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

Implicit Object Pose Estimation on RGB Images Using Deep Learning Methods

With the rise of robotic and camera systems and the success of deep learning in computer vision, there is growing interest in precisely determining object positions and orientations. This is crucial for tasks like automated bin picking, where a camera sensor analyzes images or point clouds to guide a robotic arm in grasping objects. Pose recognition has broader applications, such as predicting a car's trajectory in autonomous driving or adapting objects in virtual reality based on the viewer's perspective. This dissertation focuses on RGB-based pose estimation methods that use depth information only for refinement, which is a challenging problem. Recent advances in deep learning have made it possible to predict object poses in RGB images, despite challenges like object overlap, object symmetries and more. We introduce two implicit deep learning-based pose estimation methods for RGB images, covering the entire process from data generation to pose selection. Furthermore, theoretical findings on Fourier embeddings are shown to improve the performance of the so-called implicit neural representations - which are then successfully utilized for the task of implicit pose estimation

Image Registration Workshop Proceedings

Automatic image registration has often been considered as a preliminary step for higher-level processing, such as object recognition or data fusion. But with the unprecedented amounts of data which are being and will continue to be generated by newly developed sensors, the very topic of automatic image registration has become and important research topic. This workshop presents a collection of very high quality work which has been grouped in four main areas: (1) theoretical aspects of image registration; (2) applications to satellite imagery; (3) applications to medical imagery; and (4) image registration for computer vision research

Statistical shape analysis in a Bayesian framework; The geometric classification of fluvial sand bodies.

We present a novel shape classification method which is embedded in the Bayesian paradigm. We focus on the statistical classification of planar shapes by using methods which replace some previous approximate results by analytic calculations in a closed form. This gives rise to a new Bayesian shape classification algorithm and we evaluate its efficiency and efficacy on available shape databases. In addition we apply our results to the statistical classification of geological sand bodies. We suggest that our proposed classification method, that utilises the unique geometrical information of the sand bodies, is more substantial and can replace ad-hoc and simplistic methods that have been used in the past. Finally, we conclude this work by extending the proposed classification algorithm for shapes in three-dimensions

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

Proceedings of the EAA Spatial Audio Signal Processing symposium: SASP 2019

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