39 research outputs found

    Computing the Similarity Between Moving Curves

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    In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fr\'echet distance between surfaces. While the Fr\'echet distance between surfaces is not even known to be computable, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on max-flow min-cut duality

    A representation of cloth states based on a derivative of the Gauss linking integral

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    Robotic manipulation of cloth is a complex task because of the infinite-dimensional shape-state space of textiles, which makes their state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a finite low-dimensional representation of cloth states that allows us to efficiently distinguish a large variety of different folded states, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and allows us to represent spatial as well as planar folded configurations in a consistent and unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the representation of cloth states and significantly more sensitive to changes in grasping affordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing that with it we can identify the different states using a distance-based classifier.This work was developed under the project CLOTHILDE which has received funding from the European Research Council (ERC) under the EU-Horizon 2020 research and innovation programme (grant agreement No. 741930). M. Alberich-Carramiñana is also with the Barcelona Graduate School of Mathematics (BGSMath) and the Institut de Matemàtiques de la UPC-BarcelonaTech (IMTech), and she and J. Amorós are partially supported by the Spanish State Research Agency AEI/10.13039/501100011033 grant PID2019-103849GB-I00 and by the AGAUR project 2021 SGR 00603 Geometry of Manifolds and Applications, GEOMVAP. J. Borràs is supported by the Spanish State Research Agency MCIN/ AEI /10.13039/501100011033 grant PID2020-118649RB-I00 (CHLOE-GRAPH project).Peer ReviewedPostprint (published version

    Realizability of Free Spaces of Curves

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    The free space diagram is a popular tool to compute the well-known Fr\'echet distance. As the Fr\'echet distance is used in many different fields, many variants have been established to cover the specific needs of these applications. Often, the question arises whether a certain pattern in the free space diagram is "realizable", i.e., whether there exists a pair of polygonal chains whose free space diagram corresponds to it. The answer to this question may help in deciding the computational complexity of these distance measures, as well as allowing to design more efficient algorithms for restricted input classes that avoid certain free space patterns. Therefore, we study the inverse problem: Given a potential free space diagram, do there exist curves that generate this diagram? Our problem of interest is closely tied to the classic Distance Geometry problem. We settle the complexity of Distance Geometry in R>2\mathbb{R}^{> 2}, showing R\exists\mathbb{R}-hardness. We use this to show that for curves in R2\mathbb{R}^{\ge 2}, the realizability problem is R\exists\mathbb{R}-complete, both for continuous and for discrete Fr\'echet distance. We prove that the continuous case in R1\mathbb{R}^1 is only weakly NP-hard, and we provide a pseudo-polynomial time algorithm and show that it is fixed-parameter tractable. Interestingly, for the discrete case in R1\mathbb{R}^1, we show that the problem becomes solvable in polynomial time.Comment: 26 pages, 12 figures, 1 table, International Symposium on Algorithms And Computations (ISAAC 2023

    Розробка метрики і методів кількісної оцінки сегментації біомедичних зображень

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    We analyzed modern digital microscopy. In order to categorize digital microscopy, the following criteria are introduced: level of automation, software level, the level of application of network technologies. To quantitatively estimate the quality of image segmentation, we devised the technique based on a metric approach using the Fréchet and Hausdorff metrics. Modern algorithms for calculating the Hausdorff and Fréchet distances were analyzed.We have introduced the Fréchet distance between trees. It was proven that the Fréchet distance between trees is a metric. We devised a method for estimating a distance between trees of the non-convex regions, based on finding skeletons of regions and determining the distance between them. The algorithm for finding the Hausdorff distance between the non-convex regions is described. We constructed the algorithm for finding a distance between the non-convex regions based on the Fréchet metric between trees.The developed algorithms are included into a hybrid intelligent system for automated microscopy, which is designed to process histological and cytological images.The algorithms were tested using the results of segmentation of histologic and cytologic images from a database as an exampleВведено расстояние Фреше между деревьями и доказано, что это расстояние является метрикой. Разработан метод и алгоритмы определения расстояния между не выпуклыми областями. Спроектирован и программно реализован модуль определения расстояния Фреше между скелетонами. Исследованы погрешности результатов сегментации для метрик Хаусдорфа и Фреше между деревьями на примере биомедицинских изображенийВведено відстань Фреше між деревами та доведено, що ця відстань є метрикою. Розроблено метод і алгоритми визначення відстані між не опуклими областями. Спроектований і програмно реалізований модуль визначення відстані Фреше між скелетонами. Досліджено похибки результатів сегментації для метрик Хаусдорфа та Фреше між деревами на прикладі біомедичних зображен

    Master index of Volumes 21–30

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    Automating Geospatial RDF Dataset Integration and Enrichment

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    Over the last years, the Linked Open Data (LOD) has evolved from a mere 12 to more than 10,000 knowledge bases. These knowledge bases come from diverse domains including (but not limited to) publications, life sciences, social networking, government, media, linguistics. Moreover, the LOD cloud also contains a large number of crossdomain knowledge bases such as DBpedia and Yago2. These knowledge bases are commonly managed in a decentralized fashion and contain partly verlapping information. This architectural choice has led to knowledge pertaining to the same domain being published by independent entities in the LOD cloud. For example, information on drugs can be found in Diseasome as well as DBpedia and Drugbank. Furthermore, certain knowledge bases such as DBLP have been published by several bodies, which in turn has lead to duplicated content in the LOD . In addition, large amounts of geo-spatial information have been made available with the growth of heterogeneous Web of Data. The concurrent publication of knowledge bases containing related information promises to become a phenomenon of increasing importance with the growth of the number of independent data providers. Enabling the joint use of the knowledge bases published by these providers for tasks such as federated queries, cross-ontology question answering and data integration is most commonly tackled by creating links between the resources described within these knowledge bases. Within this thesis, we spur the transition from isolated knowledge bases to enriched Linked Data sets where information can be easily integrated and processed. To achieve this goal, we provide concepts, approaches and use cases that facilitate the integration and enrichment of information with other data types that are already present on the Linked Data Web with a focus on geo-spatial data. The first challenge that motivates our work is the lack of measures that use the geographic data for linking geo-spatial knowledge bases. This is partly due to the geo-spatial resources being described by the means of vector geometry. In particular, discrepancies in granularity and error measurements across knowledge bases render the selection of appropriate distance measures for geo-spatial resources difficult. We address this challenge by evaluating existing literature for point set measures that can be used to measure the similarity of vector geometries. Then, we present and evaluate the ten measures that we derived from the literature on samples of three real knowledge bases. The second challenge we address in this thesis is the lack of automatic Link Discovery (LD) approaches capable of dealing with geospatial knowledge bases with missing and erroneous data. To this end, we present Colibri, an unsupervised approach that allows discovering links between knowledge bases while improving the quality of the instance data in these knowledge bases. A Colibri iteration begins by generating links between knowledge bases. Then, the approach makes use of these links to detect resources with probably erroneous or missing information. This erroneous or missing information detected by the approach is finally corrected or added. The third challenge we address is the lack of scalable LD approaches for tackling big geo-spatial knowledge bases. Thus, we present Deterministic Particle-Swarm Optimization (DPSO), a novel load balancing technique for LD on parallel hardware based on particle-swarm optimization. We combine this approach with the Orchid algorithm for geo-spatial linking and evaluate it on real and artificial data sets. The lack of approaches for automatic updating of links of an evolving knowledge base is our fourth challenge. This challenge is addressed in this thesis by the Wombat algorithm. Wombat is a novel approach for the discovery of links between knowledge bases that relies exclusively on positive examples. Wombat is based on generalisation via an upward refinement operator to traverse the space of Link Specifications (LS). We study the theoretical characteristics of Wombat and evaluate it on different benchmark data sets. The last challenge addressed herein is the lack of automatic approaches for geo-spatial knowledge base enrichment. Thus, we propose Deer, a supervised learning approach based on a refinement operator for enriching Resource Description Framework (RDF) data sets. We show how we can use exemplary descriptions of enriched resources to generate accurate enrichment pipelines. We evaluate our approach against manually defined enrichment pipelines and show that our approach can learn accurate pipelines even when provided with a small number of training examples. Each of the proposed approaches is implemented and evaluated against state-of-the-art approaches on real and/or artificial data sets. Moreover, all approaches are peer-reviewed and published in a conference or a journal paper. Throughout this thesis, we detail the ideas, implementation and the evaluation of each of the approaches. Moreover, we discuss each approach and present lessons learned. Finally, we conclude this thesis by presenting a set of possible future extensions and use cases for each of the proposed approaches

    Robotic manipulation of cloth: mechanical modeling and perception

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    (Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado.Postprint (published version

    Robotic manipulation of cloth: mechanical modeling and perception

    Get PDF
    (Eng) In this work we study various mathematical problems arising from the robotic manipulation of cloth. First, we develop a locking-free continuous model for the physical simulation of inextensible textiles. We present a novel 'finite element' discretization of our inextensibility constraints which results in a unified treatment of triangle and quadrilateral meshings of the cloth. Next, we explain how to incorporate contacts, self-collisions and friction into the equations of motion, so that frictional forces and inextensibility and collision constraints may be integrated implicitly and without any decoupling. We develop an efficient 'active-set' solver tailored to our non-linear problem which takes into account past active constraints to accelerate the resolution of unresolved contacts and moreover can be initialized from any non-necessarily feasible point. Then, we embark ourselves in the empirical validation of the developed model. We record in a laboratory setting --with depth cameras and motion capture systems-- the motions of seven types of textiles (including e.g. cotton, denim and polyester) of various sizes and at different speeds and end up with more than 80 recordings. The scenarios considered are all dynamic and involve rapid shaking and twisting of the textiles, collisions with frictional objects and even strong hits with a long stick. We then, compare the recorded textiles with the simulations given by our inextensible model, and find that on average the mean error is of the order of 1 cm even for the largest sizes (DIN A2) and the most challenging scenarios. Furthermore, we also tackle other problems relevant to robotic cloth manipulation, such as cloth perception and classification of its states. We present a reconstruction algorithm based on Morse theory that proceeds directly from a point-cloud to obtain a cellular decomposition of a surface with or without boundary: the results are a piecewise parametrization of the cloth surface as a union of Morse cells. From the cellular decomposition the topology of the surface can be then deduced immediately. Finally, we study the configuration space of a piece of cloth: since the original state of a piece of cloth is flat, the set of possible states under the inextensible assumption is the set of developable surfaces isometric to a fixed one. We prove that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. Inspired on this result we introduce the dGLI cloth coordinates, a low-dimensional representation of the state of a piece of cloth based on a directional derivative of the Gauss Linking Integral. These coordinates --computed from the position of the cloth's boundary-- allow to distinguish key qualitative changes in folding sequences.(Esp) En este trabajo estudiamos varios problemas matemáticos relacionados con la manipulación robótica de textiles. En primer lugar, desarrollamos un modelo continuo libre de 'locking' para la simulación física de textiles inextensibles. Presentamos una novedosa discretización usando 'elementos finitos' de nuestras restricciones de inextensibilidad resultando en un tratamiento unificado de mallados triangulares y cuadrangulares de la tela. A continuación, explicamos cómo incorporar contactos, autocolisiones y fricción en las ecuaciones de movimiento, de modo que las fuerzas de fricción y las restricciones de inextensibilidad y colisiones puedan integrarse implícitamente y sin ningún desacoplamiento. Desarrollamos un 'solver' de tipo 'conjunto-activo' adaptado a nuestro problema no lineal que tiene en cuenta las restricciones activas pasadas para acelerar la resolución de los contactos no resueltos y, además, puede inicializarse desde cualquier punto no necesariamente factible. Posteriormente, nos embarcamos en la validación empírica del modelo desarrollado. Grabamos en un entorno de laboratorio -con cámaras de profundidad y sistemas de captura de movimiento- los movimientos de siete tipos de textiles (entre los que se incluyen, por ejemplo, algodón, tela vaquera y poliéster) de varios tamaños y a diferentes velocidades, terminando con más de 80 grabaciones. Los escenarios considerados son todos dinámicos e implican sacudidas y torsiones rápidas de los textiles, colisiones con obstáculos e incluso golpes con una varilla cilíndrica. Finalmente, comparamos las grabaciones con las simulaciones dadas por nuestro modelo inextensible, y encontramos que, de media, el error es del orden de 1 cm incluso para las telas más grandes (DIN A2) y los escenarios más complicados. Además, también abordamos otros problemas relevantes para la manipulación robótica de telas, como son la percepción y la clasificación de sus estados. Presentamos un algoritmo de reconstrucción basado en la teoría de Morse que procede directamente de una nube de puntos para obtener una descomposición celular de una superficie con o sin borde: los resultados son una parametrización a trozos de la superficie de la tela como una unión de celdas de Morse. A partir de la descomposición celular puede deducirse inmediatamente la topología de la superficie. Por último, estudiamos el espacio de configuración de un trozo de tela: dado que el estado original de la tela es plano, el conjunto de estados posibles bajo la hipótesis de inextensibilidad es el conjunto de superficies desarrollables isométricas a una fija. Demostramos que una curva genérica simple, cerrada y regular a trozos en el espacio puede ser el borde de un número finito de superficies desarrollables con curvatura media no nula. Inspirándonos en este resultado, introducimos las coordenadas dGLI, una representación de dimensión baja del estado de un pedazo de tela basada en una derivada direccional de la integral de enlazamiento de Gauss. Estas coordenadas -calculadas a partir de la posición del borde de la tela- permiten distinguir cambios cualitativos clave en distintas secuencias de plegado
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