Singularity theory has long played a key role in the study of dynamical systems. Much like assessing the stability of a control system by studying the trajectory of its
poles as a feedbak system, we extract the topological information of an object, viewed as a 2-manifold, by properly defining on it a function h(x,y) and by tracking its
critical points. Upon ensuring a pose-independent graphical representation for the object, its geometrical information is captured and encoded as weights on the graph. The resulting weighted graph representation is sufficient for classification and/or reconstruction if necessary.