{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:56:12Z","timestamp":1777715772022,"version":"3.51.4"},"reference-count":33,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1177\/02783640022067184","type":"journal-article","created":{"date-parts":[[2004,12,17]],"date-time":"2004-12-17T20:23:10Z","timestamp":1103314990000},"page":"795-816","source":"Crossref","is-referenced-by-count":91,"title":["Reconstructing the Shape of a Deformable Membrane from Image Data"],"prefix":"10.1177","volume":"19","author":[{"given":"Nicola J.","family":"Ferrier","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, University of                         Wisconsin\u2013Madison, 1513 University Avenue, Madison, WI 53706 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roger W.","family":"Brockett","sequence":"additional","affiliation":[{"name":"Division of Engineering and Applied Sciences, Harvard University, 29                         Oxford Street, Cambridge, MA 02138 USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Akella, P., and Cutkosky, M. 1989. Manipulation with soft fingers: Modeling contacts and dynamics . Proceedings of the IEEE Int. Conference on Robotics and Automation, Scottsdale, AZ, pp. 764\u2013769 .","DOI":"10.1109\/ROBOT.1989.100076"},{"key":"atypb2","unstructured":"Beardsley, P., and Zisserman, A. 1995. Affine structure from motion . Proc. 4th Int. Conf. on Computer Vision, Boston, MA, pp. 58\u201364 ."},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Belhumeur, P. 1993. A binocular stereo algorithm for reconstructing sloping, creased, and broken surfaces in the presence of half-occlusion . Proc. 3th Int. Conf. on Computer Vision, Berlin, Germany, pp. 431\u2013438 .","DOI":"10.1109\/ICCV.1993.378184"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.6.001052"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Brockett, R. W. 1985. Robotic hand with rheological surfaces . Proceedings of the 1985 IEEE Conference on Robotics and Automaton, Philadelphia, PA, pp. 942\u2013946 .","DOI":"10.1109\/ROBOT.1985.1087360"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"Brockett, R. W. 1989. Least squares matching problems . Linear Algebra and Its Applications 124: 761\u2013777 .","DOI":"10.1016\/0024-3795(89)90675-7"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"Chang, D., and Cutkosky, M. 1995. Rolling with deformable fingertips . Proceedings of the IEEE Int. Conference on Intelligent Robots and Systems, Pittsburgh, PA, pp. 194\u2013199 .","DOI":"10.1109\/IROS.1995.526159"},{"key":"atypb8","unstructured":"Courant, R., and Hilbert, D. 1953. Methods of Mathematical Physics, vol. 1. New York: John Wiley ."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/10.1.1"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.2307\/2373037"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(86)90003-9"},{"key":"atypb12","unstructured":"Harris, C. 1992. Geometry from visual motion. In Active Vision, ed. A. Blake and A. Yuille, 263\u2013284. Cambridge, MA: MIT Press ."},{"key":"atypb13","unstructured":"Horn, B. 1986. Robot Vision. New York: McGraw-Hill ."},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"Hristu, D. 1999. Optimal Control with Limited Communication. Ph.D.thesis, Harvard University, Cambridge, MA.","DOI":"10.1016\/S0167-6911(99)00020-1"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1177\/027836499301200602"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.8.000377"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"Lipson, P., Yuille, A., Keeffe, D., Cavanaugh, J., Taaffe, J., and Rosenthal, D. 1990. Deformable templates for feature extraction from medical images. In Proc. 1st European Conference on Computer Vision, ed. O. Faugeras, 413\u2013417 New York: Springer-Verlag .","DOI":"10.1007\/BFb0014891"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00127170"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"Maekawa, H., Komoriya, K., and Tanie, K. 1992. Manipulation of an unknown object by multifingered hands with rolling contact using tactile feedback . Proceedings of the IEEE Int. Conference on Intelligent Robots and Systems, Raleigh, NC, pp. 1877\u20131882 .","DOI":"10.1109\/IROS.1992.601506"},{"key":"atypb20","unstructured":"Marsden, J. E., and Hughes, T. J. 1983. Mathematical Foundations of Elasticity. Englewood Cliffs, NJ: Prentice Hall ."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1177\/027836498800700302"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"Montana, D. 1989. The kinematics of contact with compliance . Proceedings of the IEEE Int. Conference on Robotics and Automation, Scottsdale, AZ, pp. 770\u2013774 .","DOI":"10.1109\/ROBOT.1989.100077"},{"key":"atypb23","unstructured":"Nowlin, W. 1991.\n                      Tactile Sensors with Compliant Manipulators\n                      . Ph.D. thesis, Harvard University, Cambridge, MA."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1177\/027836499401300101"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Perkins, W. 1978. A model-based system for industrial parts . IEEE Trans. Comp. 27(2): 126\u2013143 .","DOI":"10.1109\/TC.1978.1675046"},{"key":"atypb26","unstructured":"Son, J., Monteverde, E., and Howe, R. 1994. A tactile sensor for localizing transient events in manipulation . Proceedings of the IEEE Int. Conference on Robotics and Automation, San Diego, CA, pp. 471\u2013476 ."},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"Terzopoulos, D., Witkin, A., and Kass, M. 1987. Symmetry-seeking models and 3d object reconstruction . International Journal of Computer Vision 1: 211\u2013221 .","DOI":"10.1007\/BF00127821"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(88)90080-X"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/BF00129684"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1109\/34.99234"},{"key":"atypb31","unstructured":"Vemuri, V., and Karplus, W. J. 1981. Digital Computer Treatment of Partial Differential Equations. Englewood Cliffs, NJ: Prentice Hall ."},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.3.000297"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1990.2.1.1"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022067184","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022067184","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:16:18Z","timestamp":1777457778000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783640022067184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":33,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["10.1177\/02783640022067184"],"URL":"https:\/\/doi.org\/10.1177\/02783640022067184","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}