The first observations of extraterrestrial environments will most likely be in the form of digital images. Given an image of a rock that contains layered structures, is it possible to determine whether the layers were created by life (biogenic)? While conclusive judgments about biogenicity are unlikely to be made solely on the basis of image features, an initial assessment of the importance of a given sample can inform decisions about follow-up searches for other types of possible biosignatures (e.g., isotopic or chemical analysis). In this study, we evaluated several quantitative measures that capture the degree of complexity in visible structures, in terms of compressibility (to detect order) and the entropy (spread) of their intensity distributions. Computing complexity inside a sliding analysis window yields a map of each of these features that indicates how they vary spatially across the sample. We conducted experiments on both biogenic and abiogenic terrestrial stromatolites and on laminated structures found on Mars. The degree to which each feature separated biogenic from abiogenic samples (separability) was assessed quantitatively. None of the techniques provided a consistent, statistically significant distinction between all biogenic and abiogenic samples. However, the PNG compression ratio provided the strongest distinction (2.80 in standard deviation units) and could inform future techniques. Increasing the analysis window size or the magnification level, or both, improved the separability of the samples. Finally, data from all four Mars samples plotted well outside the biogenic field suggested by the PNG analyses, although we caution against a direct comparison of terrestrial stromatolites and martian non-stromatolites.