# 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
##### References:
 [1] A. Bodnarova, M. Bennamoun and K. K. Kubik, Suitability analysis of techniques for flaw detection in textiles using texture analysis,, Pattern Analysis and Applications, 3 (2000), 254.  doi: 10.1007/s100440070010.  Google Scholar [2] A. Bodnarova, M. Bennamoun and S. Latham, Optimal Gabor filters for textile flaw detection,, Pattern Recognition, 35 (2002), 2973.  doi: 10.1016/S0031-3203(02)00017-1.  Google Scholar [3] D. Chetverikov and A. Hanbury, Finding defects in texture using regularity and local orientation,, Pattern Recognition, 35 (2002), 2165.  doi: 10.1016/S0031-3203(01)00188-1.  Google Scholar [4] C. H. Chan and G. Pang, Fabric defect detection by Fourier analysis,, IEEE Trans. Ind. Application, 36 (2000), 1267.  doi: 10.1109/28.871274.  Google Scholar [5] Z. G. Feng and K. L. Teo, Optimal feedback control for stochastic impulsive linear systems subject to Poisson processes,, in, 39 (2010), 241.   Google Scholar [6] Z. G. Feng, K. L. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica J. IFAC, 44 (2008), 1295.  doi: 10.1016/j.automatica.2007.09.024.  Google Scholar [7] W. G. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291.   Google Scholar [8] S. V. Lomov, G. Huysmans, Y. Luo, R. S. Parnas, A. Prodromou, I. Verpoest and F. R. Phelan, Textile composites: Modelling strategies,, Composites Part A: Applied Science and Manufacturing, 32 (2001), 1379.  doi: 10.1016/S1359-835X(01)00038-0.  Google Scholar [9] R. Li, K. L. Teo, K. H. Wong and G. R. Duan, Control parameterization enhancing transform for optimal control of switched systems,, Mathematical and Computer Modelling, 43 (2006), 1393.  doi: 10.1016/j.mcm.2005.08.012.  Google Scholar [10] K. L. Mak, P. Peng and K. F. C. Yiu, Fabric defect detection using morphological filters,, Image and Vision Computing, 27 (2009), 1585.  doi: 10.1016/j.imavis.2009.03.007.  Google Scholar [11] K. L. Mak and P. Peng, An automated inspection system for textile fabrics based on Gabor filters,, Robotics and Computer-Integrated Manufacturing, 24 (2008), 359.  doi: 10.1016/j.rcim.2007.02.019.  Google Scholar [12] M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations,, in, 630 (1978), 144.   Google Scholar [13] Pablo Rodriguez-Ramirez and Michael Basin, An optimal impulsive control regulator for linear systems,, Numerical Algebra, 1 (2011), 275.   Google Scholar [14] M. Tarfaoui and S. Akesbi, A finite element model of mechanical properties of plain weave,, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 187-188 (2001), 187.  doi: 10.1016/S0927-7757(01)00611-2.  Google Scholar [15] K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems," Pitman Monographs and Surveys in Pure and Applied Mathematics, 55,, Longman Scientific & Technical, (1991).   Google Scholar [16] K. F. C. Yiu, K. L. Mak and K. L. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133.  doi: 10.3934/jimo.2005.1.133.  Google Scholar [17] D. J. Yao, H. L. Yang and R. M. Wang, Optimal financing and dividend strategies in a dual model with proportional costs,, Journal of Industrial and Management Optimization, 6 (2010), 761.   Google Scholar

show all references

##### References:
 [1] A. Bodnarova, M. Bennamoun and K. K. Kubik, Suitability analysis of techniques for flaw detection in textiles using texture analysis,, Pattern Analysis and Applications, 3 (2000), 254.  doi: 10.1007/s100440070010.  Google Scholar [2] A. Bodnarova, M. Bennamoun and S. Latham, Optimal Gabor filters for textile flaw detection,, Pattern Recognition, 35 (2002), 2973.  doi: 10.1016/S0031-3203(02)00017-1.  Google Scholar [3] D. Chetverikov and A. Hanbury, Finding defects in texture using regularity and local orientation,, Pattern Recognition, 35 (2002), 2165.  doi: 10.1016/S0031-3203(01)00188-1.  Google Scholar [4] C. H. Chan and G. Pang, Fabric defect detection by Fourier analysis,, IEEE Trans. Ind. Application, 36 (2000), 1267.  doi: 10.1109/28.871274.  Google Scholar [5] Z. G. Feng and K. L. Teo, Optimal feedback control for stochastic impulsive linear systems subject to Poisson processes,, in, 39 (2010), 241.   Google Scholar [6] Z. G. Feng, K. L. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica J. IFAC, 44 (2008), 1295.  doi: 10.1016/j.automatica.2007.09.024.  Google Scholar [7] W. G. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291.   Google Scholar [8] S. V. Lomov, G. Huysmans, Y. Luo, R. S. Parnas, A. Prodromou, I. Verpoest and F. R. Phelan, Textile composites: Modelling strategies,, Composites Part A: Applied Science and Manufacturing, 32 (2001), 1379.  doi: 10.1016/S1359-835X(01)00038-0.  Google Scholar [9] R. Li, K. L. Teo, K. H. Wong and G. R. Duan, Control parameterization enhancing transform for optimal control of switched systems,, Mathematical and Computer Modelling, 43 (2006), 1393.  doi: 10.1016/j.mcm.2005.08.012.  Google Scholar [10] K. L. Mak, P. Peng and K. F. C. Yiu, Fabric defect detection using morphological filters,, Image and Vision Computing, 27 (2009), 1585.  doi: 10.1016/j.imavis.2009.03.007.  Google Scholar [11] K. L. Mak and P. Peng, An automated inspection system for textile fabrics based on Gabor filters,, Robotics and Computer-Integrated Manufacturing, 24 (2008), 359.  doi: 10.1016/j.rcim.2007.02.019.  Google Scholar [12] M. J. D. Powell, A fast algorithm for nonlinearly constrained optimization calculations,, in, 630 (1978), 144.   Google Scholar [13] Pablo Rodriguez-Ramirez and Michael Basin, An optimal impulsive control regulator for linear systems,, Numerical Algebra, 1 (2011), 275.   Google Scholar [14] M. Tarfaoui and S. Akesbi, A finite element model of mechanical properties of plain weave,, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 187-188 (2001), 187.  doi: 10.1016/S0927-7757(01)00611-2.  Google Scholar [15] K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems," Pitman Monographs and Surveys in Pure and Applied Mathematics, 55,, Longman Scientific & Technical, (1991).   Google Scholar [16] K. F. C. Yiu, K. L. Mak and K. L. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133.  doi: 10.3934/jimo.2005.1.133.  Google Scholar [17] D. J. Yao, H. L. Yang and R. M. Wang, Optimal financing and dividend strategies in a dual model with proportional costs,, Journal of Industrial and Management Optimization, 6 (2010), 761.   Google Scholar
 [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] 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 [8] 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 [9] 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 [10] 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 [11] 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 [12] 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 [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] Micah Webster, Patrick Guidotti. Boundary dynamics of a two-dimensional diffusive free boundary problem. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 713-736. doi: 10.3934/dcds.2010.26.713

2019 Impact Factor: 1.27