Interpolation in Discrete Single Figure Medial Objects

The discrete m-rep, a medial representation of anatomical objects made from one or more meshes of medial atoms, has many attractive properties for biomedical image analysis. The nonlinear nature of the m-rep parameters captures nonlinear deformations in anatomical objects such as twisting and bending. Most uses of m-reps require extending them to one or more continuous sheets of medial atoms. To guarantee that a continuous sheet of medial atoms does not fold, we propose an interpolation method on the medial atoms based on two medial shape operators. The radial shape operator describes the rate of swing of a medial atom’s spoke. The edge shape operator describes the rate of swing of a planar curve defining the object crest. The two shape operators generate interpolated internal and end atoms, and they join together smoothly. We show the application of our interpolation method on m-reps of synthetic and real-world objects.