Discrete Wavelet Transform (DWT). The DWT transforms image into different frequency bands. Wavelet coefficients histogram should be modeled by generalized Laplacian probability density function (PDF). The Laplacian parameters were estimated by moment method using derived equation system. Furthermore, the images, where the thermally generated charge was suppressed, were estimated using Bayesian estimators.

The security imaging systems have special qualitative requirements - the general perceptive image quality is not so important compared to the preservation of selected security image characteristics such as an identification or classification. In the first part we have tested the impact of image enhancing algorithms on the display readability in presence of noise. We have chosen the registration plate as an example and two noise types have been added in order to find the readability threshold. The second part has been devoted to de-noising techniques for image noise removal and deals with advanced WT based method of noise suppression for security purposes. Specific requirements on the proposed noise suppression technique can be stated. It should be efficient, both in the sense of low computational complexity but also by means of high noise suppression performance. Moreover, the system must preserve all the important features of the scene being watched.

A number of the methods for parameters estimation in many statistical books were described. Many of these are quite suboptimal, because it is impossible to estimate the model parameters directly from noisy wavelet coefficients. So because of this the method using Jeffrey divergence (JD) was proposed. This method for parameters estimation is based on minimizing of JD between the noisy wavelet coefficients histogram and the modeled noisy PDF.

This paper deals with advanced image noise removal methods based on the Bayesian statistics. There will be discussed some algorithms for additive image noise suppression and also algorithm for the elimination of the thermally generated charge in the astronomical images, which were acquired by CCD (Charged Coupled Device sensor).

V tomto příspěvku je popsána metoda pro potlačení obrazového šumu ve videozáznamu. Tato metoda využívá pokročilých algoritmů založených na vlnkové transformaci (Wavelet Transform - WT) zejména s ohledem na použití v bezpečnostních kamerových systémech. V reálném kamerovém systému se vyskytuje řada nežádoucích zkreslení obrazu, zejména pokud je videozáznam snímán za zhoršených světelných podmínek. Naším cílem bylo optimalizovat rekonstrukční algoritmy založené na WT, tak aby je bylo možno použít pro potlačení šumu v záznamu z bezpečnostní kamery při zachování vysoké účinnosti a přijatelných výpočetních nároků.

This paper deals with evaluation and processing of astronomical image data, which are obtained by WFC (Wide-Field Camera) or UWFC (Ultra Wide-Field Camera) systems. Precision of astronomical image data post-processing and analyzing is very important. Large amount of different kinds of optical aberrations and distortions is included in these systems. The amplitude of wavefront aberration error increases towards margins of the FOV (Field of View). Relation between amount of high order optical aberrations and astrometry measurement precision is discussed in this paper. There are descriptions of the transfer characteristics of astronomical optical systems presented in this paper. Spatially variant (SV) optical aberrations negatively affect the transfer characteristics of all system and make it spatially variant as well. SV model of optical system is presented in this paper. Partially invariant model of optical systems allows using Fourier methods for deconvolution.

A number of the methods for parameters estimation in many statistical books were described. Many of these are quite suboptimal, because it is impossible to estimate the model parameters directly from noisy wavelet coefficients. So because of this the method using Jeffrey divergence (JD) was proposed. This method for parameters estimation is based on minimizing of JD between the noisy wavelet coefficients histogram and the modeled noisy PDF.

Algoritmy pro odstranění šumu z obrazu.

Tato práce se zabývá metodami pro odstranění šumu z obrazu pracujícími ve waveletové doméně. Nejperspektivnější a nejúčinnější metody jsou založeny na statistickém modelu obrazu ve waveletové doméně. Původní nezašuměný obraz je potom odhadován pomocí BLSE (Bayesian least square error) estimátoru popř. MAP (maximum aposteriori) estimátoru. Statistický model obrazu vystupuje v těchto estimátorech jako apriorní hustota pravděpodobnosti. Pro porovnání účinnosti BLSE a MAP estimátoru, byl obraz odšuměn ještě za pomoci dalšího algoritmu. Princip tohoto algoritmu tkví ve vhodném prahování waveletových koeficientů na dané dekomposiční hladině.

It is generally known that every astronomical image which was acquired by CCD sensor, have to be corrected by dark frame. The Dark frame is mapping the dark current of the CCD. May become that we don't have the dark frame image and we cannot directly to correct the astronomical images. This work deals with dark frame correction based on Bayesian estimator in the wavelet domain. The models of the marginal probability density function (PDF) of the wavelet coefficients of astronomical images and dark frame images based on generalized Laplacian is used by this estimator. The parameters of the models, which were mentioned above, were estimated by least square error method on set of the images from our image database.The correction of the astronomical images by dark frame is better than the Bayesian estimator, but further work will deal with more sophisticated Bayesian estimator with more robust statistical description of the images.

In this paper, the concept of Modulation Transfer Function (MTF) analysis is generalized to be applicable to the sampled structures of CMOS APS. Recalling theoretical results, we have analytically derived the detector MTF in the closed form for some special active area shapes. The paper also deals with the method based on pseudorandom image pattern with uniform power spectral density (PSD). This method allows to evaluate (in contrast to other methods) spatial invariant MTF including sampling MTF. It is generally known that a signal acquired by image sensor contains different types of noises. The superposition of these noises produces noise with a Gaussian distribution. The denoising method based on Bayesian estimator for implementation into the smart imager is presented.

This work deals with noise removal from an image data based on Bayesian estimator. Statistical model of the marginal probability density function (PDF) of digital images in the wavelet domain based on generalized Laplacian is used by this estimator. The model parameters was trained on our image database. There has been presented powerful method for additive noise suppression. This method was also compared with other denoisng algorithm based on suitable thresholding (Donoho-Johnston algorithm) of the wavelet coefficients.

PDF Model of Multimedia and Scientific Images in the Wavelet Domain

The image quality of image or video information is a crucial issue in security imaging systems. Our paper deals with three different points - a posteriori image improvement, objective image quality assessment and noise removal. In the first part we have tested and evaluated the impact of edge-enhancing operators. Their performance is of two contradictory effects - edge sharpening and noise level increase. The second part summarizes the ANN application in the objective image quality evaluation procedure. The advanced approach is based upon two advanced methods - Mutual Information MI and Principal Component Analysis PCA. The third part is devoted to the DWT noise-removal technique and the experimental results are presented.

It is generally known, that the image usually contains a noise, which induces a degradation of image. We have a lot of methods, more or less suitable, for his removing. For the first time we can divide this method like a linear and nonlinear. To linear methods mainly belongs in spatial domain, convolutions filtering and the frequency mask in spectral domain. Nowadays is popular to use Discrete Wavelet Transform (DWT), because this transform is a very good tool for denoising. Two methods will be discussed in this paper using two types of Wavelet Transform. The first of them is based on feasible thresholding (hard or soft) of wavelet coefficients on a suitable decomposition level (see [1]). This method uses Wavelet Transform, which is usually named dyadic decomposition. The second one, more sophisticated, uses special type of Wavelet Transform - the steerable pyramid. The estimation of the image is proceeded using Bayesian least square estimator.

Šum je v obraze prakticky vždy přítomen, což způsobuje degradaci obrazu. Existuje celá řada více či méně účinných metod sloužících k jeho potlačení. Metody lze v principu rozdělit na metody lineární a metody nelineární. Do lineárních metod (platí princip superposice) lze zahrnout zejména konvoluční filtraci v prostorové oblasti popř. kmitočtovou masku v oblasti spektrální. K nelineárním metodám patří kupř. metoda mediánového filtru apod. V dnešní době je velmi populární využívat vlnkovou transformaci, která rovněž představuje účinný nástroj pro potlačení šumu a tato její aplikace je naplní tohoto článku.

Mezi nejdůležitější charakteristiky hodnotící vlastnosti zobrazovacích systémů patří bezesporu modulační přenosová funkce (MTF). Tato charakteristika nám pomůže udělat si představu o tom, jak je daný systém schopen přenášet prostorové kmitočty. Systémem zde rozumíme kupř. digitální fotoaparát objektiv kamery apod.. Jestliže tedy chceme zjistit přenosové vlastnosti zobrazovacího systému, potom je nutné vybrat vhodnou měřící metodu a tu na daný systém aplikovat. Metod vhodných pro měření existuje celá řada. Můžeme sem zahrnout kupř. metody založené na vyhodnocení kontrastu obrazu, měření odezvy soustavy a na metody využívající pseudonáhodných obrazových vzorů. Posledně jmenovaná metoda byla využita pro měření přenosových vlastností digitálních fotoaparátu, výsledky měření jsou uvedeny v tomto příspěvku.