Reconstructing the shape of a deformable membrane from image data

In this paper we study the problem of determining a mathematical descriptio n of the surface defined by the shape of a membrane based on an image of it and present an algorithm for reconstructing the surface when the membrane is deformed by unknown external elements. The given data are the projection on an image plane of markings on the surface of the membrane, the undeform ed configuration of the membrane, and a model for the membrane mechanics. T he method of reconstruction is based on the principle that the shape assume d by the membrane will minimize the elastic energy stored in the membrane s ubject to the constraints implied by the measurements. Energy minimization leads to a set of nonlinear partial differential equations. An approximate solution is found using linearization. The initial motivation, and our firs t application of these ideas, comes from tactile sensing. Experimental resu lts affirm that this approach can be very effective in this context.