Abstract: The study of planar simple closed curves (or "2D shapes") and their similarities is a central problem in the field of computer vision. It arises in the task of characterizing and classifying objects from their observed silhouette. Defining natural distance between 2D shapes creates a metric on the infinite-dimensional space of shapes. In this talk I will describe one particular metric, which comes from the conformal mapping of the 2D shapes, via the theory of Teichm\"uller spaces. In this space every simple closed curve (or a 2D shape) is represented by a smooth self-map of a circle. I will talk about a specific class of soliton-like geodesics on the space of shapes, called teichons. Some numerical examples of geodesics and effects of the curvature will be demonstrated.