Feature extraction of the deformed patterned textile

Deformation is very common in textile materials. In this paper, we consider the feature extraction problem in a deformable textile image, where the original shape is required to be recovered. We formulated this problem as a combined optimal control and optimal parameter selection problem, where the dynamical system is governed by 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. Several numerical examples are illustrated to demonstrate the method.