The Gradient and laplacien filtered back projection operators

Abstract : This paper presents a new method, based on the Filtered Back Projection technique (FBP) to compute directly the values of the gradient and the laplacien of an X-Ray image. We propose a way to pre-process the raw data that allow us to compute directly the reconstructed values of the gradient or of the laplacien at any location in the plane (defined with real coordinates) without reconstructing an image of the absorption coefficients. The reconstructed values of the gradient and of the laplacien correspond to the exact mathematical definition of the differentials of the image and do not imply the use of a band limited filter depending on a constant s, as proposed previously by other authors. For noisy data, we propose also an extension of existing FBP techniques, adapted to the computation of the gradient and of the laplacien. At last, we show how to use those new algorithms to perform the segmentation of a slice, without image reconstruction. Images of the reconstructed gradient, laplacien and segmented objects are presented.
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Rapport
[Research Report] RR-1787, INRIA. 1992, pp.18
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https://hal.inria.fr/inria-00077027
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Soumis le : lundi 29 mai 2006 - 11:55:35
Dernière modification le : vendredi 25 mai 2018 - 12:02:06
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Jean-Philippe Thirion. The Gradient and laplacien filtered back projection operators. [Research Report] RR-1787, INRIA. 1992, pp.18. 〈inria-00077027〉

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