Comparison of ground- and aerial-based approaches for quantifying polygonal terrain network geometry on Earth and Mars via spatial point pattern analysis

Recently, a particular statistical method - spatial point pattern analysis (SPPA) - has been introduced as an effective means by which qualitative, observable variations in polygonal terrain network arrangements on Earth and Mars can be quantified. A number of ground- and aerial-based techniques are available from which to derive the required input data: the spatial (x-y) coordinates of all polygon trough intersections within the site. However, each of the data collection methods may contain some level of error. Thus, the overarching question addressed by this research is: “how are the results of SPPA affected by the method by which the input data were generated?” At two polygonal terrain sites in the Canadian High Arctic, we performed ground-based surveys using differential and non-differential Global Positioning Systems (GPS) as well as photogrammetric analysis of aerial and satellite images of varying resolution to determine the trough intersection coordinates. It was found that the most robust statistical results were produced when using data from a combination of differential GPS surveys and high-resolution (∼0.25 m/pixel) aerial images. Images of pixel size ≥1 m were found to be unsuitable for this type of analysis. With respect to the investigation of similar Martian landforms, HiRISE and MOC images of polygonal terrain sites in southwestern Utopia Planitia were analyzed. Our results show that it is strongly preferable to perform SPPA using HiRISE images, though an empirical model is outlined that could be used to correct for errors arising from the reduced resolution inherent to MOC images.     

Identifying degrees of freedom in pushbroom bundle adjustment

An analytical method of detecting and enumerating degrees of freedom (DOF) in bundle adjustment (BA) is developed, and used to analyze several scene geometries for pushbroom cameras. While it is well recognized in the photogrammetric community that BA can be poorly constrained, especially with pushbroom imagery, the literature is absent of techniques to study the DOF in BA except through numerical analysis, which does not delineate them except through the suggestion of their existence in degraded results. The analytical methods presented here provide insight into the DOF. The method is based on finding the singular values, and the associated singular directions, of a Hessian matrix from the minimization process in BA. These directions are scrutinized as possible DOF along which the minimal cost of BA will not change from the true solution. To demonstrate the use of the methods six different scene geometries are analyzed, some of which are commonly employed by current remote sensing satellites. Several of the scene geometries are shown to have multiple DOF beyond the well known scaling and absolute position and orientation that are not recoverable from stereo imagery without exterior orientation control of the cameras or ground control points. As a simple example, the effects of these DOF images from the HiRISE camera on the Mars Reconnaissance Orbiter are used along with the associated ephemeris data to demonstrate possible distortions in the results of a terrain reconstruction problem.