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<p>—Curved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys. Existing curvature estimators fail here. The characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvature-dependent confidence measure. Using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature. Minimizing the residual energy yields a closed-form solution for the local curvature estimate and the corresponding confidence measure. We show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns.</p>

P. Verbeek, L. v. Vliet, J. v. Weijer and M. v. Ginkel, "Curvature Estimation in Oriented Patterns Using Curvilinear Models Applied to Gradient Vector Fields," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 23, no. , pp. 1035-1042, 2001.
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