Structure from Motion refers to the process of estimating the camera motion and the rigid or deforming three-dimensional structure from image measurements taken over a period of time. The problem is the one of the most difficult problem in the field of Computer Vision and many researchers have worked on it.

In this project, we reduce Structure from Motion Problem into an optimization problem in a Shape Space with a Riemannian metric which discourages non-isometric deformations. This converts the problem into a non-convex optimization problem which is applied on multiple consecutive frames of image data. We also propose another isometry based purely geometrical approach which takes one frame at a time and gives a good initialization for our non-convex optimization.

Keywords: Structure from motion (SFM), Isometry, Riemannian Geometry, Shape Space, Isometric Deformations.