Application of Manifolds in Computer Vision: Representation and Recognition of Objects
In its broadest sense, computer vision tackles the problem of understanding the visual world from a spatio-temporal set of 2d (or 3d) electro-optical projections. These projections are images or videos captured from a single camera or a set of cameras that may have known or unknown relationships to each other in space or time. Although the captured data lies in very high dimensional spaces, the objects (or object classes) of interest can often lie on manifolds with a small intrinsic dimensionality. Thus, manifolds enter into computer vision in a natural way and capture intrinsic properties of objects (or object classes) – for example, their shape, appearance and/ or poses. It turns out that for a variety of problems in computer vision, it is useful to describe these objects using Riemmanian manifolds and to solve inverse problems on these manifolds. This talk will introduce the audience to a sampling from the rich array of such problems in computer vision. It will also provide some examples from the speaker’s research in the area of object recognition.