Heuristical Cone Beam Computed Optics
Résumé
Imaging a three-dimensional scene from a set of optical data is crucial for many applications, and is still an academical challenge. A new high-performant heuristic is emerging to solve this problem, from a set of cone beam reflective projections. The basis is visualizing appropriately a 3D heuristical reconstruction. The reconstruction step is the so-called reflective tomography: it rests on the filtered backprojection from Computed Tomography. The visualization step is based on volume rendering: the Maximum Intensity Projection. Combining these two steps is an original computational method to get new images of the initial reflective scene. Several questions concerning the validity of this new heuristic have emerged. Giving a mathematical meaning to the filtered backprojection of reflective projections is an open problem. Also controlling quantitatively the reconstruction and the obtained renderings has never been done. To answer such questions, we propose a new mathematical framework for the description of reflective tomography, and we design new criterions to check the amount of true informations in the renderings. We illustrate several properties of the method, by the means of a wide variety of numerical tests, including a real case. We show in particular that the images generated by the process are contrasted representations of the surfaces of the initial scene. This paper validates reflective tomography and the full heuristic as general computational imaging methods. The main perspective is the design of a device for real-time high-resolution 3D imaging in optics, useful for the recognition of occluded objects emitting countermeasurements.
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