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Shape Reconstruction in XRay Tomography
"... Xray tomographic image reconstruction consists in determining an object function from its projections. In many ap plications such as non destructive testing, we look for a default region (air) in a homogeneous known background (metal). The image reconstruction problem becomes then the determinatio ..."
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Xray tomographic image reconstruction consists in determining an object function from its projections. In many ap plications such as non destructive testing, we look for a default region (air) in a homogeneous known background (metal). The image reconstruction problem becomes then the determination of the shape of the default region. Two approaches can bc used: modelling the image as a binary Markov random field and estimating the whole pixels of the image or modeling the shape of the default and estimating it directly from the projections. In this work wc model the default shape by a polygonal disc and propose a new method for estimating directly the coordinates of its vertices from a very limited number of its projections. The idea is not new, but in other competing methods, in general, the default shape is modelled by a small number of parameters (polygonal shapes with very small number of vertices, snakes and deformable templates) and these parameters are estimated either by least squares or by maximum likelihood methods. What wc propose is to model the shape of the default region by a polygon with a great number of vertices to bc able to model any shapes and to estimate directly its vertices coordinates from the projections by defining the solution as the minimizer of an appropriate rcgularizcd criterion which can also bc interpreted as a maximum a postcriori (MAP) estimate in a Bayesian estimation framework. To optimize this criterion we use either a simulated annealing or a special purpose deterministic algorithm based on iterated conditional modes (ICM). The simulated results are very encouraging specially when the number and the angles of projections arc very limited (5 projections limited in45 to 45 degrees). Some comparisons with classical methods are prov...
Level set segmentation of biological volume data sets
 In Handbook of Medical Image Analysis, Volume I: Segmentation Part A
, 2005
"... This chapter describes level set techniques for extracting surface models from a broad variety of biological volume datasets. These techniques have been incorporated into a more general framework that includes other volume processing algorithms. The volume datasets are produced from standard 3D ima ..."
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This chapter describes level set techniques for extracting surface models from a broad variety of biological volume datasets. These techniques have been incorporated into a more general framework that includes other volume processing algorithms. The volume datasets are produced from standard 3D imaging devices, and are all noisy samplings of complex biological structures with boundaries that have low and often varying contrasts. The level set segmentation method, which is well documented in the literature, creates a new volume from the input data by solving an initial value partial differential equation (PDE) with userdefined featureextracting terms. Given the local/global nature of these terms, proper initialization of the level set algorithm is extremely important. Thus, level set deformations alone are not sufficient, they must be combined with powerful preprocessing and data analysis techniques in order to produce successful segmentations. This chapter describes the preprocessing and data analysis techniques that have been developed for a number of segmen
Mapping A 3D Model into Abstract Cellular Complex Format
 Columns on Last Page Should Be Made As Close As Possible to Equal Length
, 2006
"... This paper describes an algorithm for converting a threedimensional object in wireframe format into the Abstract Cellular Complex format described by Kovalevsky, a format designed to efficiently represent topological data in 3D images. The algorithm is partially based on previouslydeveloped algor ..."
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This paper describes an algorithm for converting a threedimensional object in wireframe format into the Abstract Cellular Complex format described by Kovalevsky, a format designed to efficiently represent topological data in 3D images. The algorithm is partially based on previouslydeveloped algorithms which convert a twodimensional wireframe drawing into a threedimensional object, adapted here for processing threedimensional wireframes to find their faces. Other steps of the algorithm determine the volumes which are bounded by the faces, and the relations between each edge and its adjacent entities. With further refinements, this work will be useful to work that utilizes computer graphics and would benefit from topological data, such as computerassisted design (CAD).
Reconstruction of Compact Homogeneous 3D Objects from their Projections
"... In this chapter we first present a review of the methods for the tomographic reconstruction of a compact homogeneous object which lies in a homogeneous background. Then we focus on contour estimation and polyhedral shapes reconstructions. We give some sucient conditions to obtain exact reconstru ..."
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In this chapter we first present a review of the methods for the tomographic reconstruction of a compact homogeneous object which lies in a homogeneous background. Then we focus on contour estimation and polyhedral shapes reconstructions. We give some sucient conditions to obtain exact reconstructions from a complete set of projections in the 2D case and present some extensions to the 3D case. Finally, due to the inherent di Mculties of the exact reconstruction methods and their inappropriateness for the practical situations, we propose an approximate reconstruction method which can handle the situations of very limited angle projections.
projections using deformable
, 2001
"... reconstruction in Xray tomography from a small number of ..."
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