Space-time scene manifolds

The space of images is known to be a nonlinear sub-space that is difficult to model. This paper derives an algorithm that walks within this space. We seek a manifold through the video volume that is constrained to lie locally in this space. Every local neighborhood within the manifold resembles some image patch. We call this the scene manifold because the solution traces the scene outline. For a broad class of inputs the problem can be posed as finding the shortest path in a graph and can thus be solved efficiently to produce the globally optimal solution. Constraining appearance rather than geometry gives rise to numerous new capabilities. Here we demonstrate the usefulness of this approach by posing the well-studied problem of mosaicing in a new way. Instead of treating it as geometrical alignment, we pose it as an appearance optimization. Since the manifold is constrained to lie in the space of valid image patches, the resulting mosaic is guaranteed to have the least distortions possible. Any small part of it can be seen in some image even though the manifold spans the whole video. Thus it can deal seamlessly with both static and dynamic scenes, with or without 3D parallax. Essentially, the method simultaneously solves two problems that have been solved only separately until now: alignment and mosaicing.