# 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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