Image Reconstruction

Electrical capacitance tomography (ECT) is considered as a promising process tomography (PT) technology. Image reconstruction algorithms play an important role in the successful applications of ECT. In this paper, a generalized objective functional, which has been developed using the combinational minimax estimation and a generalized stabilizing functional, is proposed. The Newton algorithm is employed to solve the proposed objective functional.

This paper presents the mathematical framework of radial Tchebichef moment invariants, and investigates their feature representation capabilities for pattern recognition applications. The radial Tchebichef moments are constructed using the discrete ...

Aims. We aim to explore the photosphere of the very cool late-type star VX Sgr and in particular the existence and characterization of molecular layers above the continuum forming photosphere. Methods. We obtained interferometric observations with the VLTI/AMBER interferometer using the fringe tracker FINITO in the spectral domain 1.45-2.50 micron with a spectral resolution of about 35 and baselines ranging from 15 to 88 meters.We perform independent image reconstruction for different wavelength bins and fit the interferometric data with a geometrical toy model.We also compare the data to 1D dynamical models of Miras atmosphere and to 3D hydrodynamical simulations of red supergiant (RSG) and asymptotic giant branch (AGB) stars. Results. Reconstructed images and visibilities show a strong wavelength dependence. The H-band images display two bright spots whose positions are confirmed by the geometrical toy model. The inhomogeneities are qualitatively predicted by 3D simulations. At about 2,00 micron and in the region 2,35 - 2,50 micron, the photosphere appears extended and the radius is larger than in the H band. In this spectral region, the geometrical toy model locates a third bright spot outside the photosphere that can be a feature of the molecular layers. The wavelength dependence of the visibility can be qualitatively explained by 1D dynamical models of Mira atmospheres. The best-fitting photospheric models show a good match with the observed visibilities and give a photospheric diameter of theta = 8,82+-0,50 mas. The H2O molecule seems to be the dominant absorber in the molecular layers. Conclusions. We show that the atmosphere of VX Sgr rather resembles Mira/AGB star model atmospheres than RSG model atmospheres. In particular, we see molecular (water) layers that are typical for Mira stars.

10 High-Dynamic Range Imaging for Dynamic Scenes Celine Loscos and Katrien Jacobs 10.1 Introduction................................................................ 259 10.2 High-Dynamic Range Images: Definition.................................... 261 10.3 HDR Image Creation from Multiple Exposures........ ...

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.

—Hough transform (HT) is a typical method to detect or segment geometry objects from images. In this paper, we study the principle of Hough Transform and its mathematical expressions, and try to use a new approach based on Hough transform for quick line and circle detection in image processing. Our method accurately detected some simple graphics, such as straight line of different direction, circles of different detection, thickness and different number. The results show that our method is less memory consumption and calculated fast, which could be applied for line detection and segmentation in 3D ultrasonic image.

We propose a unification framework for three-dimensional shape reconstruction using physically based models. A variety of 3D shape reconstruction techniques have been developed in the past two decades, such as shape from stereopsis, from shading, from texture gradient, and from structured lighting. However, the lack of a general theory that unifies these shape reconstruction techniques into one framework hinders the effort of a synergistical image interpretation scheme using multiple sensors/information sources. Most shape-from-X techniques use an “observable” (e.g., the stereo disparity, intensity, or texture gradient) and a model, which is based on specific domain knowledge (e.g., the triangulation principle, reflectance function, or texture distortion equation) to predict the observable, in 3D shape reconstruction. We show that all these “observable–prediction-model” types of techniques can be incorporated into our framework of energy constraint on a flexible, deformable image frame. In our algorithm, if the observable does not confirm to the predictions obtained using the corresponding model, a large “error” potential results. The error potential gradient forces the flexible image frame to deform in space. The deformation brings the flexible image frame to “wrap” onto the surface of the imaged 3D object. Surface reconstruction is thus achieved through a “package wrapping” or a “shape deformation” process by minimizing the discrepancy in the observable and the model prediction. The dynamics of such a wrapping process are governed by the least action principle which is physically correct. A physically based model is essential in this general shape reconstruction framework because of its capability to recover the desired 3D shape, to provide an animation sequence of the reconstruction, and to include the regularization principle into the theory of surface reconstruction.

GT Herman optimized (on a sufficiently large data set so as to lead to statistically significant results) without outrageous demands on computational resources. In the rest of this section we discuss how the image reconstruction problem arises in a number of bio- medical areas. ...

Este articulo presenta una revision de los fundamentos de la tomografia computarizada, empezando por un recuento de los inicios y progresos de esta tecnica a traves del tiempo, y continuando con una descripcion de los principios fisicos que rigen la produccion de los rayos X. El articulo tambien discute las bases matematicas para la reconstruccion de las imagenes a partir de proyecciones utilizando metodos analiticos o iterativos. En una seccion independiente, se revisan los conceptos mas importantes relacionados con los riesgos de la radiacion ionizante y se discuten investigaciones recientes, algunas polemicas, acerca de los beneficios y riesgos asociados con la tomografia computarizada y como estos afectan los protocolos de adquisicion de las imagenes. Finalmente, con base en los avances cientificos y tendencias mas recientes, el articulo propone las areas que, presumiblemente, continuaran siendo el centro de atencion de la tomografia computarizada de rayos X en los proximos anos.