Tactile recognition of algebraic shapes using differential invariants

This paper studies the recognition and localization of 2-D shapes bounded by low-degree polynomial curve segments based on minimal tactile data. We have derived differential invariants for quadratic curves and two special classes of cubic curves. Such an invariant, independent of translation and rotation, is computed from the local geometry at any two points on the curve. Recognition of a curve class becomes verifying the corresponding invariant with more than one pairs of data points. Next, the actual curve is determined in its canonical parametric form using the same tactile data. Finally, the contact locations on the curve are computed, thereby localizing the shape completely relative to the touching hand. Simulation results support the working of the method in the presence of small noise, although real experiments need to be carried out in the future to demonstrate its applicability. The presented work distinguishes from traditional model-based recognition in its ability to simultaneously recognize as well as localize a shape from one of several classes, each consisting of a continuum of shapes.