How Well Do We Know Europa’s Topography? An Evaluation of the Variability in Digital Terrain Models of Europa

Jupiter’s moon Europa harbors one of the most likely environments for extant extraterrestrial life. Determining whether Europa is truly habitable requires understanding the structure and thickness of its ice shell, including the existence of perched water or brines. Stereo-derived topography from images acquired by NASA Galileo’s Solid State Imager (SSI) of Europa are often used as a constraint on ice shell structure and heat flow, but the uncertainty in such topography has, to date, not been rigorously assessed. To evaluate the current uncertainty in Europa’s topography we generated and compared digital terrain models (DTMs) of Europa from SSI images using both the open-source Ames Stereo Pipeline (ASP) software and the commercial SOCET SET® software. After first describing the criteria for assessing stereo quality in detail, we qualitatively and quantitatively describe both the horizontal resolution and vertical precision of the DTMs. We find that the horizontal resolution of the SOCET SET® DTMs is typically 8–11× the root mean square (RMS) pixel scale of the images, whereas the resolution of the ASP DTMs is 9–13× the maximum pixel scale of the images. We calculate the RMS difference between the ASP and SOCET SET® DTMs as a proxy for the expected vertical precision (EP), which is a function of the matching accuracy and stereo geometry. We consistently find that the matching accuracy is ~0.5 pixels, which is larger than well-established “rules of thumb” that state that the matching accuracy is 0.2–0.3 pixels. The true EP is therefore ~1.7× larger than might otherwise be assumed. In most cases, DTM errors are approximately normally distributed, and errors that are several times the derived EP occur as expected. However, in two DTMs, larger errors (differences) occur and correlate with real topography. These differences primarily result from manual editing of the SOCET SET® DTMs. The product of the DTM error and the resolution is typically 4–8 pixel2 if calculated using the RMS image scale for SOCET SET® DTMs and the maximum images scale for the ASP DTMs, which is consistent with recent work using martian data sets and suggests that the relationship applies more broadly. We evaluate how ASP parameters affect DTM quality and find that using a smaller subpixel refinement kernel results in DTMs with smaller (better) resolution but, in some cases, larger gaps, which are sometimes reduced by increasing the size of the correlation kernel. We conclude that users of ASP should always systematically evaluate the choice of parameters for a given dataset.

Evaluating Stereo Digital Terrain Model Quality at Mars Rover Landing Sites with HRSC, CTX, and HiRISE Images

We have used high-resolution digital terrain models (DTMs) of two rover landing sites based on mosaicked images from the High-Resolution Imaging Science Experiment (HiRISE) camera as a reference to evaluate DTMs based on High-Resolution Stereo Camera (HRSC) and Context Camera (CTX) images. The Next-Generation Automatic Terrain Extraction (NGATE) matcher in the SOCET SET and GXP® commercial photogrammetric systems produces DTMs with good (small) horizontal resolution but large vertical error. Somewhat surprisingly, results for NGATE are terrain dependent, with poorer resolution and smaller errors on smoother surfaces. Multiple approaches to smoothing the NGATE DTMs give similar tradeoffs between resolution and error; a 5 × 5 lowpass filter is near optimal in terms of both combined resolution-error performance and local slope estimation. Smoothing with an area-based matcher, the standard processing for U.S. Geological Survey planetary DTMs, yields similar errors to the 5 × 5 filter at slightly worse resolution. DTMs from the HRSC team processing pipeline fall within this same trade space but are less sensitive to terrain roughness. DTMs produced with the Ames Stereo Pipeline also fall in this space at resolutions intermediate between NGATE and the team pipeline. Considered individually, resolution and error each varied by approximately a factor of 2. Matching errors were 0.2–0.5 pixels but most results fell in the 0.2–0.3 pixel range that has been stated as a rule of thumb in multiple prior studies. Horizontal resolutions of 10–20 image pixels were found, consistently greater than the 3–5 pixel spacing generally used for stereo DTM production. Resolution and precision were inversely correlated; their product varied by ≤20% (4–5 pixels squared). Refinement of the stereo DTM by photoclinometry can yield quantitative improvement in resolution (more than a factor of 2), provided that albedo variations over distances smaller than the stereo DTM resolution are not too severe. We offer specific guidance for both producers and users of planetary stereo DTMs, based on our results.