Front propagation and phase field theory
SIAM Journal on Control and Optimization
Geometrical image segmentation by the Allen-Cahn equation
Applied Numerical Mathematics
Automated vision system for localizing structural defects in textile fabrics
Pattern Recognition Letters
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Phase field models provide a well-established framework for the mathematical description of free boundary problems for image segmentation. In phase field models interfaces represent edges of jacquard images and the determination of the edges of jacquard images is the main goal of image segmentation. In this paper, the phase field model was applied to segment and recognize pattern structures of jacquard images. The segmentation was performed in two major steps. Firstly, a pattern extraction and representation was performed by an adaptive mesh generation scheme. For the conjugate gradient method has been successfully used in solving the symmetric and positive definite systems obtained by the finite element approximation of energy functionals, a novel conjugate gradient algorithm was adapted to the minimization of energy functional of discrete phase model. Experimental results show efficiency of our approach.