Statistical biases and errors inherent in photoclinometric surface slope estimation with natural light
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Bertsatos_Makris_manuscript_revised2.pdf
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Author(s)
Bertsatos, Ioannis
Makris, Nicholas
Date Issued
March 2010
Journal
Icarus
Publisher
Elsevier
Citation
Bertsatos, Ioannis, and Nicholas C. Makris. “Statistical Biases and Errors Inherent in Photoclinometric Surface Slope Estimation with Natural Light.” Icarus 208, no. 2 (August 2010): 798-810.
Version
Author's final manuscript
Abstract
Photoclinometry is the most common method used to obtain high-resolution topographic maps of planetary terrain. We derive the likelihood function of photoclinometric surface slope from (1) the probability distribution of the measured photon count of natural sunlight through a Charge-Coupled Device (CCD) including uncertainty due to camera shot noise, camera read noise, small-scale albedo fluctuation and atmospheric haze, and (2) a photometric model relating photocount to surface orientation. We then use classical estimation theory to determine the theoretically exact biases and errors inherent in photoclinometric surface slope and show when they may be approximated by asymptotic expressions for sufficiently high sample size. We show how small-scale albedo variability often dominates biases and errors, which may become an order of magnitude larger than surface slopes when surface reflectance has a weak dependence on surface tilt. We provide bounds on the minimum possible error of any unbiased photoclinometric surface slope estimate, and compute the sample sizes necessary to constrain errors within desired design thresholds.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.icarus.2010.03.019
