3,566 research outputs found

    Generic iterative subset algorithms for discrete tomography

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    AbstractDiscrete tomography deals with the reconstruction of images from their projections where the images are assumed to contain only a small number of grey values. In particular, there is a strong focus on the reconstruction of binary images (binary tomography). A variety of binary tomography problems have been considered in the literature, each using different projection models or additional constraints. In this paper, we propose a generic iterative reconstruction algorithm that can be used for many different binary reconstruction problems. In every iteration, a subproblem is solved based on at most two of the available projections. Each of the subproblems can be solved efficiently using network flow methods. We report experimental results for various reconstruction problems. Our results demonstrate that the algorithm is capable of reconstructing complex objects from a small number of projections

    Reconstructing binary images from discrete X-rays

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    We present a new algorithm for reconstructing binary images from their projections along a small number of directions. Our algorithm performs a sequence of related reconstructions, each using only two projections. The algorithm makes extensive use of network flow algorithms for solving the two-projection subproblems. Our experimental results demonstrate that the algorithm can compute reconstructions which resemble the original images very closely from a small number of projections, even in the presence of noise. Although the effectiveness of the algorithm is based on certain smoothness assumptions about the image, even tiny, non-smooth details are reconstructed exactly. The class of images for which the algorithm is most effective includes images of convex objects, but images of objects that contain holes or consist of multiple components can also be reconstructed with great accurac

    3D particle tracking velocimetry using dynamic discrete tomography

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    Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics, combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle trajectories from projections. The algorithm is efficient for data from two projection directions and exact in the sense that it finds a solution consistent with the experimental data. Non-uniqueness of solutions can be detected and solutions can be tracked individually

    Network Flow Algorithms for Discrete Tomography

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    Tomography is a powerful technique to obtain images of the interior of an object in a nondestructive way. First, a series of projection images (e.g., X-ray images) is acquired and subsequently a reconstruction of the interior is computed from the available project data. The algorithms that are used to compute such reconstructions are known as tomographic reconstruction algorithms. Discrete tomography is concerned with the tomographic reconstruction of images that are known to contain only a few different gray levels. By using this knowledge in the reconstruction algorithm it is often possible to reduce the number of projections required to compute an accurate reconstruction, compared to algorithms that do not use prior knowledge. This thesis deals with new reconstruction algorithms for discrete tomography. In particular, the first five chapters are about reconstruction algorithms based on network flow methods. These algorithms make use of an elegant correspondence between certain types of tomography problems and network flow problems from the field of Operations Research. Chapter 6 deals with a problem that occurs in the application of discrete tomography to the reconstruction of nanocrystals from projections obtained by electron microscopy.The research for this thesis has been financially supported by the Netherlands Organisation for Scientific Research (NWO), project 613.000.112.UBL - phd migration 201

    A Novel Convex Relaxation for Non-Binary Discrete Tomography

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    We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations

    Reconstruction of Binary Image Using Techniques of Discrete Tomography

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    Discrete tomography deals with the reconstruction of images, in particular binary images, from their projections. A number of binary image reconstruction methods have been considered in the literature, using different projection models or additional constraints. Here, we will consider reconstruction of a binary image with some prescribed numerical information on the rows of the binary image treated as a binary matrix of 0's and 1's. The problem involves information, referred to as row projection, on the number of 1's and the number of subword 01's in the rows of the binary image to be constructed. The algorithm proposed constructs one among the many binary images having the same numerical information on the number of 1's and the number of subword 01. This proposed algorithm will also construct the image uniquely for a special kind of a binary image with its rows in some specific form

    The Discrete radon transform: A more efficient approach to image reconstruction

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    The Radon transform and its inversion are the mathematical keys that enable tomography. Radon transforms are defined for continuous objects with continuous projections at all angles in [0,Ï€). In practice, however, we pre-filter discrete projections take

    Multi-View Stereo with Single-View Semantic Mesh Refinement

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    While 3D reconstruction is a well-established and widely explored research topic, semantic 3D reconstruction has only recently witnessed an increasing share of attention from the Computer Vision community. Semantic annotations allow in fact to enforce strong class-dependent priors, as planarity for ground and walls, which can be exploited to refine the reconstruction often resulting in non-trivial performance improvements. State-of-the art methods propose volumetric approaches to fuse RGB image data with semantic labels; even if successful, they do not scale well and fail to output high resolution meshes. In this paper we propose a novel method to refine both the geometry and the semantic labeling of a given mesh. We refine the mesh geometry by applying a variational method that optimizes a composite energy made of a state-of-the-art pairwise photo-metric term and a single-view term that models the semantic consistency between the labels of the 3D mesh and those of the segmented images. We also update the semantic labeling through a novel Markov Random Field (MRF) formulation that, together with the classical data and smoothness terms, takes into account class-specific priors estimated directly from the annotated mesh. This is in contrast to state-of-the-art methods that are typically based on handcrafted or learned priors. We are the first, jointly with the very recent and seminal work of [M. Blaha et al arXiv:1706.08336, 2017], to propose the use of semantics inside a mesh refinement framework. Differently from [M. Blaha et al arXiv:1706.08336, 2017], which adopts a more classical pairwise comparison to estimate the flow of the mesh, we apply a single-view comparison between the semantically annotated image and the current 3D mesh labels; this improves the robustness in case of noisy segmentations.Comment: {\pounds}D Reconstruction Meets Semantic, ICCV worksho
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