Image Description using Radial Associated Laguerre Moments

This study proposes a new set of moment functions for describing gray-level and color images based on the associated Laguerre polynomials, which are orthogonal over the whole right-half plane. Moreover, the mathematical frameworks of radial associated Laguerre moments (RALMs) and associated rotation invariants are introduced. The proposed radial Laguerre invariants retain the basic form of disc-based moments, such as Zernike moments (ZMs), pseudo-Zernike moments (PZMs), Fourier-Mellin moments (OFMMs), and so on. Therefore, the rotation invariants of RALMs can be easily obtained. In addition, the study extends the proposed moments and invariants defined in a gray-level image to a color image using the algebra of quaternion to avoid losing some significant color information. Finally, the paper verifies the feature description capacities of the proposed moment function in terms of image reconstruction and invariant pattern recognition accuracy. Experimental results confirmed that the associated Laguerre moments (ALMs) perform better than orthogonal OFMMs in both noise-free and noisy conditions

On The Potential of Image Moments for Medical Diagnosis

Medical imaging is widely used for diagnosis and postoperative or post-therapy monitoring. The ever-increasing number of images produced has encouraged the introduction of automated methods to assist doctors or pathologists. In recent years, especially after the advent of convolutional neural networks, many researchers have focused on this approach, considering it to be the only method for diagnosis since it can perform a direct classification of images. However, many diagnostic systems still rely on handcrafted features to improve interpretability and limit resource consumption. In this work, we focused our efforts on orthogonal moments, first by providing an overview and taxonomy of their macrocategories and then by analysing their classification performance on very different medical tasks represented by four public benchmark data sets. The results confirmed that convolutional neural networks achieved excellent performance on all tasks. Despite being composed of much fewer features than those extracted by the networks, orthogonal moments proved to be competitive with them, showing comparable and, in some cases, better performance. In addition, Cartesian and harmonic categories provided a very low standard deviation, proving their robustness in medical diagnostic tasks. We strongly believe that the integration of the studied orthogonal moments can lead to more robust and reliable diagnostic systems, considering the performance obtained and the low variation of the results. Finally, since they have been shown to be effective on both magnetic resonance and computed tomography images, they can be easily extended to other imaging techniques

Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

Validation of computational solid mechanics simulations requires full-field comparison methodologies between numerical and experimental results. The continuous Zernike and Chebyshev moment descriptors are applied to decompose data obtained from numerical simulations and experimental measurements, in order to reduce the high amount of ‘raw’ data to a fairly modest number of features and facilitate their comparisons. As Zernike moments are defined over a unit disk space, a geometric transformation (mapping) of rectangular to circular domain is necessary, before Zernike decomposition is applied to non-circular geometry. Four different mapping techniques are examined and their decomposition/ reconstruction efficiency is assessed. A deep mathematical investigation to the reasons of the different performance of the four methods has been performed, comprising the effects of image mapping distortion and the numerical integration accuracy. Special attention is given to the Schwarz–Christoffel conformal mapping, which in most cases is proven to be highly efficient in image description when combined to Zernike moment descriptors. In cases of rectangular structures, it is demonstrated that despite the fact that Zernike moments are defined on a circular domain, they can be more effective even from Chebyshev moments, which are defined on rectangular domains, provided that appropriate mapping techniques have been applied

A Quaternionic Version Theory related to Spheroidal Functions

In dieser Arbeit wird eine neue Theorie der quaternionischen Funktionen vorgestellt, welche das Problem der Bestapproximation von Familien prolater und oblater sphäroidalen Funktionen im Hilberträumen behandelt. Die allgemeine Theorie beginnt mit der expliziten Konstruktion von orthogonalen Basen für Räume, definiert auf sphäroidalen Gebieten mit beliebiger Exzentrizität, deren Elemente harmonische, monogene und kontragene Funktionen sind und durch die Form der Gebiete parametrisiert werden. Eine detaillierte Studie dieser grundlegenden Elemente wird in dieser Arbeit durchgeführt. Der Begriff der kontragenen Funktion hängt vom Definitionsbereich ab und ist daher keine lokale Eigenschaft, während die Begriffe der harmonischen und monogenen Funktionen lokal sind. Es werden verschiedene Umwandlungsformeln vorgestellt, die Systeme harmonischer, monogener und kontragener Funktionen auf Sphäroiden unterschiedlicher Exzentrizität in Beziehung setzen. Darüber hinaus wird die Existenz gemeinsamer nichttrivialer kontragener Funktionen für Sphäroide jeglicher Exzentrizität gezeigt. Der zweite wichtige Beitrag dieser Arbeit betrifft eine quaternionische Raumfrequenztheorie für bandbegrenzte quaternionische Funktionen. Es wird eine neue Art von quaternionischen Signalen vorgeschlagen, deren Energiekonzentration im Raum und in den Frequenzbereichen unter der quaternionischen Fourier-Transformation maximal ist. Darüber hinaus werden diese Signale im Kontext der Spektralkonzentration als Eigenfunktionen eines kompakten und selbstadjungierteren quaternionischen Integraloperators untersucht und die grundlegenden Eigenschaften ihrer zugehörigen Eigenwerte werden detailliert beschrieben. Wenn die Konzentrationsgebiete beider Räume kugelförmig sind, kann der Winkelanteil dieser Signale explizit gefunden werden, was zur Lösung von mehreren eindimensionalen radialen Integralgleichungen führt. Wir nutzen die theoretischen Ergebnisse und harmonische Konjugierten um Klassen monogener Funktionen in verschiedenen Räumen zu konstruieren. Zur Charakterisierung der monogenen gewichteten Hardy- und Bergman-Räume in der Einheitskugel werden zwei konstruktive Algorithmen vorgeschlagen. Für eine reelle harmonische Funktion, die zu einem gewichteten Hardy- und Bergman-Raum gehört, werden die harmonischen Konjugiert in den gleichen Räumen gefunden. Die Beschränktheit der zugrundeliegenden harmonischen Konjugationsoperatoren wird in den angegebenen gewichteten Räumen bewiesen. Zusätzlich wird ein quaternionisches Gegenstück zum Satz von Bloch für monogene Funktionen bewiesen.This work presents a novel Quaternionic Function Theory associated with the best approximation problem in the setting of Hilbert spaces concerning families of prolate and oblate spheroidal functions. The general theory begins with the explicit construction of orthogonal bases for the spaces of harmonic, monogenic, and contragenic functions defined in spheroidal domains of arbitrary eccentricity, whose elements are parametrized by the shape of the corresponding spheroids. A detailed study regarding the elements that constitute these bases is carried out in this thesis. The notion of a contragenic function depends on the domain, and, therefore, it is not a local property in contrast to the concepts of harmonic and monogenic functions. Various conversion formulas that relate systems of harmonic, monogenic, and contragenic functions associated with spheroids of differing eccentricity are presented. Furthermore, the existence of standard nontrivial contragenic functions is shown for spheroids of any eccentricity. The second significant contribution presented in this work pertains to a quaternionic space-frequency theory for band-limited quaternionic functions. A new class of quaternionic signals is proposed, whose energy concentration in the space and the frequency domains are maximal under the quaternion Fourier transform. These signals are studied in the context of spatial-frequency concentration as eigenfunctions of a compact and self-adjoint quaternion integral operator. The fundamental properties of their associated eigenvalues are described in detail. When the concentration domains are spherical in both spaces, the angular part of these signals can be found explicitly, leading to a set of one-dimensional radial integral equations. The theoretical framework described in this work is applied to the construction of classes of monogenic functions in different spaces via harmonic conjugates. Two constructive algorithms are proposed to characterize the monogenic weighted Hardy and Bergman spaces in the Euclidean unit ball. For a real-valued harmonic function belonging to a Hardy and a weighted Bergman space, the harmonic conjugates in the same spaces are found. The boundedness of the underlying harmonic conjugation operators is proven in the given weighted spaces. Additionally, a quaternionic counterpart of Bloch’s Theorem is established for monogenic functions

Numerical methods for computing the discrete and continuous Laplace transforms

We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating the Laplace transform for noisy data. We revisited a Meijer-G symbolic approach to compute the Laplace transform and alternative approaches to extend canonical observed time-series. A discrete quantization scheme provides the foundation for rapid and reliable estimation of the inverse Laplace transform. We derive theoretic estimates for the inverse Laplace transform of analytic functions and demonstrate empirical results validating the algorithmic performance using observed and simulated data. We also introduce a generalization of the Laplace transform in higher dimensional space-time. We tested the discrete LT algorithm on data sampled from analytic functions with known exact Laplace transforms. The validation of the discrete ILT involves using complex functions with known analytic ILTs

Design and Development of Robotic Part Assembly System under Vision Guidance

Robots are widely used for part assembly across manufacturing industries to attain high productivity through automation. The automated mechanical part assembly system contributes a major share in production process. An appropriate vision guided robotic assembly system further minimizes the lead time and improve quality of the end product by suitable object detection methods and robot control strategies. An approach is made for the development of robotic part assembly system with the aid of industrial vision system. This approach is accomplished mainly in three phases. The first phase of research is mainly focused on feature extraction and object detection techniques. A hybrid edge detection method is developed by combining both fuzzy inference rule and wavelet transformation. The performance of this edge detector is quantitatively analysed and compared with widely used edge detectors like Canny, Sobel, Prewitt, mathematical morphology based, Robert, Laplacian of Gaussian and wavelet transformation based. A comparative study is performed for choosing a suitable corner detection method. The corner detection technique used in the study are curvature scale space, Wang-Brady and Harris method. The successful implementation of vision guided robotic system is dependent on the system configuration like eye-in-hand or eye-to-hand. In this configuration, there may be a case that the captured images of the parts is corrupted by geometric transformation such as scaling, rotation, translation and blurring due to camera or robot motion. Considering such issue, an image reconstruction method is proposed by using orthogonal Zernike moment invariants. The suggested method uses a selection process of moment order to reconstruct the affected image. This enables the object detection method efficient. In the second phase, the proposed system is developed by integrating the vision system and robot system. The proposed feature extraction and object detection methods are tested and found efficient for the purpose. In the third stage, robot navigation based on visual feedback are proposed. In the control scheme, general moment invariants, Legendre moment and Zernike moment invariants are used. The selection of best combination of visual features are performed by measuring the hamming distance between all possible combinations of visual features. This results in finding the best combination that makes the image based visual servoing control efficient. An indirect method is employed in determining the moment invariants for Legendre moment and Zernike moment. These moments are used as they are robust to noise. The control laws, based on these three global feature of image, perform efficiently to navigate the robot in the desire environment

Detection of intentionally made changes in image content

Digital images and video signals represent the most frequently transmitted contents. Namely, with the development of modern digital cameras and smartphones, the use of multimedia content increases every day. They are used in everyday life, for getting information and also as authenticated proofs or corroboratory evidence in different areas like: forensic studies, law enforcement, journalism and others...Multifraktalna analiza se pokazala kao dobar alat za analizu postojećih slika, kao i segmentaciju određenih regiona, izdvajanje ivica, uglova slike i slično. Kako kopirani i nalepljeni delovi imaju sličnu strukturu, može se primeniti multifraktalna analiza, koja u osnovi analizira samosličnost. Multifraktalni spektar daje globalni opis slike (ili, opštije, fenomena koji se ispituje). Vrednost Hölder-ovog eksponenta zavisi od položaja u strukturi i opisuje lokalnu regularnost signala. Naime, različiti objekti na slici imaju različite spektre, različite pozicije maksimuma, minimuma, prve nule itd, što se pokazalo kao interesantan skup različitih parametara pomoću kojih se mogu detektovati namerne promene na slikama..

ACS Without an Attitude

The book (ACS without an Attitude) is an introduction to spacecraft attitude control systems. It is based on a series of lectures that Dr. Hallock presented in the early 2000s to members of the GSFC flight software branch, the target audience being flight software engineers (developers and testers), fairly new to the field that desire an introductory understanding of spacecraft attitude determination and control

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 04. bis 06.07. 2012, Bauhaus-Universität Weimar

The 19th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 4th till 6th July 2012. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference