The skeletonization of optical fringes with high density and high noise has been an open problem. We describe a skeletonization process for gray-scale optical fringe patterns with high density and high noise based on the gradient vector fields (GVFs). We derive the new oriented couple governing partial differential equations (PDEs) for calculating the GVFs of dense, noisy optical fringes based on the variational methods, in which the fringe orientation is taken into account fully. We test the proposed PDEs on a computer simulation and experimentally obtained fringe patterns, in which the fringes contain obvious high density regions and heavy noise, and compare them with related PDEs and the fringe extreme tracking method, respectively. The experimental results demonstrate that the new governing PDEs perform favorably.
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