With cedram.org version française Home Presentation Advanced Search All online articles Latest articles Search for an article Table of contents for this volume | Previous article | Next article Jean-Baptiste BelletMultiresolution greedy algorithm dedicated to reflective tomographySMAI-Journal of computational mathematics, 4 (2018), p. 259-296, doi: 10.5802/smai-jcm.35 Article PDF Class. Math.: 78A97, 94A12, 65B99, 65Y20Keywords: Computational optics, reconstruction, acceleration, complexity AbstractReflective tomography recovers the surfaces of a scene to be imaged, from optical images: a tomographic algorithm computes a full volumic reconstruction and then the surfaces are extracted from this reconstruction. For better performance, we would like to avoid computing accurately the full reconstruction, and we want to focus computations on the sought surfaces. For that purpose we propose an iterative multiresolution process. The initialization computes a coarse reconstruction, and the iterations refines it. To identify the voxels to be refined, we take advantage of the asymptotic behaviour of the reconstruction, with respect to its cut-off frequency: it discriminates the surfaces to be extracted. By the way the proposed algorithm is greedy: each iteration maximizes the accumulated intensity of the selected voxels, with prescribed volume. The combination of the complexity analysis and the numerical results shows that this novel approach succeeds in reconstructing surfaces and is relatively efficient compared with the standard method. These works pave the way towards accelerated algorithms in reflective tomography. They can be extended to a general class of problems concerning the determination of asymptotically discriminated sets, what is related to the computation of singular support of distributions. Bibliography[1] Jean-Baptiste Bellet, “Analyse asymptotique et géométrique de la tomographie réflective”, $<$hal-01571707$>$, 2017 [2] Jean-Baptiste Bellet & Gérard Berginc, “Reflective Filtered Backprojection”, Comptes rendus - Mathématique 354 (2016), p. 960-964 [3] I. Berechet & G. Berginc, Advanced algorithms for identifying targets from a three-dimensional reconstruction of sparse 3D Ladar data, in G. Berginc, ed., Optical Complex Systems: OCS11, 81720Z, Proc. of SPIE, 2011 [4] Stefan Berechet, Ion Berechet, Jean-Baptiste Bellet & Gérard Berginc, “Procédé de discrimination et d’identification par imagerie 3D d’objets d’une scène”, Patent WO2016097168 A1 2015 [5] G. Berginc, J.-B. Bellet, I. Berechet & S. Berechet, Optical 3D imaging and visualization of concealed objects, in Proc. SPIE, 2016 [6] G. Berginc & M. Jouffroy, Simulation of 3D laser systems, in Geoscience and Remote Sensing Symposium, 2009 IEEE International, IGARSS 2009, IEEE, 2009, p. 440-444 [7] G. Berginc & M. Jouffroy, “Simulation of 3D laser imaging”, PIERS Online 6 (2010) no. 5, p. 415-419 [8] Gérard Berginc, “Scattering models for 1-D–2-D–3-D laser imagery”, Optical Engineering 56 (2016) no. 3 Article[9] David T. Gering & W.M. Wells, Object modeling using tomography and photography, in Multi-View Modeling and Analysis of Visual Scenes, 1999.(MVIEW’99) Proceedings. IEEE Workshop on, IEEE, 1999, p. 11-18 [10] Henri Gouraud, “Continuous shading of curved surfaces”, IEEE transactions on computers 100 (1971) no. 6, p. 623-629 [11] Markus Henriksson, Tomas Olofsson, Christina Grönwall, Carl Brännlund & Lars Sjöqvist, Optical reflectance tomography using TCSPC laser radar, in Proc. SPIE, 2012 [12] Berthold Horn, Robot vision, MIT press, 1986 [13] F.K. Knight, S.R. Kulkarni, R.M. Marino & J.K. Parker, “Tomographic Techniques Applied to Laser Radar Reflective Measurements”, Lincoln Laboratory Journal 2 (1989) no. 2, p. 143-160 [14] Aldo Laurentini, “The visual hull concept for silhouette-based image understanding”, IEEE Transactions on pattern analysis and machine intelligence 16 (1994) no. 2, p. 150-162 [15] Charles Soussen & Jérôme Idier, 3D reconstruction of localized objects from radiographs and based on multiresolution and sparsity, in IEEE International Conference on Image Processing, IEEE, 2005, p. 744-747 [16] Greg Turk & Marc Levoy, Zippered polygon meshes from range images, in Proceedings of the 21st annual conference on Computer graphics and interactive techniques, ACM, 1994, p. 311-318 [17] J.W. Wallis & T.R. Miller, “Three-Dimensional Display in Nuclear Medicine and Radiology”, The Journal of Nuclear Medicine (1991), p. 534-546 © 2015SMAI Journal of Computational Mathematics ISSN 2426-8399 Papers are published under the licence Creative Commons CC BY-NC-ND 3.0