An Algebraic Framework for Discrete Tomography: Revealing the Structure of Dependencies

Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on Ring Theory and Commutative Algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving Discrete Tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason-Ludwig consistency conditions from continuous tomography.Comment: 20 pages, 1 figure, updated to reflect reader inpu

A Survey of Methods for Volumetric Scene Reconstruction from Photographs

Scene reconstruction, the task of generating a 3D model of a scene given multiple 2D photographs taken of the scene, is an old and difficult problem in computer vision. Since its introduction, scene reconstruction has found application in many fields, including robotics, virtual reality, and entertainment. Volumetric models are a natural choice for scene reconstruction. Three broad classes of volumetric reconstruction techniques have been developed based on geometric intersections, color consistency, and pair-wise matching. Some of these techniques have spawned a number of variations and undergone considerable refinement. This paper is a survey of techniques for volumetric scene reconstruction

Reconstructing parameterized objects from projections : a statistical view

Includes bibliographical references (p. 49-51).Supported by the National Science Foundation. 9015281-MIP Supported by the Office of Naval Research. N00014-91-J-1004 Supported by the Clement Vaturi Fellowship in Biomedical Imaging Sciences at MIT.Peyman Milanfar, W. Clem. Karl, Alan S. Willsky

Accurate geometry reconstruction of vascular structures using implicit splines

3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy

Feature Extraction for image super-resolution using finite rate of innovation principles

To understand a real-world scene from several multiview pictures, it is necessary to find the disparities existing between each pair of images so that they are correctly related to one another. This process, called image registration, requires the extraction of some specific information about the scene. This is achieved by taking features out of the acquired images. Thus, the quality of the registration depends largely on the accuracy of the extracted features. Feature extraction can be formulated as a sampling problem for which perfect re- construction of the desired features is wanted. The recent sampling theory for signals with finite rate of innovation (FRI) and the B-spline theory offer an appropriate new frame- work for the extraction of features in real images. This thesis first focuses on extending the sampling theory for FRI signals to a multichannel case and then presents exact sampling results for two different types of image features used for registration: moments and edges. In the first part, it is shown that the geometric moments of an observed scene can be retrieved exactly from sampled images and used as global features for registration. The second part describes how edges can also be retrieved perfectly from sampled images for registration purposes. The proposed feature extraction schemes therefore allow in theory the exact registration of images. Indeed, various simulations show that the proposed extraction/registration methods overcome traditional ones, especially at low-resolution. These characteristics make such feature extraction techniques very appropriate for applications like image super-resolution for which a very precise registration is needed. The quality of the super-resolved images obtained using the proposed feature extraction meth- ods is improved by comparison with other approaches. Finally, the notion of polyphase components is used to adapt the image acquisition model to the characteristics of real digital cameras in order to run super-resolution experiments on real images

Sistemas automáticos de informação e segurança para apoio na condução de veículos

Doutoramento em Engenharia MecânicaO objeto principal desta tese é o estudo de algoritmos de processamento e representação automáticos de dados, em particular de informação obtida por sensores montados a bordo de veículos (2D e 3D), com aplicação em contexto de sistemas de apoio à condução. O trabalho foca alguns dos problemas que, quer os sistemas de condução automática (AD), quer os sistemas avançados de apoio à condução (ADAS), enfrentam hoje em dia. O documento é composto por duas partes. A primeira descreve o projeto, construção e desenvolvimento de três protótipos robóticos, incluindo pormenores associados aos sensores montados a bordo dos robôs, algoritmos e arquitecturas de software. Estes robôs foram utilizados como plataformas de ensaios para testar e validar as técnicas propostas. Para além disso, participaram em várias competições de condução autónoma tendo obtido muito bons resultados. A segunda parte deste documento apresenta vários algoritmos empregues na geração de representações intermédias de dados sensoriais. Estes podem ser utilizados para melhorar técnicas já existentes de reconhecimento de padrões, deteção ou navegação, e por este meio contribuir para futuras aplicações no âmbito dos AD ou ADAS. Dado que os veículos autónomos contêm uma grande quantidade de sensores de diferentes naturezas, representações intermédias são particularmente adequadas, pois podem lidar com problemas relacionados com as diversas naturezas dos dados (2D, 3D, fotométrica, etc.), com o carácter assíncrono dos dados (multiplos sensores a enviar dados a diferentes frequências), ou com o alinhamento dos dados (problemas de calibração, diferentes sensores a disponibilizar diferentes medições para um mesmo objeto). Neste âmbito, são propostas novas técnicas para a computação de uma representação multi-câmara multi-modal de transformação de perspectiva inversa, para a execução de correcção de côr entre imagens de forma a obter mosaicos de qualidade, ou para a geração de uma representação de cena baseada em primitivas poligonais, capaz de lidar com grandes quantidades de dados 3D e 2D, tendo inclusivamente a capacidade de refinar a representação à medida que novos dados sensoriais são recebidos.The main object of this thesis is the study of algorithms for automatic information processing and representation, in particular information provided by onboard sensors (2D and 3D), to be used in the context of driving assistance. The work focuses on some of the problems facing todays Autonomous Driving (AD) systems and Advanced Drivers Assistance Systems (ADAS). The document is composed of two parts. The first part describes the design, construction and development of three robotic prototypes, including remarks about onboard sensors, algorithms and software architectures. These robots were used as test beds for testing and validating the developed techniques; additionally, they have participated in several autonomous driving competitions with very good results. The second part of this document presents several algorithms for generating intermediate representations of the raw sensor data. They can be used to enhance existing pattern recognition, detection or navigation techniques, and may thus benefit future AD or ADAS applications. Since vehicles often contain a large amount of sensors of different natures, intermediate representations are particularly advantageous; they can be used for tackling problems related with the diverse nature of the data (2D, 3D, photometric, etc.), with the asynchrony of the data (multiple sensors streaming data at different frequencies), or with the alignment of the data (calibration issues, different sensors providing different measurements of the same object). Within this scope, novel techniques are proposed for computing a multicamera multi-modal inverse perspective mapping representation, executing color correction between images for obtaining quality mosaics, or to produce a scene representation based on polygonal primitives that can cope with very large amounts of 3D and 2D data, including the ability of refining the representation as new information is continuously received

Blinking cubes : a method for polygon-based scene reconstruction

Thesis (S.B. and M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (p. 50-51).by John Andrew Harvey.S.B.and M.Eng