LOCAL HEIGHT CALCULATION ERRORS IN THE PLANET SURFACE RELIEF RETRIEVED FROM IMAGES BY THE IMPROVED PHOTOCLINOMETRY METHOD

Subject and Purpose. In this work, the planet surface area relief is calculated using the Improved Photoclinometry Method (IPCM) and starting from a set of source images. Height deviations from the true relief altitudes are studied by computer simulation at small spatial scales (smaller than a quarter of the area’s size). We seek to estimate these "local" errors in surface heights and slopes using source images with different signal-to-noise ratios (SNRs). Methods and Methodology. The improved photoclinometry method calculates the most probable relief of a planet surface area from its images. Two optional techniques implement this method. The IPCM-F technique employs the optimum Fourier- transform-based fi ltering in the spatial frequency domain. The IPCM-T uses the finite diff erence method to solve the Poisson equation. Results. Computer experiments on retrieving the surface topography from the source images have shown that the higher the signal-to-noise ratio (SNR) of the initial image, the smaller the size of small-scale features that are reliably reproduced in shape. In the calculations by the IPCM-T technique, the smallest reliably reproduced features are four times the initial image resolution G at SNR ≥ 50 and five times at SNR = 10. With the IPCM-F, the relief features are reliably reproduced starting from spatial scales 9G (SNR ≥ 50) and 17G (SNR ≥ 10). With the IPCM-T, the worst local height error characterizing the smallest reliably reproduced surface features is 0.35σ0 (SNR = 1) and 0.17σ0 (SNR = 50), where σ0is the root-mean-square deviation of the modeled relief height. For both IPCM implementations, larger topographic objects are characterized by local height errors 0.01σ0 to 0.08σ0 (SNR = 50). Conclusions. It has been shown that the surface topography retrieval by the improved photoclinometry method from a set of images with SNR ≥ 50 reliably reproduces shapes of size features ≥ 4G (IPCM-T) and ≥ 9G (IPCM-F). For 8G to 64G size features, the retrieved height local errors are 0.004σ0 to 0.07σ0 (IPCM–T) and 0.01σ0 to 0.08σ0 (IPCM–F). To study smaller, 4G to 8G size features, the topography relief should be reconstructed using the IPCM-F upon the finite diff erence method.