Pan Agathoklis

A Robust, Feature-based Algorithm for Aerial Image Registration

In this paper an algorithm for aerial image registration is proposed. The objective of this algorithm is to register aerial images having only partial overlap, which are also geometrically distorted due to the different sensing conditions and in addition they may be contaminated with noise, may be blurred, etc. The geometric distortions considered in the registration process are rotation, translation and scaling. The proposed algorithm consists of three main steps: feature point extraction using a feature point extractor based on scale-interaction of Mexican-hat wavelets, obtaining the correspondence between the feature points of the first (reference) and the second image based on Zernike moments of neighborhoods centered on the feature points, and estimating the transformation parameters between the first and the second images using an iterative weighted least squares algorithm. Experimental results illustrate the accuracy of image registration for images with partial overlap in the presence of additional image distortions, such as noise contamination and image blurring.

A feature-based image registration technique for images of different scale

In this paper a technique for image registration of two geometrically distorted images is presented. These images may be further degraded by noise, blurring, etc., and may have only partial overlap. The geometric distortions considered in the registration process are the global 2D affine transformations including scaling and shearing. The proposed technique consists of three main steps: extracting feature point using a feature point extractor based on scale-interaction of Mexican-hat wavelets, obtaining the correspondence between the feature points of the reference and the target images based on Zernike moments of neighborhoods centered on the feature points, and estimating the transformation parameters between the first and the second images using an iterative weighted least squares algorithm. Experimental results illustrate the accuracy of image registration of images with various geometric distortions including different scales in the presence of additional image degradations.

Control of a woofer tweeter system of deformable mirrors

This paper describes the control of two deformable mirrors (DM) and a tip tilt mirror for adaptive optics. The purpose of this experimental adaptive optics system at the University of Victoria is to prove the Woofer Tweeter concept for use in instruments for the Thirty Meter Telescope (TMT) which is currently under development. The first deformable mirror is a large stroke DM (Woofer) capable of lower frequency correction in both the temporal and spatial domains. The other DM (Tweeter) is capable of the high temporal and spatial frequency corrections of the turbulence. The response speed of the Woofer is incorporated into the Tweeter controller in order to allow for appropriate offloading from the Tweeter to the Woofer. In order to determine which Tweeter shapes must compensate for the slower Woofer and which are not coupled to the Woofer, the cross correlation of the devices is determined. The method of converting the wave front sensor (WFS) measurements to control signal error is given. The transfer functions of the controller are provided, along with rejection ratio plots, bandwidths and amplitude response to system noise.

On the attenuation of interference and mutual coupling in antenna arrays using 3D space-time filters

A 3D space-time filtering method is proposed for attenuating undesirable electromagnetic signals that propagate at or close to light speed across the surface of the plane that contains an array of antennas. Such signals may include the so-called radio frequency interference (RFI) that emanate from sources that lie well outside the directions of arrival (DOAs) of the signals of interest (SOIs). They may also include the intra-plane inter-antenna signals that result from the undesirable electromagnetic mutual coupling that exists between rectangularly-spaced antennas in aperture arrays (AAs) and in the focal plane arrays (FPAs) of paraboloidal dishes. Such signals have 3D space-time spectra possessing regions of support (ROSs) that are close to the surface of the 3D spectral light cone. They can therefore be attenuated by means of 3D space-time filters having 3D stopbands that include and encompass the surface of this light cone. Such a 3D space-time filter is described here and used to evaluate the validity of the proposed approach. Numerical results confirm that the proposed method significantly attenuates broadband RFI signals and moderately suppresses mutual coupling.

A New Wave-Front Reconstruction Method for Adaptive Optics Systems Using Wavelets

A new technique for wave-front reconstruction from gradient measurements on a square data set is presented. This technique is based on obtaining the Haar wavelet image decomposition of the original wave-front by appropriate filtering and down-sampling of the gradient measurement data. The use of the wavelet decomposition leads to an algorithm with complexity of O(N), where N is the number of data points in the reconstruction, and at the same time allows denoising of the data using the wavelet coefficients. The proposed technique is illustrated with two examples and its reconstruction accuracy, computational speed and denoising performance are discussed. Results indicate that the proposed technique is a computationally efficient and accurate technique for wave-front and/or image reconstruction from gradient measurements.

Lossless compression of color images using an improved integer-based nonlinear wavelet transform

New technique for lossless color images is proposed. The technique is based on a new color image transformation using integer arithmetic and an improved integer-based nonlinear discrete wavelet transform. The proposed mapping is compared with the existing RGB (red, green, blue) and YIQ (luminance and chrominance) transformations. The compression technique is illustrated by applying the proposed wavelet-based algorithm on various color images. Comparisons with other techniques are made with respect to compression efficiency (bits per pixel) and computational complexity. The results indicate that the proposed technique leads to higher compression without increasing the computation time.

An efficiency enhanced isosurface generation algorithm for volume visualization

Abstract. An algorithm for computing isosurfaces from 3D volume data is presented that extends the standard marching-cube algorithm with two modifications. The first modification is that in the proposed algorithm, the status of a sample point on the isosurface depends on the number of edges (leading to this vertex) intersected by the isosurface. The second modification is that polygon vertices between two adjacent sample points are located at the middle point, which leads, in many cases, to co-planar triangles being merged to a polygon. The proposed algorithm reduces the number of polygons generated and thus increases efficiency, which is confirmed by experiments.

On the Positive Definite Solutions to the 2-D Continuous-timeLyapunov Equation

The very strict positive real lemma is further developed for nonminimal 1-D continuous-time systems and is used to study the 2-D continuous-time Lyapunov equation. Based on it, an extended condition for the bivariate characteristic polynomial of a matrix to be very strict Hurwitz is proposed for general 2-D analog systems with characteristic polynomials involving 1-D factor polynomials. It is also shown that in such a case the bivariate polynomial can be decomposed into a 2-D bivariate polynomial with the corresponding matrix satisfying certain controllability and observability conditions and into up to two 1-D polynomials. Further, two algorithms for computing the positive definite solutions to the 2-D Lyapunov equation are presented.

Closed-loop control of a woofer–tweeter adaptive optics system using wavelet-based phase reconstruction

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer-tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O(N) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O(N) reconstruction techniques. The controller configuration is based on the woofer-tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer-tweeter controller leads to very good results with respect to speed and accuracy.

Broadband Beamforming of Focal Plane Array (FPA) Signals Using Real-Time Spatio-Temporal 3D FIR Frustum Digital Filters

A real-time spatio-temporal (ST) 3D FIR Frustum filter is proposed for improving the SNR of broadband focal plane array (FPA) signals. The 3D stop band of the proposed filter attenuates non-reflected off-dish signals, such as radio frequency interference (RFI), and also attenuates noise due to local thermal sources (e.g., ground) as well as receiver noise. The frustum-shaped 3D pass band transmits, with low distortion, desired broadband reflected celestial signals, as received by the focal plane array (FPA) of receiving elements. It is shown that, for pulsar-timing and pulsar-profile studies, the pre-processing of FPA signals using the proposed 3D ST Frustum filter-based beamforming method, prior to coherent de-dispersion, yields lower distortion than the 3D conjugate field matching (CFM) method (when appropriately extended from 2D to 3D) and also lower distortion than the conventional 2D spatial-only beamforming method.