This paper presents an original approach for shape-based analysis of ancient Maya hieroglyphs based on an interdisciplinary collaboration between computer vision and archaeology. Our work is guided by realistic needs of archaeologists and scholars who critically need support for search and retrieval tasks in large Maya imagery collections. Our paper has three main contributions. First, we introduce an overview of our interdisciplinary approach towards the improvement of the documentation, analysis, and preservation of Maya pictographic data. Second, we present an objective evaluation of the performance of two state-of-the-art shape-based contextual descriptors (Shape Context and Generalized Shape Context) in retrieval tasks, using two datasets of syllabic Maya glyphs. Based on the identification of their limitations, we propose a new shape descriptor named HOOSC, which is more robust and suitable for description of Maya hieroglyphs. Third, we present what to our knowledge constitutes the first automatic analysis of visual variability of syllabic glyphs along historical periods and across geographic regions of the ancient Maya world via the HOOSC descriptor. Overall, our approach is promising, as it improves performance on the retrieval task, is successfully validated under an epigraphic viewpoint, and has the potential of offering both novel insights in archaeology and practical solutions for real daily scholar needs.