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.