Features in Scale Space: Progress on the 2D 2nd Order Jet

We present theoretical and computational results that develop Koenderink's theory of feature analysis in human vision [1,7]. Employing a scale space framework, the method aims to classify image points into one of a limited number of feature categories on the basis of local derivative measurements up to some order. At the heart of the method is the use of a family of functions, members of which can be used to account for any set of image measurements. We will show how certain families of simple functions naturally induce a categorical structure onto the space of possible measurements. We present two such families suitable for 1D images measured up to 2nd order, and various results relevant to similar analysis of 2D images.