# American Institute of Mathematical Sciences

November  2011, 16(4): 1055-1069. doi: 10.3934/dcdsb.2011.16.1055

## Feature extraction of the patterned textile with deformations via optimal control theory

 1 College of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong 3 Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong

Received  September 2010 Revised  April 2011 Published  August 2011

In handling textile materials, deformation is very common and is unavoidable. When the fabrics are dispatched for further feature extractions, it's necessary to recover the original shape for comparison with a standard template. This recovery problem is investigated in this paper. By introducing a set of recovered functions, the problem is formulated as a combined optimal control and optimal parameter selection problem, governed by the dynamical system of a set of two-dimensional control functions. After parameterization of the control functions, the problem is transformed into a nonlinear optimization problem, where gradient based optimization methods can be applied. We also analyze the convergence of the parameterization method. Several numerical examples are used to demonstrate the method.
Citation: Zhi Guo Feng, K. F. Cedric Yiu, K.L. Mak. Feature extraction of the patterned textile with deformations via optimal control theory. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1055-1069. doi: 10.3934/dcdsb.2011.16.1055
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##### References:
 [1] Scott Gordon. Nonuniformity of deformation preceding shear band formation in a two-dimensional model for Granular flow. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1361-1374. doi: 10.3934/cpaa.2008.7.1361 [2] Lars Lamberg, Lauri Ylinen. Two-Dimensional tomography with unknown view angles. Inverse Problems & Imaging, 2007, 1 (4) : 623-642. doi: 10.3934/ipi.2007.1.623 [3] Elissar Nasreddine. Two-dimensional individual clustering model. Discrete & Continuous Dynamical Systems - S, 2014, 7 (2) : 307-316. doi: 10.3934/dcdss.2014.7.307 [4] Jerzy Gawinecki, Wojciech M. Zajączkowski. Global regular solutions to two-dimensional thermoviscoelasticity. Communications on Pure & Applied Analysis, 2016, 15 (3) : 1009-1028. doi: 10.3934/cpaa.2016.15.1009 [5] Ibrahim Fatkullin, Valeriy Slastikov. Diffusive transport in two-dimensional nematics. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 323-340. doi: 10.3934/dcdss.2015.8.323 [6] Min Chen. Numerical investigation of a two-dimensional Boussinesq system. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1169-1190. doi: 10.3934/dcds.2009.23.1169 [7] Lihui Guo, Wancheng Sheng, Tong Zhang. The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$. Communications on Pure & Applied Analysis, 2010, 9 (2) : 431-458. doi: 10.3934/cpaa.2010.9.431 [8] Florian Kogelbauer. On the symmetry of spatially periodic two-dimensional water waves. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 7057-7061. doi: 10.3934/dcds.2016107 [9] Anke D. Pohl. Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2173-2241. doi: 10.3934/dcds.2014.34.2173 [10] Muriel Boulakia, Anne-Claire Egloffe, Céline Grandmont. Stability estimates for a Robin coefficient in the two-dimensional Stokes system. Mathematical Control & Related Fields, 2013, 3 (1) : 21-49. doi: 10.3934/mcrf.2013.3.21 [11] Fang-Di Dong, Wan-Tong Li, Li Zhang. Entire solutions in a two-dimensional nonlocal lattice dynamical system. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2517-2545. doi: 10.3934/cpaa.2018120 [12] Qing Yi. On the Stokes approximation equations for two-dimensional compressible flows. Kinetic & Related Models, 2013, 6 (1) : 205-218. doi: 10.3934/krm.2013.6.205 [13] Tong Zhang, Yuxi Zheng. Exact spiral solutions of the two-dimensional Euler equations. Discrete & Continuous Dynamical Systems - A, 1997, 3 (1) : 117-133. doi: 10.3934/dcds.1997.3.117 [14] Marc Briane, David Manceau. Duality results in the homogenization of two-dimensional high-contrast conductivities. Networks & Heterogeneous Media, 2008, 3 (3) : 509-522. doi: 10.3934/nhm.2008.3.509 [15] Wen Deng. Resolvent estimates for a two-dimensional non-self-adjoint operator. Communications on Pure & Applied Analysis, 2013, 12 (1) : 547-596. doi: 10.3934/cpaa.2013.12.547 [16] Al-hassem Nayam. Constant in two-dimensional $p$-compliance-network problem. Networks & Heterogeneous Media, 2014, 9 (1) : 161-168. doi: 10.3934/nhm.2014.9.161 [17] Lorenzo Sella, Pieter Collins. Computation of symbolic dynamics for two-dimensional piecewise-affine maps. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 739-767. doi: 10.3934/dcdsb.2011.15.739 [18] Piotr Biler, Tomasz Cieślak, Grzegorz Karch, Jacek Zienkiewicz. Local criteria for blowup in two-dimensional chemotaxis models. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 1841-1856. doi: 10.3934/dcds.2017077 [19] Paolo Tilli. Compliance estimates for two-dimensional problems with Dirichlet region of prescribed length. Networks & Heterogeneous Media, 2012, 7 (1) : 127-136. doi: 10.3934/nhm.2012.7.127 [20] Simone Creo, Maria Rosaria Lancia, Alexander Nazarov, Paola Vernole. On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 57-64. doi: 10.3934/dcdss.2019004

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