TVL₁shape approximation from scattered 3D data

With the emergence in 3D sensors such as laser scanners and 3D reconstruction from cameras, large 3D point clouds can now be sampled from physical objects within a scene. The raw 3D samples delivered by these sensors however, contain only a limited degree of information about the environment the objects exist in, which means that further geometrical high-level modelling is essential. In addition, issues like sparse data measurements, noise, missing samples due to occlusion, and the inherently huge datasets involved in such representations makes this task extremely challenging. This paper addresses these issues by presenting a new 3D shape modelling framework for samples acquired from 3D sensor. Motivated by the success of nonlinear kernel-based approximation techniques in the statistics domain, existing methods using radial basis functions are applied to 3D object shape approximation. The task is framed as an optimization problem and is extended using non-smooth L1 total variation regularization. Appropriate convex energy functionals are constructed and solved by applying the Alternating Direction Method of Multipliers approach, which is then extended using Gauss-Seidel iterations. This significantly lowers the computational complexity involved in generating 3D shape from 3D samples, while both numerical and qualitative analysis confirms the superior shape modelling performance of this new framework compared with existing 3D shape reconstruction techniques

TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

A Knowledge Integration Framework for 3D Shape Reconstruction

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points in sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment in which the robots operate with. This means unstructured 3D samples must be processed by application-specific models to enable a robot, for instance, to detect and identify objects and infer the scene geometry for path-planning more efficiently than by using raw 3D data. This thesis specifically focuses on the fundamental task of 3D shape reconstruction and modelling by presenting a new knowledge integration framework for unstructured 3D samples. The novelty lies in the representation of surfaces by algebraic functions with limited support, which enables the extraction of smooth consistent shapes from noisy samples with a heterogeneous density. Moreover, many surfaces in urban environments can reasonably be assumed to be planar, and the framework exploits this knowledge to enable effective noise suppression without loss of detail. This is achieved by using a convex optimization technique which has linear computational complexity. Thus is much more efficient than existing solutions. The new framework has been validated by critical experimental analysis and evaluation and has been shown to increase the accuracy of the reconstructed shape significantly compared to state-of-the-art methods. Applying this new knowledge integration framework means that less accurate, low-cost 3D sensors can be employed without sacrificing the high demands that 3D perception must achieve. This links well into the area of robotic inspection, as for example regarding small drones that use inaccurate and lightweight image sensors

Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning

Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al, Proc. Natl. Acad. Sci. 116, 19848-19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as better fit to regularize the reconstructions. We devised a recurrent neural network (RNN) architecture with a novel split-convolutional gated recurrent unit (SC-GRU) as the fundamental building block. Through comprehensive comparison of several quantitative metrics, we show that the dynamic method improves upon previous static approaches with fewer artifacts and better overall reconstruction fidelity.Comment: 12 pages, 7 figures, 2 table

Omnidirectional Light Field Analysis and Reconstruction

Digital photography exists since 1975, when Steven Sasson attempted to build the first digital camera. Since then the concept of digital camera did not evolve much: an optical lens concentrates light rays onto a focal plane where a planar photosensitive array transforms the light intensity into an electric signal. During the last decade a new way of conceiving digital photography emerged: a photography is the acquisition of the entire light ray field in a confined region of space. The main implication of this new concept is that a digital camera does not acquire a 2-D signal anymore, but a 5-D signal in general. Acquiring an image becomes more demanding in terms of memory and processing power; at the same time, it offers the users a new set of possibilities, like choosing dynamically the focal plane and the depth of field of the final digital photo. In this thesis we develop a complete mathematical framework to acquire and then reconstruct the omnidirectional light field around an observer. We also propose the design of a digital light field camera system, which is composed by several pinhole cameras distributed around a sphere. The choice is not casual, as we take inspiration from something already seen in nature: the compound eyes of common terrestrial and flying insects like the house fly. In the first part of the thesis we analyze the optimal sampling conditions that permit an efficient discrete representation of the continuous light field. In other words, we will give an answer to the question: how many cameras and what resolution are needed to have a good representation of the 4-D light field? Since we are dealing with an omnidirectional light field we use a spherical parametrization. The results of our analysis is that we need an irregular (i.e., not rectangular) sampling scheme to represent efficiently the light field. Then, to store the samples we use a graph structure, where each node represents a light ray and the edges encode the topology of the light field. When compared to other existing approaches our scheme has the favorable property of having a number of samples that scales smoothly for a given output resolution. The next step after the acquisition of the light field is to reconstruct a digital picture, which can be seen as a 2-D slice of the 4-D acquired light field. We interpret the reconstruction as a regularized inverse problem defined on the light field graph and obtain a solution based on a diffusion process. The proposed scheme has three main advantages when compared to the classic linear interpolation: it is robust to noise, it is computationally efficient and can be implemented in a distributed fashion. In the second part of the thesis we investigate the problem of extracting geometric information about the scene in the form of a depth map. We show that the depth information is encoded inside the light field derivatives and set up a TV-regularized inverse problem, which efficiently calculates a dense depth map of the scene while respecting the discontinuities at the boundaries of objects. The extracted depth map is used to remove visual and geometrical artifacts from the reconstruction when the light field is under-sampled. In other words, it can be used to help the reconstruction process in challenging situations. Furthermore, when the light field camera is moving temporally, we show how the depth map can be used to estimate the motion parameters between two consecutive acquisitions with a simple and effective algorithm, which does not require the computation nor the matching of features and performs only simple arithmetic operations directly in the pixel space. In the last part of the thesis, we introduce a novel omnidirectional light field camera that we call Panoptic. We obtain it by layering miniature CMOS imagers onto an hemispherical surface, which are then connected to a network of FPGAs. We show that the proposed mathematical framework is well suited to be embedded in hardware by demonstrating a real time reconstruction of an omnidirectional video stream at 25 frames per second

TV-Stokes And Its Variants For Image Processing

The total variational minimization with a Stokes constraint, also known as the TV-Stokes model, has been considered as one of the most successful models in image processing, especially in image restoration and sparse-data-based 3D surface reconstruction. This thesis studies the TV-Stokes model and its existing variants, proposes new and more effective variants of the model and their algorithms applied to some of the most interesting image processing problems. We first review some of the variational models that already exist, in particular the TV-Stokes model and its variants. Common techniques like the augmented Lagrangian and the dual formulation, are also introduced. We then present our models as new variants of the TV-Stokes. The main focus of the work has been on the sparse surface reconstruction of 3D surfaces. A model (WTR) with a vector fidelity, that is the gradient vector fidelity, has been proposed, applying it to both 3D cartoon design and height map reconstruction. The model employs the second-order total variation minimization, where the curl-free condition is satisfied automatically. Because the model couples both the height and the gradient vector representing the surface in the same minimization, it constructs the surface correctly. A variant of this model is then introduced, which includes a vector matching term. This matching term gives the model capability to accurately represent the shape of a geometry in the reconstruction. Experiments show a significant improvement over the state-of-the-art models, such as the TV model, higher order TV models, and the anisotropic third-order regularization model, when applied to some general applications. In another work, the thesis generalizes the TV-Stokes model from two dimensions to an arbitrary number of dimensions, introducing a convenient form for the constraint in order it to be extended to higher dimensions. The thesis explores also the idea of feature accumulation through iterative regularization in another work, introducing a Richardson-like iteration for the TV-Stokes. Thisis then followed by a more general model, a combined model, based on the modified variant of the TV-stokes. The resulting model is found to be equivalent to the well-known TGV model. The thesis introduces some interesting numerical strategies for the solution of the TV-Stokes model and its variants. Higher order PDEs are turned into inhomogeneous modified Helmholtz equations through transformations. These equations are then solved using the preconditioned conjugate gradients method or the fast Fourier transformation. The thesis proposes a simple but quite general approach to finding closed form solutions to a general L1 minimization problem, and applies it to design algorithms for our models.Doktorgradsavhandlin

A Survey of Surface Reconstruction from Point Clouds

International audienceThe area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations – not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques, and provide directions for future work in surface reconstruction

Compressive sensing for 3D microwave imaging systems

Compressed sensing (CS) image reconstruction techniques are developed and experimentally implemented for wideband microwave synthetic aperture radar (SAR) imaging systems with applications to nondestructive testing and evaluation. These techniques significantly reduce the number of spatial measurement points and, consequently, the acquisition time by sampling at a level lower than the Nyquist-Shannon rate. Benefiting from a reduced number of samples, this work successfully implemented two scanning procedures: the nonuniform raster and the optimum path. Three CS reconstruction approaches are also proposed for the wideband microwave SAR-based imaging systems. The first approach reconstructs a full-set of raw data from undersampled measurements via L1-norm optimization and consequently applies 3D forward SAR on the reconstructed raw data. The second proposed approach employs forward SAR and reverse SAR (R-SAR) transforms in each L1-norm optimization iteration reconstructing images directly. This dissertation proposes a simple, elegant truncation repair method to combat the truncation error which is a critical obstacle to the convergence of the CS iterative algorithm. The third proposed CS reconstruction algorithm is the adaptive basis selection (ABS) compressed sensing. Rather than a fixed sparsifying basis, the proposed ABS method adaptively selects the best basis from a set of bases in each iteration of the L1-norm optimization according to a proposed decision metric that is derived from the sparsity of the image and the coherence between the measurement and sparsifying matrices. The results of several experiments indicate that the proposed algorithms recover 2D and 3D SAR images with only 20% of the spatial points and reduce the acquisition time by up to 66% of that of conventional methods while maintaining or improving the quality of the SAR images --Abstract, page iv

Aspetti avanzati di radioprotezione nell'uso di acceleratori di particelle in campo medico

In this work, the well-known MC code FLUKA was used to simulate the GE PETrace cyclotron (16.5 MeV) installed at “S. Orsola-Malpighi” University Hospital (Bologna, IT) and routinely used in the production of positron emitting radionuclides. Simulations yielded estimates of various quantities of interest, including: the effective dose distribution around the equipment; the effective number of neutron produced per incident proton and their spectral distribution; the activation of the structure of the cyclotron and the vault walls; the activation of the ambient air, in particular the production of 41Ar, the assessment of the saturation yield of radionuclides used in nuclear medicine. The simulations were validated against experimental measurements in terms of physical and transport parameters to be used at the energy range of interest in the medical field. The validated model was also extensively used in several practical applications uncluding the direct cyclotron production of non-standard radionuclides such as 99mTc, the production of medical radionuclides at TRIUMF (Vancouver, CA) TR13 cyclotron (13 MeV), the complete design of the new PET facility of “Sacro Cuore – Don Calabria” Hospital (Negrar, IT), including the ACSI TR19 (19 MeV) cyclotron, the dose field around the energy selection system (degrader) of a proton therapy cyclotron, the design of plug-doors for a new cyclotron facility, in which a 70 MeV cyclotron will be installed, and the partial decommissioning of a PET facility, including the replacement of a Scanditronix MC17 cyclotron with a new TR19 cyclotron.In questo lavoro, il codice Monte Carlo (MC) FLUKA è stato utilizzato per simulare il ciclotrone GE PETtrace (16.5 MeV) installato presso l’azienda ospedaliera “S. Orsola-Malpighi” (Bologna, IT), quotidianamente utilizzato per la produzione di radiofarmaci PET. Le simulazioni sono state effettuate per valutare diversi fenomeni e quantità d’interesse radiologico tra cui l’equivalente di dose ambientale nell’intorno dell’acceleratore, il numero di neutroni emessi per protone incidente e la loro distribuzione spettrale, l’attivazione dei componenti del ciclotrone e delle pareti del bunker, l’attivazione dell’aria interna al bunker ed in particolare la produzione di 41Ar, la resa a saturazione di radionuclidi d’interesse in medicina nucleare. Le simulazioni sono state validate, in termini di parametri fisici e di trasporto da utilizzare nel range energetico caratteristico delle applicazioni mediche, con una serie di misure sperimentali. Il modello MC validato è stato quindi applicato ad altri casi pratici quali lo studio di fattibilità della produzione diretta in ciclotrone di 99mTc, la produzione di radionuclidi ad uso medico con il ciclotrone TR13 (13 MeV) installato presso il centro di ricerca TRIUMF (Vancouver, CA), la progettazione completa del nuovo centro PET dell’ospedale “Sacro Cuore-Don Calabria” di Negrar (Verona, IT), incluso il ciclotrone ACSI TR19 (19 MeV), lo studio del campo di dose nell’intorno di un sistema di selezione dell’energia (degrader) di un ciclotrone per terapia, la progettazione di specifiche “porte a tappo” per un sito di produzione di radionuclidi ad uso medico, in cui verrà installato un ciclotrone da 70 MeV e sei diverse beam line, e per il parziale decommissioning di un centro PET e la sostituzione di un ciclotrone Scanditronix MC17 (17 MeV), attualmente installato, con una nuova unità TR19

Recent Techniques for Regularization in Partial Differential Equations and Imaging

abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201