Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models

The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models. To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions. The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation. We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision

Part Description and Segmentation Using Contour, Surface and Volumetric Primitives

The problem of part definition, description, and decomposition is central to the shape recognition systems. The Ultimate goal of segmenting range images into meaningful parts and objects has proved to be very difficult to realize, mainly due to the isolation of the segmentation problem from the issue of representation. We propose a paradigm for part description and segmentation by integration of contour, surface, and volumetric primitives. Unlike previous approaches, we have used geometric properties derived from both boundary-based (surface contours and occluding contours), and primitive-based (quadric patches and superquadric models) representations to define and recover part-whole relationships, without a priori knowledge about the objects or object domain. The object shape is described at three levels of complexity, each contributing to the overall shape. Our approach can be summarized as answering the following question : Given that we have all three different modules for extracting volume, surface and boundary properties, how should they be invoked, evaluated and integrated? Volume and boundary fitting, and surface description are performed in parallel to incorporate the best of the coarse to fine and fine to coarse segmentation strategy. The process involves feedback between the segmentor (the Control Module) and individual shape description modules. The control module evaluates the intermediate descriptions and formulates hypotheses about parts. Hypotheses are further tested by the segmentor and the descriptors. The descriptions thus obtained are independent of position, orientation, scale, domain and domain properties, and are based purely on geometric considerations. They are extremely useful for the high level domain dependent symbolic reasoning processes, which need not deal with tremendous amount of data, but only with a rich description of data in terms of primitives recovered at various levels of complexity

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

Model-Based Shape and Motion Analysis: Left Ventricle of a Heart

The accurate and clinically useful estimation of the shape, motion, and deformation of the left ventricle of a heart (LV) is an important yet open research problem. Recently, computer vision techniques for reconstructing the 3-D shape and motion of the LV have been developed. The main drawback of these techniques, however, is that their models are formulated in terms of either too many local parameters that require non-trivial processing to be useful for close to real time diagnosis, or too few parameters to offer an adequate approximation to the LV motion. To address the problem, we present a new class of volumetric primitives for a compact and accurate LV shape representation in which model parameters are functions. Lagrangian dynamics are employed to convert geometric models into dynamic models that can deform according to the forces manifested in the data points. It is thus possible to make a precise estimation of the deformation of the LV shape endocardial, epicardial and anywhere in between with a small number of intuitive parameter functions. We believe that the proposed technique has a wide range of potential applications. In this thesis, we demonstrate the possibility by applying it to the 3-D LV shape and motion characterization from magnetic tagging data (MRI-SPAMM). We show that the results of our experiments with normal and abnormal heart data enable us to quantitatively verify the physicians\u27 qualitative conception of the left ventricular wall motion

Exobiology in Earth orbit: The results of science workshops held at NASA, Ames Research Center

The Workshops on Exobiology in Earth Orbit were held to explore concepts for orbital experiments of exobiological interest and make recommendations on which classes of experiments should be carried out. Various observational and experimental opportunities in Earth orbit are described including those associated with the Space Shuttle laboratories, spacecraft deployed from the Space Shuttle and expendable launch vehicles, the Space Station, and lunar bases. Specific science issues and technology needs are summarized. Finally, a list of recommended experiments in the areas of observational exobiology, cosmic dust collection, and in situ experiments is presented

Physics-Based Modeling of Nonrigid Objects for Vision and Graphics (Dissertation)

This thesis develops a physics-based framework for 3D shape and nonrigid motion modeling for computer vision and computer graphics. In computer vision it addresses the problems of complex 3D shape representation, shape reconstruction, quantitative model extraction from biomedical data for analysis and visualization, shape estimation, and motion tracking. In computer graphics it demonstrates the generative power of our framework to synthesize constrained shapes, nonrigid object motions and object interactions for the purposes of computer animation. Our framework is based on the use of a new class of dynamically deformable primitives which allow the combination of global and local deformations. It incorporates physical constraints to compose articulated models from deformable primitives and provides force-based techniques for fitting such models to sparse, noise-corrupted 2D and 3D visual data. The framework leads to shape and nonrigid motion estimators that exploit dynamically deformable models to track moving 3D objects from time-varying observations. We develop models with global deformation parameters which represent the salient shape features of natural parts, and local deformation parameters which capture shape details. In the context of computer graphics, these models represent the physics-based marriage of the parameterized and free-form modeling paradigms. An important benefit of their global/local descriptive power in the context of computer vision is that it can potentially satisfy the often conflicting requirements of shape reconstruction and shape recognition. The Lagrange equations of motion that govern our models, augmented by constraints, make them responsive to externally applied forces derived from input data or applied by the user. This system of differential equations is discretized using finite element methods and simulated through time using standard numerical techniques. We employ these equations to formulate a shape and nonrigid motion estimator. The estimator is a continuous extended Kalman filter that recursively transforms the discrepancy between the sensory data and the estimated model state into generalized forces. These adjust the translational, rotational, and deformational degrees of freedom such that the model evolves in a consistent fashion with the noisy data. We demonstrate the interactive time performance of our techniques in a series of experiments in computer vision, graphics, and visualization

Simulazioni della Coalescenza di Stelle di Neutroni Binarie nell'Era dell'Astrofisica Multimessaggera

The recent ground-breaking detection of gravitational waves (GW) from the merger of two neutron stars (NS), known as the GW170817 event, along with the observations of electromagnetic counterparts across the entire spectrum including a short gamma-ray burst (SGRB) and a radioactively powered kilonova, has given birth to the era of multimessenger astrophysics with GW sources. In order to probe the underlying physical mechanisms at play in such systems, it is necessary to employ fully general relativistic magnetohydrodynamic (GRMHD) simulations, including effects of magnetic fields and neutrino emission/reabsorption for a more realistic description. In the first part of this Thesis, we introduce our newly-developed GRMHD code Spritz, that solves the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime. We present its salient features including the staggered formulation of the vector potential as well as support for any arbitrary equation of state (EOS), followed by a series of tests for code validation. We then describe the implementation of an approximate neutrino leakage scheme in Spritz, shedding some light on the involved equations, physical assumptions, and implemented numerical methods including higher order schemes, along with a large battery of general relativistic tests performed with and without magnetic fields and/or neutrino leakage. Since flux-conserving GRMHD codes like Spritz depend upon a technical algorithm to recover the fundamental `primitive' variables from the evolved `conserved' ones, which is often error-prone, we propose a new robust, accurate and efficient conservative-to-primitive variable recovery scheme named `RePrimAnd', along with the proof of existence of a solution and its uniqueness. As a next natural step, we implemented this scheme in Spritz, and performed a number of demanding GRMHD tests including critical cases like a NS collapse to a black hole (BH) as well as the evolution of a BH-accretion disk system. The second part of the thesis focusses instead on the application of GRMHD codes to perform magnetized BNS merger simulations. In particular, using the WhiskyMHD code, we present a detailed study of BNS merger simulations forming a long-lived NS remnant and including long post-merger evolution. Exploring this `magnetar scenario' allows us to address some of the open questions in the context of the SGRB and accompanying kilonova of the GW170817 event. Finally, we also discuss the results of the first magnetized BNS merger simulation performed with Spritz and the RePrimAnd scheme, concluding with an outlook on the next steps.The recent ground-breaking detection of gravitational waves (GW) from the merger of two neutron stars (NS), known as the GW170817 event, along with the observations of electromagnetic counterparts across the entire spectrum including a short gamma-ray burst (SGRB) and a radioactively powered kilonova, has given birth to the era of multimessenger astrophysics with GW sources. In order to probe the underlying physical mechanisms at play in such systems, it is necessary to employ fully general relativistic magnetohydrodynamic (GRMHD) simulations, including effects of magnetic fields and neutrino emission/reabsorption for a more realistic description. In the first part of this Thesis, we introduce our newly-developed GRMHD code Spritz, that solves the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime. We present its salient features including the staggered formulation of the vector potential as well as support for any arbitrary equation of state (EOS), followed by a series of tests for code validation. We then describe the implementation of an approximate neutrino leakage scheme in Spritz, shedding some light on the involved equations, physical assumptions, and implemented numerical methods including higher order schemes, along with a large battery of general relativistic tests performed with and without magnetic fields and/or neutrino leakage. Since flux-conserving GRMHD codes like Spritz depend upon a technical algorithm to recover the fundamental `primitive' variables from the evolved `conserved' ones, which is often error-prone, we propose a new robust, accurate and efficient conservative-to-primitive variable recovery scheme named `RePrimAnd', along with the proof of existence of a solution and its uniqueness. As a next natural step, we implemented this scheme in Spritz, and performed a number of demanding GRMHD tests including critical cases like a NS collapse to a black hole (BH) as well as the evolution of a BH-accretion disk system. The second part of the thesis focusses instead on the application of GRMHD codes to perform magnetized BNS merger simulations. In particular, using the WhiskyMHD code, we present a detailed study of BNS merger simulations forming a long-lived NS remnant and including long post-merger evolution. Exploring this `magnetar scenario' allows us to address some of the open questions in the context of the SGRB and accompanying kilonova of the GW170817 event. Finally, we also discuss the results of the first magnetized BNS merger simulation performed with Spritz and the RePrimAnd scheme, concluding with an outlook on the next steps

Correction of Errors in Time of Flight Cameras

En esta tesis se aborda la corrección de errores en cámaras de profundidad basadas en tiempo de vuelo (Time of Flight - ToF). De entre las más recientes tecnologías, las cámaras ToF de modulación continua (Continuous Wave Modulation - CWM) son una alternativa prometedora para la creación de sensores compactos y rápidos. Sin embargo, existen gran variedad de errores que afectan notablemente la medida de profundidad, poniendo en compromiso posibles aplicaciones. La corrección de dichos errores propone un reto desafiante. Actualmente, se consideran dos fuentes principales de error: i) sistemático y ii) no sistemático. Mientras que el primero admite calibración, el último depende de la geometría y el movimiento relativo de la escena. Esta tesis propone métodos que abordan i) la distorsión sistemática de profundidad y dos de las fuentes de error no sistemático más relevantes: ii.a) la interferencia por multicamino (Multipath Interference - MpI) y ii.b) los artefactos de movimiento. La distorsión sistemática de profundidad en cámaras ToF surge principalmente debido al uso de señales sinusoidales no perfectas para modular. Como resultado, las medidas de profundidad aparecen distorsionadas, pudiendo ser reducidas con una etapa de calibración. Esta tesis propone un método de calibración basado en mostrar a la cámara un plano en diferentes posiciones y orientaciones. Este método no requiere de patrones de calibración y, por tanto, puede emplear los planos, que de manera natural, aparecen en la escena. El método propuesto encuentra una función que obtiene la corrección de profundidad correspondiente a cada píxel. Esta tesis mejora los métodos existentes en cuanto a precisión, eficiencia e idoneidad. La interferencia por multicamino surge debido a la superposición de la señal reflejada por diferentes caminos con la reflexión directa, produciendo distorsiones que se hacen más notables en superficies convexas. La MpI es la causa de importantes errores en la estimación de profundidad en cámaras CWM ToF. Esta tesis propone un método que elimina la MpI a partir de un solo mapa de profundidad. El enfoque propuesto no requiere más información acerca de la escena que las medidas ToF. El método se fundamenta en un modelo radio-métrico de las medidas que se emplea para estimar de manera muy precisa el mapa de profundidad sin distorsión. Una de las tecnologías líderes para la obtención de profundidad en imagen ToF está basada en Photonic Mixer Device (PMD), la cual obtiene la profundidad mediante el muestreado secuencial de la correlación entre la señal de modulación y la señal proveniente de la escena en diferentes desplazamientos de fase. Con movimiento, los píxeles PMD capturan profundidades diferentes en cada etapa de muestreo, produciendo artefactos de movimiento. El método propuesto en esta tesis para la corrección de dichos artefactos destaca por su velocidad y sencillez, pudiendo ser incluido fácilmente en el hardware de la cámara. La profundidad de cada píxel se recupera gracias a la consistencia entre las muestras de correlación en el píxel PMD y de la vecindad local. Este método obtiene correcciones precisas, reduciendo los artefactos de movimiento enormemente. Además, como resultado de este método, puede obtenerse el flujo óptico en los contornos en movimiento a partir de una sola captura. A pesar de ser una alternativa muy prometedora para la obtención de profundidad, las cámaras ToF todavía tienen que resolver problemas desafiantes en relación a la corrección de errores sistemáticos y no sistemáticos. Esta tesis propone métodos eficaces para enfrentarse con estos errores