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

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)

Efficient Methods for Continuous and Discrete Shape Analysis

When interpreting an image of a given object, humans are able to abstract from the presented color information in order to really see the presented object. This abstraction is also known as shape. The concept of shape is not defined exactly in Computer Vision and in this work, we use three different forms of these definitions in order to acquire and analyze shapes. This work is devoted to improve the efficiency of methods that solve important applications of shape analysis. The most important problem in order to analyze shapes is the problem of shape acquisition. To simplify this very challenging problem, numerous researchers have incorporated prior knowledge into the acquisition of shapes. We will present the first approach to acquire shapes given a certain shape knowledge that computes always the global minimum of the involved functional which incorporates a Mumford-Shah like functional with a certain class of shape priors including statistic shape prior and dynamical shape prior. In order to analyze shapes, it is not only important to acquire shapes, but also to classify shapes. In this work, we follow the concept of defining a distance function that measures the dissimilarity of two given shapes. There are two different ways of obtaining such a distance function that we address in this work. Firstly, we model the set of all shapes as a metric space induced by the shortest path on an orbifold. The shortest path will provide us with a shape morphing, i.e., a continuous transformation from one shape into another. Secondly, we address the problem of shape matching that finds corresponding points on two shapes with respect to a preselected feature. Our main contribution for the problem of shape morphing lies in the immense acceleration of the morphing computation. Instead of solving partial resp. ordinary differential equations, we are able to solve this problem via a gradient descent approach that subsequently shortens the length of a path on the given manifold. During our runtime test, we observed a run-time acceleration of up to a factor of 1000. Shape matching is a classical discrete problem. If each shape is discretized by N shape points, most Computer Vision methods needed a cubic run-time. We will provide two approaches how to reduce this worst-case complexity to O(N2 log(N)). One approach exploits the planarity of the involved graph in order to efficiently compute N shortest path in a graph of O(N2) vertices. The other approach computes a minimal cut in a planar graph in O(N log(N)). In order to make this approach applicable to shape matching, we improved the run-time of a recently developed graph cut approach by an empirical factor of 2–4

Patterns in Motion - From the Detection of Primitives to Steering Animations

In recent decades, the world of technology has developed rapidly. Illustrative of this trend is the growing number of affrdable methods for recording new and bigger data sets. The resulting masses of multivariate and high-dimensional data represent a new challenge for research and industry. This thesis is dedicated to the development of novel methods for processing multivariate time series data, thus meeting this Data Science related challenge. This is done by introducing a range of different methods designed to deal with time series data. The variety of methods re ects the different requirements and the typical stage of data processing ranging from pre-processing to post- processing and data recycling. Many of the techniques introduced work in a general setting. However, various types of motion recordings of human and animal subjects were chosen as representatives of multi-variate time series. The different data modalities include Motion Capture data, accelerations, gyroscopes, electromyography, depth data (Kinect) and animated 3D-meshes. It is the goal of this thesis to provide a deeper understanding of working with multi-variate time series by taking the example of multi-variate motion data. However, in order to maintain an overview of the matter, the thesis follows a basic general pipeline. This pipeline was developed as a guideline for time series processing and is the first contribution of this work. Each part of the thesis represents one important stage of this pipeline which can be summarized under the topics segmentation, analysis and synthesis. Specific examples of different data modalities, processing requirements and methods to meet those are discussed in the chapters of the respective parts. One important contribution of this thesis is a novel method for temporal segmentation of motion data. It is based on the idea of self-similarities within motion data and is capable of unsupervised segmentation of range of motion data into distinct activities and motion primitives. The examples concerned with the analysis of multi-variate time series re ect the role of data analysis in different inter-disciplinary contexts and also the variety of requirements that comes with collaboration with other sciences. These requirements are directly connected to current challenges in data science. Finally, the problem of synthesis of multi-variate time series is discussed using a graph-based example and examples related to rigging or steering of meshes. Synthesis is an important stage in data processing because it creates new data from existing ones in a controlled way. This makes exploiting existing data sets and and access of more condensed data possible, thus providing feasible alternatives to otherwise time-consuming manual processing.Muster in Bewegung - Von der Erkennung von Primitiven zur Steuerung von Animationen In den letzten Jahrzehnten hat sich die Welt der Technologie rapide entwickelt. Beispielhaft für diese Entwicklung ist die wachsende Zahl erschwinglicher Methoden zum Aufzeichnen neuer und immer größerer Datenmengen. Die sich daraus ergebenden Massen multivariater und hochdimensionaler Daten stellen Forschung wie Industrie vor neuartige Probleme. Diese Arbeit ist der Entwicklung neuer Verfahren zur Verarbeitung multivariater Zeitreihen gewidmet und stellt sich damit einer großen Herausforderung, welche unmittelbar mit dem neuen Feld der sogenannten Data Science verbunden ist. In ihr werden ein Reihe von verschiedenen Verfahren zur Verarbeitung multivariater Zeitserien eingeführt. Die verschiedenen Verfahren gehen jeweils auf unterschiedliche Anforderungen und typische Stadien der Datenverarbeitung ein und reichen von Vorverarbeitung bis zur Nachverarbeitung und darüber hinaus zur Wiederverwertung. Viele der vorgestellten Techniken eignen sich zur Verarbeitung allgemeiner multivariater Zeitreihen. Allerdings wurden hier eine Anzahl verschiedenartiger Aufnahmen von menschlichen und tierischen Subjekte ausgewählt, welche als Vertreter für allgemeine multivariate Zeitreihen gelten können. Zu den unterschiedlichen Modalitäten der Aufnahmen gehören Motion Capture Daten, Beschleunigungen, Gyroskopdaten, Elektromyographie, Tiefenbilder ( Kinect ) und animierte 3D -Meshes. Es ist das Ziel dieser Arbeit, am Beispiel der multivariaten Bewegungsdaten ein tieferes Verstndnis für den Umgang mit multivariaten Zeitreihen zu vermitteln. Um jedoch einen Überblick ber die Materie zu wahren, folgt sie jedoch einer grundlegenden und allgemeinen Pipeline. Diese Pipeline wurde als Leitfaden für die Verarbeitung von Zeitreihen entwickelt und ist der erste Beitrag dieser Arbeit. Jeder weitere Teil der Arbeit behandelt eine von drei größeren Stationen in der Pipeline, welche sich unter unter die Themen Segmentierung, Analyse und Synthese eingliedern lassen. Beispiele verschiedener Datenmodalitäten und Anforderungen an ihre Verarbeitung erläutern die jeweiligen Verfahren. Ein wichtiger Beitrag dieser Arbeit ist ein neuartiges Verfahren zur zeitlichen Segmentierung von Bewegungsdaten. Dieses basiert auf der Idee der Selbstähnlichkeit von Bewegungsdaten und ist in der Lage, verschiedenste Bewegungsdaten voll-automatisch in unterschiedliche Aktivitäten und Bewegungs-Primitive zu zerlegen. Die Beispiele fr die Analyse multivariater Zeitreihen spiegeln die Rolle der Datenanalyse in verschiedenen interdisziplinären Zusammenhänge besonders wider und illustrieren auch die Vielfalt der Anforderungen, die sich in interdisziplinären Kontexten auftun. Schließlich wird das Problem der Synthese multivariater Zeitreihen unter Verwendung eines graph-basierten und eines Steering Beispiels diskutiert. Synthese ist insofern ein wichtiger Schritt in der Datenverarbeitung, da sie es erlaubt, auf kontrollierte Art neue Daten aus vorhandenen zu erzeugen. Dies macht die Nutzung bestehender Datensätze und den Zugang zu dichteren Datenmodellen möglich, wodurch Alternativen zur ansonsten zeitaufwendigen manuellen Verarbeitung aufgezeigt werden

Context-Aware Parameter Estimation for Forecast Models in the Energy Domain

Continuous balancing of energy demand and supply is a fundamental prerequisite for the stability and efficiency of energy grids. This balancing task requires accurate forecasts of future electricity consumption and production at any point in time. For this purpose, database systems need to be able to rapidly process forecasting queries and to provide accurate results in short time frames. However, time series from the electricity domain pose the challenge that measurements are constantly appended to the time series. Using a naive maintenance approach for such evolving time series would mean a re-estimation of the employed mathematical forecast model from scratch for each new measurement, which is very time consuming. We speed-up the forecast model maintenance by exploiting the particularities of electricity time series to reuse previously employed forecast models and their parameter combinations. These parameter combinations and information about the context in which they were valid are stored in a repository. We compare the current context with contexts from the repository to retrieve parameter combinations that were valid in similar contexts as starting points for further optimization. An evaluation shows that our approach improves the maintenance process especially for complex models by providing more accurate forecasts in less time than comparable estimation methods

Example-Based Urban Modeling

The manual modeling of virtual cities or suburban regions is an extremely time-consuming task, which expects expert knowledge of different fields. Existing modeling tool-sets have a steep learning curve and may need special education skills to work with them productively. Existing automatic methods rely on rule sets and grammars to generate urban structures; however, their expressiveness is limited by the rule-sets. Expert skills are necessary to typeset rule sets successfully and, in many cases, new rule-sets need to be defined for every new building style or street network style. To enable non-expert users, the possibility to construct urban structures for individual experiments, this work proposes a portfolio of novel example-based synthesis algorithms and applications for the controlled generation of virtual urban environments. The notion example-based denotes here that new virtual urban environments are created by computer programs that re-use existing digitized real-world data serving as templates. The data, i.e., street networks, topography, layouts of building footprints, or even 3D building models, necessary to realize the envisioned task is already publicly available via online services. To enable the reuse of existing urban datasets, novel algorithms need to be developed by encapsulating expert knowledge and thus allow the controlled generation of virtual urban structures from sparse user input. The focus of this work is the automatic generation of three fundamental structures that are common in urban environments: road networks, city block, and individual buildings. In order to achieve this goal, the thesis proposes a portfolio of algorithms that are briefly summarized next. In a theoretical chapter, we propose a general optimization technique that allows formulating example-based synthesis as a general resource-constrained k-shortest path (RCKSP) problem. From an abstract problem specification and a database of exemplars carrying resource attributes, we construct an intermediate graph and employ a path-search optimization technique. This allows determining either the best or the k-best solutions. The resulting algorithm has a reduced complexity for the single constraint case when compared to other graph search-based techniques. For the generation of road networks, two different techniques are proposed. The first algorithm synthesizes a novel road network from user input, i.e., a desired arterial street skeleton, topography map, and a collection of hierarchical fragments extracted from real-world road networks. The algorithm recursively constructs a novel road network reusing these fragments. Candidate fragments are inserted into the current state of the road network, while shape differences will be compensated by warping. The second algorithm synthesizes road networks using generative adversarial networks (GANs), a recently introduced deep learning technique. A pre- and postprocessing pipeline allows using GANs for the generation of road networks. An in-depth evaluation shows that GANs faithfully learn the road structure present in the example network and that graph measures such as area, aspect ratio, and compactness, are maintained within the virtual road networks. To fill empty city blocks in road networks we propose two novel techniques. The first algorithm re-uses real-world city blocks and synthesizes building footprint layouts into empty city blocks by retrieving viable candidate blocks from a database. We evaluate the algorithm and synthesize a multitude of city block layouts reusing real-world building footprint arrangements from European and US-cities. In addition, we increase the realism of the synthesized layouts by performing example-based placement of 3D building models. This technique is evaluated by placing buildings onto challenging footprint layouts using different example building databases. The second algorithm computes a city block layout, resembling the style of a real-world city block. The original footprint layout is deformed to construct a textit{guidance map}, i.e., the original layout is transferred to a target city block using warping. This guidance map and the original footprints are used by an optimization technique that computes a novel footprint layout along the city block edges. We perform a detailed evaluation and show that using the guidance map allows transferring of the original layout, locally as well as globally, even when the source and target shapes drastically differ. To synthesize individual buildings, we use the general optimization technique described first and formulate the building generation process as a resource-constrained optimization problem. From an input database of annotated building parts, an abstract description of the building shape, and the specification of resource constraints such as length, area, or a number of architectural elements, a novel building is synthesized. We evaluate the technique by synthesizing a multitude of challenging buildings fulfilling several global and local resource constraints. Finally, we show how this technique can even be used to synthesize buildings having the shape of city blocks and might also be used to fill empty city blocks in virtual street networks. All algorithms presented in this work were developed to work with a small amount of user input. In most cases, simple sketches and the definition of constraints are enough to produce plausible results. Manual work is necessary to set up the building part databases and to download example data from mapping services available on the Internet

Probabilistic procrustean models for shape recognition with an application to robotic grasping

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 92-98).Robot manipulators largely rely on complete knowledge of object geometry in order to plan their motion and compute successful grasps. If an object is fully in view, the object geometry can be inferred from sensor data and a grasp computed directly. If the object is occluded by other entities in the scene, manipulations based on the visible part of the object may fail; to compensate, object recognition is often used to identify the location of the object and compute the grasp from a prior model. However, new instances of a known class of objects may vary from the prior model, and known objects may appear in novel configurations if they are not perfectly rigid. As a result, manipulation can pose a substantial modeling challenge when objects are not fully in view. In this thesis, we will attempt to model the shapes of objects in a way that is robust to both deformations and occlusions. In addition, we will develop a model that allows us to recover the hidden parts of occluded objects (shape completion), and which maintains information about the object boundary for use in robotic grasp planning. Our approach will be data-driven and generative, and we will base our probabilistic models on Kendall's Procrustean theory of shape.by Jared Marshall Glover.S.M