Department of Computer, Control and Management Engineering

Curvature,  as a descriptor of shape (e.g. describing the boundary of planar shapes) possesses a rare combination of good properties: It is intrinsic, intuitive, well defined, extensively studied and of an undisputed perceptual importance. However, there are at least two serious problems concerning its such use in computer vision: One has to do with noise. In a noisy curve, having, that is, high frequency Fourier components (hfFc) of no perceptual importance, the local nature of curvature restricts it in describing the noise itself rather than the underlying shape. Knowing whether hfFc of a curve represent noise or not, would require solving the harder problem of recognizing the object. Since hfFc might be defining for certain shapes or just noise in others, their presence in unrecognized (unknown) shapes is considered problematic, albeit they may present useful shape information. In practice, they are usually eliminated from the boundary of all shapes, by means of a blind step of smoothing, at the risk of losing useful discriminating shape information. Smoothing also distorts the shape's metrics in an unpredictable manner, a highly undesirable effect whenever certain "morphometric" measurements are defining for classification. Another problem in relation to curvature as a descriptor has to do with "meaningfulness". Even in noise free curves, the local nature of curvature doesn't permit any kind of "context" by means of which one could differentiate between points of similar curvature with respect to their perceptual characteristics on different parts of the curve. Behind both of these problems is curvature's local nature as It seems that any solution would have to defy the local definition of curvature.

In this talk  the local nature of curvature will be challenged at a theoretical level as an attempt to address the above problems based on an alternative Global definition of curvature will be discussed. The new concept of "noising" (as opposed to smoothing) emerges as a paradox and a new method for identifying vertices without even having to calculate curvature will be presented. Experiments with smooth and noisy KIMIA and MPEG silhouettes and a comparison to localized methods support the theoretical findings.