Geometric Analysis for Classification and Reassembly of Broken Bones

破损物体的重组是许多现实应用中的一个基本问题。该项目的目标是将现代机器学习和几何工具应用于考古背景下的断骨碎片的分类和自动重组问题，以确定断骨的原因(例如，食肉动物、人等)，改进分类识别，并通过改装的空间分析更好地了解遗址形成过程。人类学方面的影响预计将影响对早期人类起源和扩散、史前、文化、避免捕食者和社会组织--狩猎、拾取、食物供应等--的研究。该项目依赖于已知代理人在当地和在佐治亚州德马尼西正在进行的实地工作产生的样本和数据；如果成功，这些方法可以应用于世界各地的考古遗址。2017年4月的声明突显了成功的潜在影响，该声明称，根据断掉的乳齿骨的几何形状，人类在美洲定居的时间比3万至4万年前的标准估计早了10万年，尽管这一说法在该领域仍存在极大争议。考古学家还没有完全确定断骨的准确和精确的方法，因此重新评估他们的骨骼分析将是最有意义的。除了动物考古应用，潜在的重大影响领域包括计算机辅助和虚拟重组其他考古物品(陶器、雕像、石器和工具等)、古生物学(恐龙和其他化石)、艺术修复和计算机辅助手术，其中数学技术可以帮助外科医生计划和进行手术，同时将对患者的侵入性和影响降至最低。这些技术已经产生了一些影响的其他领域包括从数字化组织碎片中重新组装拼图、粉碎的文档和整个组织切片，以及诊断乳腺肿瘤中的癌症和区分葡萄胎和黑色素瘤。研究生和本科生参与了这项研究。该项目试图使已知的几何方法、数据分析和数值方案，特别是基于连续和离散不变签名的方法，适应和扩展到分析和重建破碎的固体物体的问题，特别是骨骼碎片。在使用微分不变量签名自动重新组装非图画拼图和破碎表面(例如蛋壳)方面取得了显著的成功，这表明该项目的关键目标之一--三维实体重建问题是可以实现的。此外，(人类学野外工作)表面几何的新几何工具--三维断裂曲线的主曲率、挠率和曲率、直方图和其他离散积分不变量--被应用于分析断裂几何，从人类使用石器和动物(密尔沃基县动物园的鬣狗和奇佩瓦瀑布的欧文动物园的鬣狗)折断的有蹄类动物(麋鹿、牛和山羊)的受控样本开始，为从德马尼西和可能的世界其他地点(如坦桑尼亚的奥杜瓦伊峡谷和南非的人类摇篮)采集的野外样本的最终分析做准备。这种分析被用来开发基于破碎剂的机器学习算法，包括完全监督和半监督，用于骨碎片的分类。我们通过计算几何不变量的直方图将骨骼碎片映射到特征空间，并训练机器学习算法，如k-近邻或支持向量机分类器，以区分不同的断裂剂。人类折断的有蹄类骨骼的受控样本被用作训练数据，来自德马尼西遗址的现场数据被用作测试数据。研究生和本科生参与了这项研究。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.