The extruded generalized cylinder: a deformable model for object recovery

There is increasing interest in the recovery of generalized cylinders (GCs) with curved spines. However, existing formulations of such GCs, for example those based an the Frenet-Serret frame or the tube model, suffer serious drawbacks: discontinuities, a lack of expressive power, ”narrowing” in the plane normal to the spine, non-intuitive twisting behavior, and/or off-axis nonorthogonality of their local coordinate systems. We discuss some of the problems associated with the non-orthogonality of the coordinate system based on the Frenet-Serret frame. This non-orthogonality is induced by torsion effects and we show how to correct for it. We then introduce a new model, the extruded GC (EGC) model, which overcomes all the problems mentioned above. For complex axes, the EGC model is also simpler to understand and use than existing models. The EGC model is further extended by including local surface deformations. Recovery of the deformable EGC via a physically-motivated paradigm is demonstrated on pre-segmented data from a human carotid artery