This research deals with the decomposition and description of curved objects. In ongoing work, a new part description for curves and surfaces using a set of curvature-based minimization operators has been developed. The decomposition operation simultaneously performs data interpolation, data smoothing, and segmentation. The unification of these three stages results in a smoothing operation that is tightly coupled with the primitives to be used in subsequent object description. Each of the minimization operators, in addition to having a curvature tuning, has a different spatial sensitivity function. As a result, different possible descriptions of an object are produced and these capture information at multiple spatial scales. Each object is described by a small number of tokens based on differential geometric properties. The set of descriptors produced for a given object can be organized into an unusual form of nonlinear scale-space. The utility of such a scale-based description by way of two methods for the characterization (i.e., recognition) of two-dimensional objects via their multi- scale signature in terms of curvature-scale-space features is demonstrated. One method is based on graph matching by dynamic programming and the other based on statistical properties of scale space ('shape texture').
"Shape metrics from curvature-scale space and curvature-tuned smoothing", Proc. SPIE 1570, Geometric Methods in Computer Vision, (1 September 1991); doi: 10.1117/12.49976; https://doi.org/10.1117/12.49976