In this study, we explore the relationship between the components of a hybrid process consisting of a spatial point process arid a lattice process using two-dimensional spectral techniques. Simulated spatial point-lattice patterns are used to demonstrate how the different cross-spectral statistics can reveal correlation between the two components. A method to adjust for jumps that normally occur in the cross-spectral phase statistic is then proposed. Such adjustment is needed to enable us to calculate the slope of the phase spectrum which measures the shift between the two components. Several methods to calculate the slope are investigated. Asymptotic properties of the cross-spectral statistics are derived and their confidence intervals estimated. .A test that the components are independent is described. In a study region, lattice processes are observed at regular grids whereas point, processes can be observed anywhere. In order to account for discrepancies that. might arise due to this, methods to discretise the point pattern are suggested. Cross-spectral techniques are then applied to analyse the joint process of the discretised point pattern and the lattice pattern. Finally, we apply the techniques suggested above to study the joint properties of two data sets. The first consists of altitude data of a region in a rain forest in French Guyana together with the locations of a number of tree species in that region. The second set consists of altitude data of the Sahel region of Africa together with location of storms and some of their characteristics. In order to incorporate the storm characteristics in the analysis, cross-spectral tools used to analyse two components are extended to three components.

The topic of this thesis is registration of image sequences captured by experimental ophthalmoscope. It contains anatomical description of the visual system as well as the description of functions of selected ophthalmoscopic devices. The next covered topic is theoretical summary of registration process, which is followed by an overview of the used methods, which forms the basis of the design and implementation of the registration algorithm in the Python programming language. After implementation, the accuracy and computational complexity of a registration was evaluated. Tests of optimalization of the proposed approach were performed with regards to the obtained results, through which sufficiently accurate registration has been achieved, evaluated on the basis of Euclidean distances, standard deviation and visual observation. In case of high-quality recorded sequences, values of Euclidean distances ranged from 0.60 to 4.07 pixels on the contrary, values higher than 20 pixels occurred in the case of poor-quality recordings. Standard deviation values in recordings with high enough resolution have not reached worse results than 4.12.

In this thesis work, the background of atmospheric turbulence degradation in imaging was reviewed and two aspects are highlighted: blurring and geometric distortion. The turbulence burring parameter is determined by the atmospheric turbulence condition that is often unknown; therefore, a blur identification technique was developed that is based on a higher order statistics (HOS). It was observed that the kurtosis generally increases as an image becomes blurred (smoothed). Such an observation was interpreted in the frequency domain in terms of phase correlation. Kurtosis minimization based blur identification is built upon this observation. It was shown that kurtosis minimization is effective in identifying the blurring parameter directly from the degraded image. Kurtosis minimization is a general method for blur identification. It has been tested on a variety of blurs such as Gaussian blur, out of focus blur as well as motion blur. To compensate for the geometric distortion, earlier work on the turbulent motion compensation was extended to deal with situations in which there is camera/object motion. Trajectory smoothing is used to suppress the turbulent motion while preserving the real motion. Though the scintillation effect of atmospheric turbulence is not considered separately, it can be handled the same way as multiple frame denoising while motion trajectories are built.

This master’s thesis is aimed at registration of frames of retinal fundus video using phase corre- lation. An introduction describes general research in topic of retinal fundus, eye movements, diff erent approaches for image registration, phase correlation and examples of phase corre- lation applications. The second, practical part of master’s thesis, is dedicated to description of the proposed algorithm for registration of frames of retinal fundus video. The description of the proposed algorithm is divided into three parts. First two parts describe how frames of retinal fundus video are rated in terms of suitability for registration. Third part describes image registration algorithm itself. In conclusion, the accuracy of algorithm and computational time are evaluated.

This master thesis deals with retinal image registration using phase correlation technique. There are described properties of retinal images and modality of scanning. A geometrical transformation encompasing scale, rotation and translation between two retinal images is considered and the whole registration framework is described. There are used retinal images from fundus camera and scanning laser ophthalmoscope (SLO). In this thesis is described corresponding bifurcations detection using phase correlation and registration using second-order polynomial transformation. The results are subjectively and objectively verificated.

This work deals with object speed measuring using image analysis method. The reader will become familiar with a mathematical theory upon which the method is based. The mathematical algorithm for obtaining the speed of a given object is illustrated. Furthermore, an original computer program has been developed and the results of real measuring are shown.

Tato práce se zabývá použitím fázové korelace k určení vzájemné rotace, změny měřítka a posunu mezi digitálními obrazy. Fázová korelace je založena na Fourierově transformaci, proto je popsána Fourierova transformace funkcí definovaných na R^2 i diskrétní Fourierova transformace funkcí definovaných na konečném počtu bodů {0, 1, ... , N-1}^2, kde N je přirozené číslo. Dále je pozornost věnována modifikacím fázové korelace, díky nimž metoda umožňuje nalezení parametrů podobnostní transformace i mezi obrazy, které mají vysoký dynamický rozsah a slabě patrné struktury, obsahují aditivní nebo impulzní šum a jsou pořízeny pomocí různých snímačů a optických soustav. Obsahem práce jsou i modifikace metody pro snímky sluneční koróny pořízené během úplných zatmění Slunce, což patří mezi nejobtížnější úlohy registrace obrazů.

Indiana University-Purdue University Indianapolis (IUPUI) / Adaptive Optics Optical Coherence Tomography (AO-OCT) is a high-speed, high-resolution ophthalmic imaging technique offering detailed 3D analysis of retina structure in vivo. However, AO-OCT volume images are sensitive to involuntary eye movements that occur even during steady fixation and include tremor, drifts, and micro-saccades. To correct eye motion artifacts within a volume and to stabilize a sequence of volumes acquired of the same retina area, we propose a stripe-wise 3D image registration algorithm with phase correlation. In addition, using several ideas such as coarse-to-fine approach, spike noise filtering, pre-computation caching, and parallel processing on a GPU, our approach can register a volume of size 512 x 512 x 512 in less than 6 seconds, which is a 33x speedup as compared to an equivalent CPU version in MATLAB. Moreover, our 3D registration approach is reliable even in the presence of large motions (micro-saccades) that distort the volumes. Such motion was an obstacle for a previous en face approach based on 2D projected images. The thesis also investigates GPU implementations for 3D phase correlation and 2D normalized cross-correlation, which could be useful for other image processing algorithms.

The entrainment process in two-phase buoyant jets differs significantly from their singlephase counterparts, and is not well understood. Entrainment models developed for singlephase flow are often used in two-phase jetting simulations, albeit with limited success. In this work, Particle Image Velocimetry (PIV) and shadowgraph flow visualization experiments have been conducted on submerged round gas jets of varying speeds and nozzle diameters with the goal of improving our understanding of the entrainment process in a two-phase (gas-liquid) jet. The total entrainment estimated using the PIV measurements is higher than the respective values suggested by a common empirical model developed for singlephase buoyant jets. A two-phase theoretical entrainment model used for comparison shows an overestimation of entrainment, but predicts the increase in the rate of entrainment with axial distance from the jet nozzle seen in the PIV results. This thesis also presents advances in PIV processing methodology that were developed concurrently with the entrainment research. The novel Spectral Phase Correlation (SPC) allows for particle displacement to be determined directly from phase information in the Fourier domain. Some of the potential benefits of the SPC explored here include (1) avoidance of errors introduced by spatial peak-finding routines; (2) use of a modal analysis that can be used to provide information such as correlation quality; and (3) introduction of a means of incorporating information from multiple image windows. At low image noise levels, the method performs as well as an advanced CC-based method. However, difficulties unwrapping the aliased phase information cause the SPC's performance to degrade at high noise levels. / Master of Science

Video stabilization methods are classified as mechanical and digital. Mechanical methods are based on motion sensors. Digital methods are computer programs and classified into two as time domain and frequency domain based on the signal processing methods used for the motion analysis. Although, mechanical methods have good real time stabilization performance, they are not suitable for small platforms such as mobile robots. On the other hand, digital video stabilization methods are easy to implement on various hardware, however, they require high computational load and long processing time. Two different digital video stabilization methods, one frequency and one time domain algorithms, are implemented on FPGA to realize their real time performances. Also, the methods are implemented and tested in MATLAB. FPGA results are compared with MATLAB&rsquo / s to see the accuracy performance.The input video format is PAL of which frame period is 40ms. The FPGA implementation is capable of producing new stabilization data at every PAL frame which allows the implementation to be classified as real time. Also, the simulation and hardware tests show that FPGA implementation can reach the MATLAB accuracy performance.