Involvement of altimetric information into planet surface relief reconstruction from a set of images

Abstract

Introduction: The photoclinometric method for surface topography reconstruction from images using known dependence of the facet brightness on its orientation was proposed by Van Diggelen in 1951 [1]. The method includes calculation of topography slope fields using available images and consequent solution of equations shown in [1] that gives height distribution over the surface area under study. This method is still widely used (for example, [2, 3]), though in its initial (simplest) formulation [1] it is a mathematically incorrectly posed problem (as shown in [4]).More accurate mathematical formulation of the problem for the topography reconstruction from images was proposed in [4], further improvements of the method were shown in [5,6], and possible errors of relief reconstruction were discussed in [7].With an improved photoclinometry (based on the accurate mathematical formulation of the problem in the frame of the Bayesian statistical approach), surface heights can be calculated up to an unknown constant. The height accuracy also depends on the noise level of image registration. To obtain the true surface heights, the relief reconstruction from images using the improved photoclinometry has to be accompanied with an account of a priori known heights in sites located in the surface area under study.Height measurements by altimeter are the most reliable method to get the true surface topography. However usually sparse net of measured points does not give detailed topography information. Altimetry data usually have high accuracy. They seem to be the most promising for the use together with relief reconstruction by the improved photoclinometry allowing calculation of true surface relief (advantage of the altimeter) with the spatial resolution as high as the resolution of initial images (advantage of the photoclinometry).Method: The main point of the Bayesian statistical approach to the problem of the relief reconstruction from images [8,9] is maximization of the posteriori density of relief probability. Assuming true relief and noise of image registration to be realizations of stationary Gaussian processes the solution of the problem is fmally reduced to minimization of the discrepancy between calculated relief and original images. Involvement of altimetry information means that the minimization procedure should include additional conditions: heights calculated during reconstruction and those measured by altimeter in corresponding sites should be equal. In general, this leads to some complication of the mathematical problem.If the accuracy of altimetry measurements is much higher then the accuracy of the photoclinometry, the problem for relief reconstruction is simpler to solve. Similar to the approach discussed in [4], the problem of relief reconstruction from images with an account of altimetry data leads to the Poisson equation with some modification of boundary conditions. The boundary now includes points represented the area boundary and points (sites) inside the area where altimeter measurements were made.At t...