Intrinsic dimension and a geometric approach to visual information processing

We will first give an overview on how we have applied differential geometry to study human vision and to improve computer-vision algorithms. Key questions are: what differential invariants should be used to describe image structure; what kind and what amount of information do these invariants encode? We will show that if the visual input is regarded as a hypersurface, the curved regions of that hypersurface determine the input uniquely although a representation by curvature is sparse. We believe that these questions can be well understood based on the concept of intrinsic dimension that refers to the number of locally used degrees of freedom.