Shapes: Their Clustering and Evolution

将相似的对象划分为互斥的组是知识发现的最基本方法之一。在现代之前，世界主要是定性研究，定性分组被用来从宇宙中提取知识。例如，亚里士多德将生物体分为两类，植物和动物，并根据动物的运动方式将其分为三类：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，即今天的银河系。门捷列夫通过对具有相似化学特性的元素进行分组发现了元素周期表。达尔文通过对生物体进行分组来研究物种的进化。现代测量系统允许收集大量数据。聚类分析或聚类是指在数据可用的情况下将相似主题分组的方法。我们的目标是开发聚类方法，用于分析许多数据集，但我们专门针对3D图像数据。如今，3D测量是可行的，并广泛应用于医学，计算机视觉，宇宙学等，我们建议开发定量工具分组的3D形状和跟踪其演变，通过时间。已知癌细胞在癌症发展的早期阶段变形。由于细胞形状的数据是目前可用的，我们的目标是使用这种方法来分离这样的细胞。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.