Shapes: Their Clustering and Evolution

将相似的对象分组为互斥的组是知识发现的最基本方法之一。在近代以前，人们对世界的研究大多是定性的，用定性分组的方法从宇宙中提取知识。例如，亚里士多德将生物分为植物和动物两类，并根据动物的运动方式将它们分为三类：行走、飞行或游泳。伽利略利用恒星群运动的相似性，发现它们位于同一个星系，也就是今天所说的银河系。门捷列夫把化学性质相似的元素分组，发现了元素周期表。达尔文通过对生物体进行分类来研究物种的进化。现代测量系统可以收集大量数据。聚类分析或聚类是指在有数据的情况下对相似的对象进行分组的方法。我们的目标是开发对许多数据集分析有用的聚类方法，但我们特别针对3D图像数据。目前，三维测量在医学、计算机视觉、宇宙学等领域具有可行性和广泛的应用。我们建议开发量化工具来分组3D形状并跟踪它们随时间的演变。众所周知，癌细胞在癌症发展的早期阶段会变形。由于目前细胞的形状数据是可用的，我们的目标是用这种方法分离这种细胞。预测更复杂的生物和物理对象，如身体、面部和星系，在生物学、犯罪学和宇宙学中有直接的应用。

Grouping similar objects into mutually exclusive groups is one of the most fundamental methods of knowledge discovery. Before the modern era the world was studied mostly qualitatively, and qualitative grouping was used to extract knowledge from the universe. For example, Aristotle divided living organisms into two groups, plants and animals, and divided animals into three groups according to how they moved: walking, flying, or swimming. Galileo used the similarity of movement of groups of stars and discovered that they are positioned in the same galaxy, which today is called the Milky Way. Mendeleev discovered the periodic table by grouping elements having similar chemical characteristics. Darwin studied the evolution of species by grouping biological bodies.Modern measurement systems allows collecting massive data. Cluster analysis or clustering refers to methods of grouping similar subjects while data are available. We aim to develop clustering methodologies useful for analysis of many data sets, but we specifically target 3D image data. Nowadays 3D measurement are feasible and widely applied in medicine, computer vision, cosmology, etc. We propose to develop quantitative tools for grouping 3D shapes and tracking their evolution through time. It is known that cancerous cells deform at the early stage of the cancer development. As the cell shape data are available nowadays, we aim to isolate such cells using this method. Predicting more complicated biological and physical objects such as body, face, and galaxy has immediate applications in biology, criminology, and cosmology.