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').
Gregory Dudek, Gregory Dudek,
"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