A Heuristic Based on the Intrinsic Dimensionality for Reducing the Number of Cyclic DTW Comparisons in Shape Classification and Retrieval Using AESA

Cyclic Dynamic Time Warping (CDTW) is a good dissimilarity of shape descriptors of high dimensionality based on contours, but it is computationally expensive. For this reason, to perform recognition tasks, a method to reduce the number of comparisons and avoid an exhaustive search is convenient. The Approximate and Eliminate Search Algorithm (AESA) is a relevant indexing method because of its drastic reduction of comparisons, however, this algorithm requires a metric distance and that is not the case of CDTW. In this paper, we introduce a heuristic based on the intrinsic dimensionality that allows to use CDTW and AESA together in classification and retrieval tasks over these shape descriptors. Experimental results show that, for descriptors of high dimensionality, our proposal is optimal in practice and significantly outperforms an exhaustive search, which is the only alternative for them and CDTW in these tasks

Speeding up the cyclic edit distance using LAESA with early abandon

The cyclic edit distance between two strings is the minimum edit distance between one of this strings and every possible cyclic shift of the other. This can be useful, for example, in image analysis where strings describe the contour of shapes or in computational biology for classifying circular permuted proteins or circular DNA/RNA molecules. The cyclic edit distance can be computed in O(mnlog m) time, however, in real recognition tasks this is a high computational cost because of the size of databases. A method to reduce the number of comparisons and avoid an exhaustive search is convenient. In this work, we present a new algorithm based on a modification of LAESA (linear approximating and eliminating search algorithm) for applying pruning in the computation of distances. It is an efficient procedure for classification and retrieval of cyclic strings. Experimental results show that our proposal considerably outperforms LAESAWork partially supported by the Spanish Government (TIN2010-18958), and the Generalitat Valenciana (PROMETEOII/2014/062)

On the Dynamic Time Warping of Cyclic Sequences for Shape Retrieval

In the last years, in shape retrieval, methods based on Dynamic Time Warping and sequences where each point of the contour is represented by elements of several dimensions have had a significant presence. In this approach each point of the closed contour contains information with respect to the other ones, this global information is very discriminant. The current state-of-the-art shape retrieval is based on the analysis of these distances to learn better ones. These methods are robust to noise and invariant to transformations, but, they obtain the invariance to the starting point with a brute force cyclic alignment which has a high computational time. In this work, we present the Cyclic Dynamic Time Warping. It can obtain the cyclic alignment in O(n2 log n) time, where n is the size of both sequences. Experimental results show that our proposal is a better alternative than the brute force cyclic alignment and other heuristics for obtaining this invariance

The Parameter-Less Self-Organizing Map algorithm

The Parameter-Less Self-Organizing Map (PLSOM) is a new neural network algorithm based on the Self-Organizing Map (SOM). It eliminates the need for a learning rate and annealing schemes for learning rate and neighbourhood size. We discuss the relative performance of the PLSOM and the SOM and demonstrate some tasks in which the SOM fails but the PLSOM performs satisfactory. Finally we discuss some example applications of the PLSOM and present a proof of ordering under certain limited conditions.Comment: 29 pages, 27 figures. Based on publication in IEEE Trans. on Neural Network

Approximate Circular Pattern Matching

We investigate the complexity of approximate circular pattern matching (CPM, in short) under the Hamming and edit distance. Under each of these two basic metrics, we are given a length-n text T, a length-m pattern P, and a positive integer threshold k, and we are to report all starting positions (called occurrences) of fragments of T that are at distance at most k from some cyclic rotation of P. In the decision version of the problem, we are to check if there is any such occurrence. All previous results for approximate CPM were either average-case upper bounds or heuristics, with the exception of the work of Charalampopoulos et al. [CKP+, JCSS'21], who considered only the Hamming distance. For the reporting version of the approximate CPM problem, under the Hamming distance we improve upon the main algorithm of [CKP+, JCSS'21] from O(n+(n/m) k4) to O(n+(n/m) k3 log log k) time; for the edit distance, we give an O(nk2)-time algorithm. Notably, for the decision versions and wide parameter-ranges, we give algorithms whose complexities are almost identical to the state-of-the-art for standard (i.e., non-circular) approximate pattern matching: For the decision version of the approximate CPM problem under the Hamming distance, we obtain an O(n + (n/m) k2 log k/ log log k)-time algorithm, which works in O(n) time whenever k = O( p mlog log m/logm). In comparison, the fastest algorithm for the standard counterpart of the problem, by Chan et al. [CGKKP, STOC'20], runs in O(n) time only for k = O(√ m). We achieve this result via a reduction to a geometric problem by building on ideas from [CKP+, JCSS'21] and Charalampopoulos et al. [CKW, FOCS'20]. For the decision version of the approximate CPM problem under the edit distance, the O(nk log3 k) runtime of our algorithm near matches the O(nk) runtime of the Landau-Vishkin algorithm [LV, J. Algorithms'89] for approximate pattern matching under edit distance; the latter algorithm remains the fastest known for k = Ω(m2/5). As a stepping stone, we propose an O(nk log3 k)-time algorithm for solving the Longest Prefix k-Approximate Match problem, proposed by Landau et al. [LMS, SICOMP'98], for all k ∈ {1, , k}. Our algorithm is based on Tiskin's theory of seaweeds [Tiskin, Math. Comput. Sci.'08], with recent advancements (see Charalampopoulos et al. [CKW, FOCS'22]), and on exploiting the seaweeds' relation to Monge matrices. In contrast, we obtain a conditional lower bound that suggests a polynomial separation between approximate CPM under the Hamming distance over the binary alphabet and its non-circular counterpart. We also show that a strongly subquadratic-time algorithm for the decision version of approximate CPM under edit distance would refute the Strong Exponential Time Hypothesis

Efficient and High-Quality Rendering of Higher-Order Geometric Data Representations

Computer-Aided Design (CAD) bezeichnet den Entwurf industrieller Produkte mit Hilfe von virtuellen 3D Modellen. Ein CAD-Modell besteht aus parametrischen Kurven und Flächen, in den meisten Fällen non-uniform rational B-Splines (NURBS). Diese mathematische Beschreibung wird ebenfalls zur Analyse, Optimierung und Präsentation des Modells verwendet. In jeder dieser Entwicklungsphasen wird eine unterschiedliche visuelle Darstellung benötigt, um den entsprechenden Nutzern ein geeignetes Feedback zu geben. Designer bevorzugen beispielsweise illustrative oder realistische Darstellungen, Ingenieure benötigen eine verständliche Visualisierung der Simulationsergebnisse, während eine immersive 3D Darstellung bei einer Benutzbarkeitsanalyse oder der Designauswahl hilfreich sein kann. Die interaktive Darstellung von NURBS-Modellen und -Simulationsdaten ist jedoch aufgrund des hohen Rechenaufwandes und der eingeschränkten Hardwareunterstützung eine große Herausforderung. Diese Arbeit stellt vier neuartige Verfahren vor, welche sich mit der interaktiven Darstellung von NURBS-Modellen und Simulationensdaten befassen. Die vorgestellten Algorithmen nutzen neue Fähigkeiten aktueller Grafikkarten aus, um den Stand der Technik bezüglich Qualität, Effizienz und Darstellungsgeschwindigkeit zu verbessern. Zwei dieser Verfahren befassen sich mit der direkten Darstellung der parametrischen Beschreibung ohne Approximationen oder zeitaufwändige Vorberechnungen. Die dabei vorgestellten Datenstrukturen und Algorithmen ermöglichen die effiziente Unterteilung, Klassifizierung, Tessellierung und Darstellung getrimmter NURBS-Flächen und einen interaktiven Ray-Casting-Algorithmus für die Isoflächenvisualisierung von NURBSbasierten isogeometrischen Analysen. Die weiteren zwei Verfahren beschreiben zum einen das vielseitige Konzept der programmierbaren Transparenz für illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle und zum anderen eine neue hybride Methode zur Reprojektion halbtransparenter und undurchsichtiger Bildinformation für die Beschleunigung der Erzeugung von stereoskopischen Bildpaaren. Die beiden letztgenannten Ansätze basieren auf rasterisierter Geometrie und sind somit ebenfalls für normale Dreiecksmodelle anwendbar, wodurch die Arbeiten auch einen wichtigen Beitrag in den Bereichen der Computergrafik und der virtuellen Realität darstellen. Die Auswertung der Arbeit wurde mit großen, realen NURBS-Datensätzen durchgeführt. Die Resultate zeigen, dass die direkte Darstellung auf Grundlage der parametrischen Beschreibung mit interaktiven Bildwiederholraten und in subpixelgenauer Qualität möglich ist. Die Einführung programmierbarer Transparenz ermöglicht zudem die Umsetzung kollaborativer 3D Interaktionstechniken für die Exploration der Modelle in virtuellenUmgebungen sowie illustrative und verständliche Visualisierungen tiefenkomplexer CAD-Modelle. Die Erzeugung stereoskopischer Bildpaare für die interaktive Visualisierung auf 3D Displays konnte beschleunigt werden. Diese messbare Verbesserung wurde zudem im Rahmen einer Nutzerstudie als wahrnehmbar und vorteilhaft befunden.In computer-aided design (CAD), industrial products are designed using a virtual 3D model. A CAD model typically consists of curves and surfaces in a parametric representation, in most cases, non-uniform rational B-splines (NURBS). The same representation is also used for the analysis, optimization and presentation of the model. In each phase of this process, different visualizations are required to provide an appropriate user feedback. Designers work with illustrative and realistic renderings, engineers need a comprehensible visualization of the simulation results, and usability studies or product presentations benefit from using a 3D display. However, the interactive visualization of NURBS models and corresponding physical simulations is a challenging task because of the computational complexity and the limited graphics hardware support. This thesis proposes four novel rendering approaches that improve the interactive visualization of CAD models and their analysis. The presented algorithms exploit latest graphics hardware capabilities to advance the state-of-the-art in terms of quality, efficiency and performance. In particular, two approaches describe the direct rendering of the parametric representation without precomputed approximations and timeconsuming pre-processing steps. New data structures and algorithms are presented for the efficient partition, classification, tessellation, and rendering of trimmed NURBS surfaces as well as the first direct isosurface ray-casting approach for NURBS-based isogeometric analysis. The other two approaches introduce the versatile concept of programmable order-independent semi-transparency for the illustrative and comprehensible visualization of depth-complex CAD models, and a novel method for the hybrid reprojection of opaque and semi-transparent image information to accelerate stereoscopic rendering. Both approaches are also applicable to standard polygonal geometry which contributes to the computer graphics and virtual reality research communities. The evaluation is based on real-world NURBS-based models and simulation data. The results show that rendering can be performed directly on the underlying parametric representation with interactive frame rates and subpixel-precise image results. The computational costs of additional visualization effects, such as semi-transparency and stereoscopic rendering, are reduced to maintain interactive frame rates. The benefit of this performance gain was confirmed by quantitative measurements and a pilot user study

Aeroelastic Stability Assessment Of a CS-25 Category Aircraft Equipped With Multi-Modal Wing Morphing Devices

Morphing wing structures have the greatest ambition to dramatically im-prove aircraft aerodynamic performance (less fuel consumption) and reduce aerodynamic noise. Several studies in the literature have shown their potential for increased aerodynamic efficiency across nearly all flight conditions, en-hanced aircraft maneuverability and control effectiveness, decreased take-off/landing length, reduced airframe noise, etc. However, despite a long herit-age of research, morphing wing technology has yet to be approved by the Euro-pean Aviation Safety Authority (EASA) for use in commercial aviation. Models and approaches capable to predict the aeroelastic impact of a morphing wing still need to be matured to safely alter design and operation of future genera-tions of aircraft. Additionally, a number of practical challenges remain to be addressed in the suitable materials, systems reliability, safety and maintenance. Due to the reduced stiffness, increased mass and increased Degree Of Freedom (DOF) with respect to conventional wings, these mechanical systems can cause significant reduction of aircraft flutter margins. This aspect requires dedicated aeroelastic assessments since the early stages of the design process of such an innovative wing. Flutter boundaries predictions need sensitivity anal-yses to evaluate bending/torsional stiffness and inertial distribution variability ranges of the aircraft wing equipped with the morphing wing devices. In such a way, aeroelastic assessments become fundamental to drive a balance between weight and stiffness of the investigated adaptive systems. Furthermore, in pseu-do rigid-body mechanisms-based morphing structures, the inner kinematics is so important that its faults may compromise the general aircraft-level functions. Similarly to the demonstration means of safety compliance, commonly applied to aircraft control surfaces, the novel functions resulting from the integration of adaptive devices into flying aircraft thus impose a detailed examination of the associated risks. In the framework of Clean Sky 2 Airgreen 2 project, the author provides advanced aeroelastic assessments of two adaptive devices enabling the camber morphing of winglets and flaps, conceived for regional aircraft integration (EASA CS-25 category). Segmented ribs architectures ensure the transition from the baseline (or un-morphed) shape to the morphed ones, driven by em-bedded electromechanical actuators. Some of the advantages resulting from the combination of the two aforementioned morphing systems are wing load con-trol, lift-over-drag ratio increase and root bending moment alleviation. The aircraft aeroelastic model was generated by means of the proprietary code SANDY 3.0. Then, the same code was adopted to solve the aeroelastic stability equa-tions through theoretical modes association in frequency domain. To carry out multi-parametric flutter analyses (P-K continuation method), the actuation lines stiffness and winglet/flap tabs inertial parameters were considered in combina-tion each other. Nominal operative conditions as well as systems malfunction-ing or failures were examined as analyses cases of the investigated morphing devices, together with actuators free-play conditions. Proper design solutions were suggested to guarantee flutter clearance in accordance with aircraft stabil-ity robustness with respect to morphing systems integration, evaluated through a combination of “worst cases” simulating the mutual interaction among the adaptive systems. The safety-driven design of the morphing wing devices required also a thorough examination of the potential hazards resulting from operational faults involving either the actuation chain, such as jamming, or the external interfaces, such as loss of power supplies and control lanes, and both. The main goal was to verify whether the morphing flap and winglet systems could comply with the standard civil flight safety regulations and airworthiness requirements (EASA CS25). More in detail, a comprehensive study of systems functions was firstly qualitatively performed at both subsystem and aircraft levels to identify poten-tial design faults, maintenance and crew faults, as well as external environment risks. The severity of the hazard effects was thus determined and then ranked in specific classes, indicative of the maximum tolerable probability of occurrence for a specific event, resulting in safety design objectives. Fault trees were final-ly produced to assess the compliance of the system architectures to the quanti-tative safety requirements resulting from the FHAs

Enhanced Query Processing on Complex Spatial and Temporal Data

Innovative technologies in the area of multimedia and mechanical engineering as well as novel methods for data acquisition in different scientific subareas, including geo-science, environmental science, medicine, biology and astronomy, enable a more exact representation of the data, and thus, a more precise data analysis. The resulting quantitative and qualitative growth of specifically spatial and temporal data leads to new challenges for the management and processing of complex structured objects and requires the employment of efficient and effective methods for data analysis. Spatial data denote the description of objects in space by a well-defined extension, a specific location and by their relationships to the other objects. Classical representatives of complex structured spatial objects are three-dimensional CAD data from the sector "mechanical engineering" and two-dimensional bounded regions from the area "geography". For industrial applications, efficient collision and intersection queries are of great importance. Temporal data denote data describing time dependent processes, as for instance the duration of specific events or the description of time varying attributes of objects. Time series belong to one of the most popular and complex type of temporal data and are the most important form of description for time varying processes. An elementary type of query in time series databases is the similarity query which serves as basic query for data mining applications. The main target of this thesis is to develop an effective and efficient algorithm supporting collision queries on spatial data as well as similarity queries on temporal data, in particular, time series. The presented concepts are based on the efficient management of interval sequences which are suitable for spatial and temporal data. The effective analysis of the underlying objects will be efficiently supported by adequate access methods. First, this thesis deals with collision queries on complex spatial objects which can be reduced to intersection queries on interval sequences. We introduce statistical methods for the grouping of subsequences. Involving the concept of multi-step query processing, these methods enable the user to accelerate the query process drastically. Furthermore, in this thesis we will develop a cost model for the multi-step query process of interval sequences in distributed systems. The proposed approach successfully supports a cost based query strategy. Second, we introduce a novel similarity measure for time series. It allows the user to focus specific time series amplitudes for the similarity measurement. The new similarity model defines two time series to be similar iff they show similar temporal behavior w.r.t. being below or above a specific threshold. This type of query is primarily required in natural science applications. The main goal of this new query method is the detection of anomalies and the adaptation to new claims in the area of data mining in time series databases. In addition, a semi-supervised cluster analysis method will be presented which is based on the introduced similarity model for time series. The efficiency and effectiveness of the proposed techniques will be extensively discussed and the advantages against existing methods experimentally proofed by means of datasets derived from real-world applications