Reflective tomography reconstructs a scene from calibrated reflective images, using algorithms from x-ray tomography. Many works on the subject are based on analytical formulas, such as the filtered backprojection. However, these formulas require constraints on the acquisition geometry, such as a circular rotation. We want to avoid such constraints; they may be seriously violated in some practical cases. To tackle this problem, we tune the algebraic reconstruction technique from x-ray tomography. More precisely, we look for a model of the scene such that the x-ray projections of the model approximate recorded calibrated reflective images. The model is computed by an iterative algebraic method: a Kaczmarz algorithm. In this way, we perform incremental supervised learning in optics, where the hypothesis space emulates reflective tomography. We get a flexible method for multiple-view reconstruction based on linear algebra. It accepts a general calibrated acquisition, such as several cameras arbitrarily located/oriented, with visible near-infrared wavelengths. It could reconstruct a scene using several devices simultaneously, such as air–ground cameras combined with ground–ground cameras. The relevance of the approach is numerically shown from calibrated CCD images of the Middlebury datasets. In particular, we get reconstructions from 16 views.
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