Deep neural network for fringe pattern filtering and normalisation

We propose a new framework for processing Fringe Patterns (FP). Our novel approach builds upon the hypothesis that the denoising and normalisation of FPs can be learned by a deep neural network if enough pairs of corrupted and cleaned FPs are provided. Although similar proposals have been reported in the literature, we propose an improvement of a well-known deep neural network architecture, which produces high-quality results in terms of stability and repeatability. We test the performance of our method in various scenarios: FPs corrupted with different degrees of noise, and corrupted with different noise distributions. We compare our methodology versus other state-of-the-art methods. The experimental results (on both synthetic and real data) demonstrate the capabilities and potential of this new paradigm for processing interferograms. We expect our work would motivate more sophisticated developments in this direction.

[1]  Yu-Bin Yang,et al.  Image Restoration Using Very Deep Convolutional Encoder-Decoder Networks with Symmetric Skip Connections , 2016, NIPS.

[2]  Francisco J. Cuevas,et al.  Multi-layer neural network applied to phase and depth recovery from fringe patterns , 2000 .

[3]  Mariano Rivera,et al.  Two-step fringe pattern analysis with a Gabor filter bank , 2016 .

[4]  Michael Unser,et al.  Deep Convolutional Neural Network for Inverse Problems in Imaging , 2016, IEEE Transactions on Image Processing.

[5]  A. Rotenberg,et al.  A New Pseudo-Random Number Generator , 1960, JACM.

[6]  Caiming Zhang,et al.  Optical Fringe Patterns Filtering Based on Multi-Stage Convolution Neural Network , 2019, Optics and Lasers in Engineering.

[7]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[8]  M Servin,et al.  Phase unwrapping with a regularized phase-tracking system. , 1998, Applied optics.

[9]  Lei Zhang,et al.  FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising , 2017, IEEE Transactions on Image Processing.

[10]  Geoffrey E. Hinton,et al.  Reducing the Dimensionality of Data with Neural Networks , 2006, Science.

[11]  Thomas Brox,et al.  U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.

[12]  Zhenkun Lei,et al.  Batch denoising of ESPI fringe patterns based on convolutional neural network. , 2019, Applied optics.

[13]  Sai Siva Gorthi,et al.  Fringe projection techniques: Whither we are? , 2010 .

[15]  Qian Kemao,et al.  Windowed Fourier transform for fringe pattern analysis. , 2004, Applied optics.

[16]  Rigoberto Juarez-Salazar,et al.  Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications. , 2015, Applied optics.

[17]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[18]  M. Servin,et al.  Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms , 2001 .

[19]  Qian Kemao,et al.  Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations , 2007 .

[20]  Mariano Rivera Robust fringe pattern analysis method for transient phenomena , 2018 .

[21]  Mariano Rivera,et al.  Robust phase demodulation of interferograms with open or closed fringes. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  Anand Asundi,et al.  Fringe pattern denoising based on deep learning , 2019, Optics Communications.

[23]  Anand Asundi,et al.  Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry , 2010 .

[24]  Zonghua Zhang,et al.  Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry , 2012 .

[25]  Vera Kurková,et al.  Kolmogorov's theorem and multilayer neural networks , 1992, Neural Networks.

[26]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[27]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[28]  Nitish Srivastava,et al.  Dropout: a simple way to prevent neural networks from overfitting , 2014, J. Mach. Learn. Res..