Geometric Analysis for Classification and Reassembly of Broken Bones

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The reassembly of broken objects is a fundamental issue in many real-world applications. The goal of this project is to apply modern machine learning and geometric tools to the problems of classification and automated reassembly of broken bone fragments from an archaeological context, to determine agents of breakage (e.g., carnivore, hominin, etc.,), improve taxonomic identifications, and better understand site formation processes through spatial analysis of refits. The anthropological implications are expected to impact the study of early human origins and dispersal, prehistory, culture, predator avoidance, and social organization -- hunting, scavenging, food provisioning, etc. The project relies on samples and data generated both locally by known agents and through ongoing field work in Dmanisi, Georgia; if successful, these methods can be applied to archaeological sites from all times around the world. The potential impact of success is underscored by the April, 2017 announcement that, based on the geometry of broken mastodon bones, humans settled the Americas 100,000 years earlier than the standard estimates of 30-40,000 years ago, although this claim remains highly controversial in the field. Accurate and precise methods of determining the agent of breakage have not yet been completely worked out by archaeologists, and hence a reassessment of their bone analysis would be of supreme interest. Besides zooarchaeological applications, potential areas of significant impact include computer-aided and virtual reassembly of other archaeological objects (pottery, statuary, lithics and tools, etc.), paleontology (dinosaurs and other fossils), art restoration, and computer-assisted surgery, where the mathematical techniques can aid the surgeon to both plan and undertake an operation while minimizing the invasiveness and impact on the patient. Other areas where these techniques have already had some impact include the reassembly of jigsaw puzzles, shredded documents, and whole histological sections from digitized tissue fragments, as well as the diagnosis of cancer in breast tumors and the distinguishing of moles from melanomas. Graduate and undergraduate students participate in the research.The project seeks to adapt and extend known geometric methods, data analysis, and numerical schemes, particularly those based on continuous and discrete invariant signatures, to the problem of analyzing and reconstructing broken solid objects, with a particular emphasis on bone fragments. Notable success in the automatic reassembly of non-pictorial jigsaw puzzles and broken surfaces, e.g., egg shells, using differential invariant signatures, suggests that one of the key goals of the project, the three-dimensional solid object reconstruction problem, is attainable. In addition, new (to anthropological field work) geometric tools of surface geometry -- principal curvatures, torsion and curvature of three-dimensional break curves, histogram and other discrete integral invariants -- are applied to analyze breakage geometry, starting with controlled samples of ungulate (elk, cow, and goat) bones that have been broken by humans using stone tools and by animals (hyenas in the Milwaukee County Zoo and the Irvine Zoo in Chippewa Falls), in preparation for the eventual analysis of field samples from Dmanisi and possibly other sites around the world, such as Olduvai Gorge in Tanzania and The Cradle of Humankind in South Africa. This analysis is used to develop machine learning algorithms, both fully supervised and semi-supervised, for classifying bone fragments based on agent of breakage. We map the bone fragments into feature spaces via computation of histograms of geometric invariants, and train a machine learning algorithm, such as k-nearest neighbors or support vector machine classifiers, to distinguish between different agents of breakage. The controlled samples of ungulate bones broken by humans are used as training data, and field data from the Dmanisi site are used as testing data. Graduate and undergraduate students participate in the research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.