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Monotonicity Prior for Cloud Tomography

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Computer Vision – ECCV 2020 (ECCV 2020)

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Abstract

We introduce a differentiable monotonicity prior, useful to express signals of monotonic tendency. An important natural signal of this tendency is the optical extinction coefficient, as a function of altitude in a cloud. Cloud droplets become larger as vapor condenses on them in an updraft. Reconstruction of the volumetric structure of clouds is important for climate research. Data for such reconstruction is multi-view images of each cloud taken simultaneously. This acquisition mode is expected by upcoming future spaceborne imagers. We achieve three-dimensional volumetric reconstruction through stochastic scattering tomography, which is based on optimization of a cost function. Part of the cost is the monotonicity prior, which helps to improve the reconstruction quality. The stochastic tomography is based on Monte-Carlo (MC) radiative transfer. It is formulated and implemented in a coarse-to-fine form, making it scalable to large fields.

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Notes

  1. 1.

    The factor \(Q_\text {eff}(r)\) depends on the wavelength \(\lambda \). For clouds, typically \(r\gg \lambda \). Then, it is reasonable to neglect the dependency of \(Q_\text {eff}\) on r and \(\lambda \) [35].

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Acknowledgments

We thank Ilan Koren, Eshkol Eytan Liebeskind, and Tom Dror-Schwartz for useful discussions. We thank Johanan Erez, Ina Talmon and Daniel Yagodin for technical support. Yoav Schechner is the Mark and Diane Seiden Chair in Science at the Technion. He is a Landau Fellow - supported by the Taub Foundation. His work was conducted in the Ollendorff Minerva Center. Minvera is funded through the BMBF. This research is funded by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No 810370: CloudCT). Aviad Levis is a Zuckerman Postdoctoral Fellow.

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Authors and Affiliations

  1. Viterbi Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel

    Tamar Loeub, Vadim Holodovsky & Yoav Y. Schechner

  2. Computing and Mathematical Sciences Department, California Institute of Technology, Pasadena, CA, USA

    Aviad Levis

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  1. Tamar Loeub
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  2. Aviad Levis
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  4. Yoav Y. Schechner
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Correspondence to Tamar Loeub , Aviad Levis , Vadim Holodovsky or Yoav Y. Schechner .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Andrea Vedaldi

  2. Graz University of Technology, Graz, Austria

    Horst Bischof

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Thomas Brox

  4. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan-Michael Frahm

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Loeub, T., Levis, A., Holodovsky, V., Schechner, Y.Y. (2020). Monotonicity Prior for Cloud Tomography. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12363. Springer, Cham. https://doi.org/10.1007/978-3-030-58523-5_17

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