A framework for the management of deformable moving objects

There is an emergence of a growing number of applications and services based on spatiotemporal data in the most diverse areas of knowledge and human activity. The Internet of Things (IoT), the emergence of technologies that make it possible to collect information about the evolution of real world phenomena and the widespread use of devices that can use the Global Positioning System (GPS), such as smartphones and navigation systems, suggest that the volume and value of these data will increase significantly in the future. It is necessary to develop tools capable of extracting knowledge from these data and for this it is necessary to manage them: represent, manipulate, analyze and store, in an efficient way. But this data can be complex, its management is not trivial and there is not yet a complete system capable of performing this task. Works on moving points, that represent the position of objects over time, are frequent in the literature. On the contrary there are much less solutions for the representation of moving regions, that represent the continuous changes in position, shape and extent of objects over time, e.g., storms, fires and icebergs. The representation of the evolution of moving regions is complex and requires the use of more elaborate techniques, e.g., morphing and interpolation techniques, capable of producing realistic and geometrically valid representations. In this dissertation we present and propose a data model for moving objects (moving points and moving regions), in particular for moving regions, based on the concept of mesh and compatible triangulation and rigid interpolation methods. This model was implemented in a framework that is not client or application dependent and we also implemented a spatiotemporal extension for PostgreSQL that uses this framework to manipulate and analyze moving objects, as a proof of concept that our framework works with real applications. The tests’ results using real data, obtained from satellite images of the evolution of 2 icebergs over time, show that our data model works. Besides the results obtained one important contribution of this work is the development of a basic framework for moving objects that can be used as a basis for further investigation in this area. A few problems still remain that must be further studied and analyzed, in particular, the ones that were found when using the compatible triangulation and rigid interpolation methods with real data.Assistimos ao aparecimento de um número crescente de aplicações e serviços baseados em dados espácio-temporais nas mais diversas áreas do conhecimento e da atividade humana. A internet das coisas (IoT), o aparecimento de novas tecnologias que permitem obter dados sobre a evolução de fenómenos do mundo real e o uso generalizado de dispositivos que usam o sistema de posicionamento global (GPS), por exemplo, smartphones e sistemas de navegação, sugerem que o volume e o valor destes dados aumente significativamente no futuro. Torna-se necessário desenvolver ferramentas capazes de extrair conhecimento destes dados e para isso é necessário geri-los: representar, manipular, analisar e armazenar, de uma forma eficiente. Mas estes dados podem ser complexos, a sua gestão não é trivial e ainda não existe um sistema completo capaz de executar essa tarefa. Existe muito trabalho na literatura sobre pontos móveis, que representam as alterações da posição de objectos ao longo do tempo, mas existe muito menos trabalho realizado sobre regiões móveis, que representam as alterações da posição e da forma de regiões ao longo do tempo, por exemplo, uma tempestade, um incêndio ou um derramamento de petroleo. A representação da evolução de regiões móveis ao longo do tempo é complexa e exige o uso de técnicas mais elaboradas, por exemplo, técnicas de morphing e interpolação, capazes de produzir representações realistas e geometricamente válidas. Nesta dissertação apresentamos e propomos um modelo de dados para trabalhar com objetos móveis (pontos móveis e regiões móveis), em particular regiões móveis, baseado no conceito de malha e em métodos de triangulação compatível e interpolação rígida. Este modelo foi implementado num framework que é independente do cliente e da aplicação. Também implementámos uma extensão espácio-temporal para o sistema de gestão de base de dados PostgreSQL, que usa este framework para manipular e analisar objectos móveis, como uma prova de conceito que o nosso framework funciona com aplicações reais. Os resultados dos testes com dados reais, obtidos a partir de imagens de satélite da evolução de 2 icebergs ao longo do tempo, demonstram que o nosso modelo funciona. Para além dos resultados obtidos, um contributo importante desta dissertação é o desenvolvimento de um framework que pode ser usado como a base para trabalho futuro e investigação nesta área. Existem alguns problemas ainda por resolver e que devem ser analisados e estudados com mais cuidado, em particular, os que foram encontrados quando usámos os métodos de triangulação compatível e interpolação rigída em dados reais.Mestrado em Engenharia Informátic

Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft

Deformable Prototypes for Encoding Shape Categories in Image Databases

We describe a method for shape-based image database search that uses deformable prototypes to represent categories. Rather than directly comparing a candidate shape with all shape entries in the database, shapes are compared in terms of the types of nonrigid deformations (differences) that relate them to a small subset of representative prototypes. To solve the shape correspondence and alignment problem, we employ the technique of modal matching, an information-preserving shape decomposition for matching, describing, and comparing shapes despite sensor variations and nonrigid deformations. In modal matching, shape is decomposed into an ordered basis of orthogonal principal components. We demonstrate the utility of this approach for shape comparison in 2-D image databases.Office of Naval Research (Young Investigator Award N00014-06-1-0661

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Simulation of cell movement through evolving environment: a fictitious domain approach

A numerical method for simulating the movement of unicellular organisms which respond to chemical signals is presented. Cells are modelled as objects of finite size while the extracellular space is described by reaction-diffusion partial differential equations. This modular simulation allows the implementation of different models at the different scales encountered in cell biology and couples them in one single framework. The global computational cost is contained thanks to the use of the fictitious domain method for finite elements, allowing the efficient solve of partial differential equations in moving domains. Finally, a mixed formulation is adopted in order to better monitor the flux of chemicals, specifically at the interface between the cells and the extracellular domain