Semi-Differential Invariants for Recognition of Albebraic Curves

Abstract

This paper studies the recognition of low-degree polynomial curves based on minimal tactile data. Differential and semi-differential invariants have been derived for quadratic curves and special cubic curves that are found in applications. Such an invariant, independent of translation and rotation, is computed from the local geometry at up to three points on a curve. Recognition of the curve reduces to invariant verification with its canonical parametric form determined along the way. In addition, the contact locations are found on the curve, thereby localizing it relative to the touch sensor. Simulation results support the method in the presence of small noise. Preliminary experiments have also been carried out. The presented work distinguishes itself from traditional model-based recognition in its ability to simultaneously recognize and localize a shape from one of several classes, each consisting of a continuum of shapes, by the use of local data.