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<p>An approach for enforcing integrability, a particular implementation of the approach, an example of its application to extending an existing shape-from-shading algorithm, and experimental results showing the improvement that results from enforcing integrability are presented. A possibly nonintegrable estimate of surface slopes is represented by a finite set of basis functions, and integrability is enforced by calculating the orthogonal projection onto a vector subspace spanning the set of integrable slopes. The integrability projection constraint was applied to extending an iterative shape-from-shading algorithm of M.J. Brooks and B.K.P. Horn (1985). Experimental results show that the extended algorithm converges faster and with less error than the original version. Good surface reconstructions were obtained with and without known boundary conditions and for fairly complicated surfaces.</p>
convergence; integrability; shape from shading; surface slopes; orthogonal projection; vector subspace spanning; surface reconstructions; computerised pattern recognition; computerised picture processing

R. Framkot and R. Chellappa, "A Method for Enforcing Integrability in Shape from Shading Algorithms," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 10, no. , pp. 439-451, 1988.
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