One of the classic problems in computer vision is recovering 3D structure from images. A class of techniques called "Structure from Motion" (SFM) attempt to do this while imposing as few restrictions on the scene and observer a possible. In particular, SFM recovers both the 3D structure of the scene and the relative position of the observer knowing neither; that is, images are uncalibrated. Despite its promise, SFM has yet to be widely used because existing techniques have serious limitations that restrict their use in real-world applications. These include sensitivity to noise, the inability to model true perspective projection and difficulty in handling occlusion.
In this talk I will present a new formulation of the SFM problem that attempts to address these deficiencies. I will introduce a novel vector-based representation for images and describe the fundamental constraints on the inverse projection problem. I will then describe an iterative refinement algorithm that alternatively optimizes the positions of features and images to quickly converge to an optimal solution - one that globally minimizes the observed error in all the images. This technique can be extended to an arbitrary number of features and images and is robust to noise, it can model true 3D perspective projection (indeed any geometric projection transformation in any dimension) and deals naturally with occlusion.