Fast Mojette Transform for Discrete Tomography

A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin

Extraction of bone structure with a single-scan skeletonization driven by distance

International audienceShape description is an important step in image analysis. Skeletonization methods are widely used in image analysis since they are a powerful tool to describe a shape. This paper presents a new single-scan skeletonization using different diskrete distances. The application of this method is the extraction of caracteristics from µCT images in order to estimate the bone state

The 2 and 3 materials scene reconstructed from some line Mojette projections

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Analysis of Mojette Transform Projections using Z3 lattice versus A3 lattice

International audienceThe Mojette Transform (MT) is an exact discrete form of the Radon transform. It has been originally defined on the cubic lattice Z n (where n is the dimension). We propose to study this transform when using the densest lattice for the dimension 3, namely the face-centered cubic lattice A 3. In order to compare the legacy MT using Z 3 , versus the new MT using A 3 , we use a fair comparison methodology between the two MT schemes. Statistic criteria have been defined to analyse the information distribution on the projections. The experimental results show the specific nature of the information distribution on the MT projections due to the compacity of the A 3 lattice

Linking bone microarchitecture to projections texture analysis

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Simulations Monte Carlo d'un faisceau de RX issus d'un accélérateur VARIAN : influence du paramétrage des électrons initiaux

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The Mojette Transform: Discrete Angles for Tomography

International audienceIn this paper, a discrete geometry way to generate projection and backprojection operators useful for tomographic reconstruction schemes is presented using the Mojette transform. A generic pixel model helps to links the discrete plane to physical rays. A completely discrete exact BP-F algorithm is presented and two other (direct and iterative) methods also derived to solve the tomographic problem