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The International Journal of Robotics Research
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Reconstructing the Shape of a Deformable Membrane from Image Data

Nicola J. Ferrier

Mechanical Engineering Department, University of Wisconsin–Madison, 1513 University Avenue, Madison, WI 53706 USAferrier{at}engr.wisc.edu

Roger W. Brockett

Division of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138 USA

In this paper, we study the problem of determining a mathematical description 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 undeformed configuration of the membrane, and a model for the membrane mechanics. The method of re construction is based on the principle that the shape assumed by the membrane will minimize the elastic energy stored in the membrane subject 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 first application of these ideas, comes from tactile sensing. Experimental results affirm that this approach can be very effective in this context.

Key Words: membrane mechanics • soft fingers • imaging shape

The International Journal of Robotics Research, Vol. 19, No. 9, 795-816 (2000)
DOI: 10.1177/02783640022067184
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