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<p>A technique for constructing a canonical surface parameterization in terms of lines of curvature is presented. Two methods of computing the canonical invariant representation are also presented. In the first method, a static instance of the controlled continuity spline is used for the stabilizer. Ways to modify it to reflect a change of parameters to the lines of curvature are described. In the second method, the dynamic instance of the controlled continuity spline called the deformable model is used. A force field defined in terms of the principal vectors is synthesized and applied to the parameter curves of the deformable model to coerce them along the lines of curvature. In essence, any transformation of parameters requires a modification of the stabilizer in the first method, whereas in the second method, it is tantamount to synthesizing a new force field. Experimental results with real and synthetic range data are included.</p>
curvature lines; active models; invariant surface reconstruction; canonical invariant representation; controlled continuity spline; deformable model; force field; principal vectors; image reconstruction; invariance; splines (mathematics)

R. Malladi and B. Vemuri, "Constructing Intrinsic Parameters with Active Models for Invariant Surface Reconstruction," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 668-681, 1993.
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