Segmentation of Multimodal Images based on Hierarchies of Partitions

International audienceHierarchies of partitions are widely used in the context of image segmentation, but when it comes to multimodal images, the fusion of multiple hierarchies remains a challenge. Recently, braids of partitions have been proposed as a possible solution to this issue, but have never been implemented in a practical case. In this paper, we propose a new methodology to achieve multimodal segmentation based on this notion of braids of partitions. We apply this new method in a practical example, namely the segmentation of hyperspectral and LiDAR data. Obtained results confirm the potential of the proposed method

Analyse hiérarchique d'images multimodales

There is a growing interest in the development of adapted processing tools for multimodal images (several images acquired over the same scene with different characteristics). Allowing a more complete description of the scene, multimodal images are of interest in various image processing fields, but their optimal handling and exploitation raise several issues. This thesis extends hierarchical representations, a powerful tool for classical image analysis and processing, to multimodal images in order to better exploit the additional information brought by the multimodality and improve classical image processing techniques. %when applied to real applications. This thesis focuses on three different multimodalities frequently encountered in the remote sensing field. We first investigate the spectral-spatial information of hyperspectral images. Based on an adapted construction and processing of the hierarchical representation, we derive a segmentation which is optimal with respect to the spectral unmixing operation. We then focus on the temporal multimodality and sequences of hyperspectral images. Using the hierarchical representation of the frames in the sequence, we propose a new method to achieve object tracking and apply it to chemical gas plume tracking in thermal infrared hyperspectral video sequences. Finally, we study the sensorial multimodality, being images acquired with different sensors. Relying on the concept of braids of partitions, we propose a novel methodology of image segmentation, based on an energetic minimization framework.Il y a un intérêt grandissant pour le développement d’outils de traitements adaptés aux images multimodales (plusieurs images de la même scène acquises avec différentes caractéristiques). Permettant une représentation plus complète de la scène, ces images multimodales ont de l'intérêt dans plusieurs domaines du traitement d'images, mais les exploiter et les manipuler de manière optimale soulève plusieurs questions. Cette thèse étend les représentations hiérarchiques, outil puissant pour le traitement et l’analyse d’images classiques, aux images multimodales afin de mieux exploiter l’information additionnelle apportée par la multimodalité et améliorer les techniques classiques de traitement d’images. Cette thèse se concentre sur trois différentes multimodalités fréquemment rencontrées dans le domaine de la télédétection. Nous examinons premièrement l’information spectrale-spatiale des images hyperspectrales. Une construction et un traitement adaptés de la représentation hiérarchique nous permettent de produire une carte de segmentation de l'image optimale vis-à-vis de l'opération de démélange spectrale. Nous nous concentrons ensuite sur la multimodalité temporelle, traitant des séquences d’images hyperspectrales. En utilisant les représentations hiérarchiques des différentes images de la séquence, nous proposons une nouvelle méthode pour effectuer du suivi d’objet et l’appliquons au suivi de nuages de gaz chimique dans des séquences d’images hyperspectrales dans le domaine thermique infrarouge. Finalement, nous étudions la multimodalité sensorielle, c’est-à-dire les images acquises par différents capteurs. Nous appuyant sur le concept des tresses de partitions, nous proposons une nouvelle méthodologie de segmentation se basant sur un cadre de minimisation d’énergie

A computational geometric approach for an ensemble-based topological entropy calculation in two and three dimensions

From the stirring of dye in viscous fluids to the availability of essential nutrients spreading over the surface of a pond, nature is rife with examples of mixing in two-dimensional fluids. The long-time exponential growth rate of a thin filament of dye stretched by the fluid is a well-known proxy for the quality of mixing in two dimensions. This growth rate in turn gives a lower bound on the flow's topological entropy, a measure quantifying the complexity of chaotic dynamics. In the real-world study of mixing, topological entropy may be hard to compute; the velocity field may not be known or may be expensive to recover or approximate, thus limiting our knowledge of the governing system and underlying mechanics driving the mixing. Central to this study are two questions: \emph{How can stretching rates in two-dimensional planar flows best be computed using only trajectory data?}, and \emph{Can a method for computing stretching rates in higher dimensions from only trajectory data be developed?}. In this spirit, we introduce the Ensemble-based Topological Entropy Calculation (E-tec), a method to derive a lower-bound on topological entropy that requires only finite number of system trajectories, like those obtained from ocean drifters, and no detailed knowledge of the velocity field. E-tec is demonstrated to be computationally more efficient than other competing methods in two dimensions that accommodate trajectory data. This is accomplished by considering the evolution of a ``rubber band" wrapped around the data points and evolving with their trajectories. E-tec records the growth of this band as the collective motion of trajectories strike, deform, and stretch it. This exponential growth rate acts as a lower bound on the topological entropy. In this manuscript, I demonstrate convergence of E-tec's approximation with respect to both the number of trajectories (ensemble size) and the duration of trajectories in time. Driving the efficiency of E-tec in two dimensions is the use of computational geometry tools. Not only this, by computing stretching rates in this new computational geometry framework, I extend E-tec to three dimensions using two methods. First, I consider a two-dimensional rubber sheet stretched around a collection of points in a three-dimensional flow. Similar to the band-stretching component of two-dimensional E-tec, a three-dimensional triangulation is used to record the growth of the sheet as it is stretched and deformed by points evolving in time. Second, I calculate the growth rates of one-dimensional rubber strings as they are stretched by the edges of this dynamic, moving triangulation

Design and Optimization in Near-term Quantum Computation

Quantum computers have come a long way since conception, and there is still a long way to go before the dream of universal, fault-tolerant computation is realized. In the near term, quantum computers will occupy a middle ground that is popularly known as the “Noisy, Intermediate-Scale Quantum” (or NISQ) regime. The NISQ era represents a transition in the nature of quantum devices from experimental to computational. There is significant interest in engineering NISQ devices and NISQ algorithms in a manner that will guide the development of quantum computation in this regime and into the era of fault-tolerant quantum computing. In this thesis, we study two aspects of near-term quantum computation. The first of these is the design of device architectures, covered in Chapters 2, 3, and 4. We examine different qubit connectivities on the basis of their graph properties, and present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and graphs with modular structure. Next, we discuss the problem of permuting qubits among the nodes of the connectivity graph using only local operations, also known as routing. Using a fast quantum primitive to reverse the qubits in a chain, we construct a hybrid, quantum/classical routing algorithm on the chain. We show via rigorous bounds that this approach is faster than any SWAP-based algorithm for the same problem. The second part, which spans the final three chapters, discusses variational algorithms, which are a class of algorithms particularly suited to near-term quantum computation. Two prototypical variational algorithms, quantum adiabatic optimization (QAO) and the quantum approximate optimization algorithm (QAOA), are studied for the difference in their control strategies. We show that on certain crafted problem instances, bang-bang control (QAOA) can be as much as exponentially faster than quasistatic control (QAO). Next, we demonstrate the performance of variational state preparation on an analog quantum simulator based on trapped ions. We show that using classical heuristics that exploit structure in the variational parameter landscape, one can find circuit parameters efficiently in system size as well as circuit depth. In the experiment, we approximate the ground state of a critical Ising model with long-ranged interactions on up to 40 spins. Finally, we study the performance of Local Tensor, a classical heuristic algorithm inspired by QAOA on benchmarking instances of the MaxCut problem, and suggest physically motivated choices for the algorithm hyperparameters that are found to perform well empirically. We also show that our implementation of Local Tensor mimics imaginary-time quantum evolution under the problem Hamiltonian

Un arbre des formes pour les images multivariées

Nowadays, the demand for multi-scale and region-based analysis in many computer vision and pattern recognition applications is obvious. No one would consider a pixel-based approach as a good candidate to solve such problems. To meet this need, the Mathematical Morphology (MM) framework has supplied region-based hierarchical representations of images such as the Tree of Shapes (ToS). The ToS represents the image in terms of a tree of the inclusion of its level-lines. The ToS is thus self-dual and contrast-change invariant which make it well-adapted for high-level image processing. Yet, it is only defined on grayscale images and most attempts to extend it on multivariate images - e.g. by imposing an “arbitrary” total ordering - are not satisfactory. In this dissertation, we present the Multivariate Tree of Shapes (MToS) as a novel approach to extend the grayscale ToS on multivariate images. This representation is a mix of the ToS's computed marginally on each channel of the image; it aims at merging the marginal shapes in a “sensible” way by preserving the maximum number of inclusion. The method proposed has theoretical foundations expressing the ToS in terms of a topographic map of the curvilinear total variation computed from the image border; which has allowed its extension on multivariate data. In addition, the MToS features similar properties as the grayscale ToS, the most important one being its invariance to any marginal change of contrast and any marginal inversion of contrast (a somewhat “self-duality” in the multidimensional case). As the need for efficient image processing techniques is obvious regarding the larger and larger amount of data to process, we propose an efficient algorithm that can be build the MToS in quasi-linear time w.r.t. the number of pixels and quadraticw.r.t. the number of channels. We also propose tree-based processing algorithms to demonstrate in practice, that the MToS is a versatile, easy-to-use, and efficient structure. Eventually, to validate the soundness of our approach, we propose some experiments testing the robustness of the structure to non-relevant components (e.g. with noise or with low dynamics) and we show that such defaults do not affect the overall structure of the MToS. In addition, we propose many real-case applications using the MToS. Many of them are just a slight modification of methods employing the “regular” ToS and adapted to our new structure. For example, we successfully use the MToS for image filtering, image simplification, image segmentation, image classification and object detection. From these applications, we show that the MToS generally outperforms its ToS-based counterpart, demonstrating the potential of our approachDe nombreuses applications issues de la vision par ordinateur et de la reconnaissance des formes requièrent une analyse de l'image multi-échelle basée sur ses régions. De nos jours, personne ne considérerait une approche orientée « pixel » comme une solution viable pour traiter ce genre de problèmes. Pour répondre à cette demande, la Morphologie Mathématique a fourni des représentations hiérarchiques des régions de l'image telles que l'Arbre des Formes (AdF). L'AdF représente l'image par un arbre d'inclusion de ses lignes de niveaux. L'AdF est ainsi auto-dual et invariant au changement de contraste, ce qui fait de lui une structure bien adaptée aux traitements d'images de haut niveau. Néanmoins, il est seulement défini aux images en niveaux de gris et la plupart des tentatives d'extension aux images multivariées (e.g. en imposant un ordre total «arbitraire ») ne sont pas satisfaisantes. Dans ce manuscrit, nous présentons une nouvelle approche pour étendre l'AdF scalaire aux images multivariées : l'Arbre des Formes Multivarié (AdFM). Cette représentation est une « fusion » des AdFs calculés marginalement sur chaque composante de l'image. On vise à fusionner les formes marginales de manière « sensée » en préservant un nombre maximal d'inclusion. La méthode proposée a des fondements théoriques qui consistent en l'expression de l'AdF par une carte topographique de la variation totale curvilinéaire depuis la bordure de l'image. C'est cette reformulation qui a permis l'extension de l'AdF aux données multivariées. De plus, l'AdFM partage des propriétés similaires avec l'AdF scalaire ; la plus importante étant son invariance à tout changement ou inversion de contraste marginal (une sorte d'auto-dualité dans le cas multidimensionnel). Puisqu'il est évident que, vis-à-vis du nombre sans cesse croissant de données à traiter, nous ayons besoin de techniques rapides de traitement d'images, nous proposons un algorithme efficace qui permet de construire l'AdF en temps quasi-linéaire vis-à-vis du nombre de pixels et quadratique vis-à-vis du nombre de composantes. Nous proposons également des algorithmes permettant de manipuler l'arbre, montrant ainsi que, en pratique, l'AdFM est une structure facile à manipuler, polyvalente, et efficace. Finalement, pour valider la pertinence de notre approche, nous proposons quelques expériences testant la robustesse de notre structure aux composantes non-pertinentes (e.g. avec du bruit ou à faible dynamique) et nous montrons que ces défauts n'affectent pas la structure globale de l'AdFM. De plus, nous proposons des applications concrètes utilisant l'AdFM. Certaines sont juste des modifications mineures aux méthodes employant d'ores et déjà l'AdF scalaire mais adaptées à notre nouvelle structure. Par exemple, nous utilisons l'AdFM à des fins de filtrage, segmentation, classification et de détection d'objet. De ces applications, nous montrons ainsi que les méthodes basées sur l'AdFM surpassent généralement leur analogue basé sur l'AdF, démontrant ainsi le potentiel de notre approch

Index to 1984 NASA Tech Briefs, volume 9, numbers 1-4

Short announcements of new technology derived from the R&D activities of NASA are presented. These briefs emphasize information considered likely to be transferrable across industrial, regional, or disciplinary lines and are issued to encourage commercial application. This index for 1984 Tech B Briefs contains abstracts and four indexes: subject, personal author, originating center, and Tech Brief Number. The following areas are covered: electronic components and circuits, electronic systems, physical sciences, materials, life sciences, mechanics, machinery, fabrication technology, and mathematics and information sciences

Enabling parallelism and optimizations in data mining algorithms for power-law data

Today's data mining tasks aim to extract meaningful information from a large amount of data in a reasonable time mainly via means of --- a) algorithmic advances, such as fast approximate algorithms and efficient learning algorithms, and b) architectural advances, such as machines with massive compute capacity involving distributed multi-core processors and high throughput accelerators. For current and future generation processors, parallel algorithms are critical for fully utilizing computing resources. Furthermore, exploiting data properties for performance gain becomes crucial for data mining applications. In this work, we focus our attention on power-law behavior –-- a common property found in a large class of data, such as text data, internet traffic, and click-stream data. Specifically, we address the following questions in the context of power-law data: How well do the critical data mining algorithms of current interest fit with today's parallel architectures? Which algorithmic and mapping opportunities can be leveraged to further improve performance?, and What are the relative challenges and gains for such approaches? Specifically, we first investigate the suitability of the "frequency estimation" problem for GPU-scale parallelism. Sketching algorithms are a popular choice for this task due to their desirable trade-off between estimation accuracy and space-time efficiency. However, most of the past work on sketch-based frequency estimation focused on CPU implementations. In our work, we propose a novel approach for sketches, which exploits the natural skewness in the power-law data to efficiently utilize the massive amounts of parallelism in modern GPUs. Next, we explore the problem of "identifying top-K frequent elements" for distributed data streams on modern distributed settings with both multi-core and multi-node CPU parallelism. Sketch-based approaches, such as Count-Min Sketch (CMS) with top-K heap, have an excellent update time but lacks the important property of reducibility, which is needed for exploiting data parallelism. On the other end, the popular Frequent Algorithm (FA) leads to reducible summaries, but its update costs are high. Our approach Topkapi, gives the best of both worlds, i.e., it is reducible like FA and has an efficient update time similar to CMS. For power-law data, Topkapi possesses strong theoretical guarantees and leads to significant performance gains, relative to past work. Finally, we study Word2Vec, a popular word embedding method widely used in Machine learning and Natural Language Processing applications, such as machine translation, sentiment analysis, and query answering. This time, we target Single Instruction Multiple Data (SIMD) parallelism. With the increasing vector lengths in commodity CPUs, such as AVX-512 with a vector length of 512 bits, efficient vector processing unit utilization becomes a major performance game-changer. By employing a static multi-version code generation strategy coupled with an algorithmic approximation based on the power-law frequency distribution of words, we achieve significant reductions in training time relative to the state-of-the-art.Ph.D

A systematic approach for integrated product, materials, and design-process design

Designers are challenged to manage customer, technology, and socio-economic uncertainty causing dynamic, unquenchable demands on limited resources. In this context, increased concept flexibility, referring to a designer s ability to generate concepts, is crucial. Concept flexibility can be significantly increased through the integrated design of product and material concepts. Hence, the challenge is to leverage knowledge of material structure-property relations that significantly affect system concepts for function-based, systematic design of product and materials concepts in an integrated fashion. However, having selected an integrated product and material system concept, managing complexity in embodiment design-processes is important. Facing a complex network of decisions and evolving analysis models a designer needs the flexibility to systematically generate and evaluate embodiment design-process alternatives. In order to address these challenges and respond to the primary research question of how to increase a designer s concept and design-process flexibility to enhance product creation in the conceptual and early embodiment design phases, the primary hypothesis in this dissertation is embodied as a systematic approach for integrated product, materials and design-process design. The systematic approach consists of two components i) a function-based, systematic approach to the integrated design of product and material concepts from a systems perspective, and ii) a systematic strategy to design-process generation and selection based on a decision-centric perspective and a value-of-information-based Process Performance Indicator. The systematic approach is validated using the validation-square approach that consists of theoretical and empirical validation. Empirical validation of the framework is carried out using various examples including: i) design of a reactive material containment system, and ii) design of an optoelectronic communication system.Ph.D.Committee Chair: Allen, Janet K.; Committee Member: Aidun, Cyrus K.; Committee Member: Klein, Benjamin; Committee Member: McDowell, David L.; Committee Member: Mistree, Farrokh; Committee Member: Yoder, Douglas P