Enhancing Fault Detection in Image Analysis: A Combined Wavelet-Fourier Technique for Advancing Manufacturing Quality Control

Document Type : Original Article


1 Department of Industrial Engineering, Yazd University, Yazd, Iran

2 Department of Industrial Engineering, Shahed University, Tehran, Iran


This study focuses on utilizing image data for statistical process control and improving quality monitoring in manufacturing and service systems. The effectiveness of individual and combined feature extraction methods is evaluated, with the Wavelet-Fourier approach identified as the most suitable. The proposed method not only identifies image processing issues but also provides valuable information for estimating change points, fault locations, and fault sizes. This enables the resolution and prediction of faults, leading to cost and time savings in production. To perform evaluation of the proposed method, an image from a tile production line is subjected to Wavelet transform, followed by Fourier transform on the obtained coefficients. The results demonstrate the superiority of the Wavelet-Fourier method over individual methods such as Fourier transform and Wavelet transform. The proposed method exhibits comparable or improved performance in fault detection and localization compared to similar research. This study highlights the potential of utilizing image data for statistical process control and quality monitoring, offering a comprehensive solution for fault detection and analysis. The findings contribute to advancements in image processing techniques and have practical implications for enhancing quality monitoring in various industries. By leveraging image data, manufacturers can make informed decisions, enhance process performance, and improve overall product quality.

Graphical Abstract

Enhancing Fault Detection in Image Analysis: A Combined Wavelet-Fourier Technique for Advancing Manufacturing Quality Control


Main Subjects

  1. Feng J, Fu J, Lin Z, Shang C, Li B. A review of the design methods of complex topology structures for 3D printing. Visual Computing for Industry, Biomedicine, and Art. 2018;1(1):1-16. https://doi.org/10.1186/s42492-018-0004-3
  2. Hu G-H, Wang Q-H, Zhang G-H. Unsupervised defect detection in textiles based on Fourier analysis and wavelet shrinkage. Applied optics. 2015;54(10):2963-80. https://doi.org/10.1364/AO.54.002963
  3. Zahn CT, Roskies RZ. Fourier descriptors for plane closed curves. IEEE Transactions on computers. 1972;100(3):269-81. https://doi.org/10.1109/TC.1972.5008949
  4. Chen G, Bui TD. Invariant Fourier-wavelet descriptor for pattern recognition. Pattern recognition. 1999;32(7):1083-8. https://doi.org/10.1016/S0031-3203(98)00148-4
  5. Liu JJ, MacGregor JF. Estimation and monitoring of product aesthetics: application to manufacturing of “engineered stone” countertops. Machine Vision and Applications. 2006;16:374-83. https://doi.org/10.1007/s00138-005-0009-8
  6. Yadav RB, Nishchal NK, Gupta AK, Rastogi VK. Retrieval and classification of shape-based objects using Fourier, generic Fourier, and wavelet-Fourier descriptors technique: A comparative study. Optics and Lasers in engineering. 2007;45(6):695-708. https://doi.org/10.1016/j.optlaseng.2006.11.001
  7. Hosntalab M, Aghaeizadeh Zoroofi R, Abbaspour Tehrani-Fard A, Shirani G. Classification and numbering of teeth in multi-slice CT images using wavelet-Fourier descriptor. International journal of computer assisted radiology and surgery. 2010;5:237-49. https://doi.org/10.1007/s11548-009-0389-8
  8. Münch B, Trtik P, Marone F, Stampanoni M. Stripe and ring artifact removal with combined wavelet—Fourier filtering. Optics express. 2009;17(10):8567-91. https://doi.org/10.1364/OE.17.008567
  9. Ward M, Xie Z, Yang D, Rundensteiner E. Quality-aware visual data analysis. Computational Statistics. 2011;26(4):567-84. https://doi.org/10.1007/s00180-010-0226-0
  10. Megahed FM, Wells LJ, Camelio JA, Woodall WH. A spatiotemporal method for the monitoring of image data. Quality and Reliability Engineering International. 2012;28(8):967-80. https://doi.org/10.1002/qre.1287
  11. Chen G, Xie W, Bui TD, Krzyżak A. Automatic epileptic seizure detection in EEG using nonsubsampled wavelet–fourier features. Journal of Medical and Biological Engineering. 2017;37:123-31. https://doi.org/10.1007/s40846-016-0214-0
  12. Knešaurek K. Fourier-wavelet restoration in PET/CT brain studies. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 2012;689:29-34. https://doi.org/10.1016/j.nima.2012.06.032
  13. Xia Y, Johnson BK, Jiang Y, Fischer N, Xia H. A new method based on artificial neural network, Wavelet Transform and Short Time Fourier Transform for Subsynchronous Resonance detection. International Journal of Electrical Power & Energy Systems. 2018;103:377-83. https://doi.org/10.1016/j.ijepes.2018.06.019
  14. Al-Salman W, Li Y, Wen P. Detecting sleep spindles in EEGs using wavelet fourier analysis and statistical features. Biomedical Signal Processing and Control. 2019;48:80-92. https://doi.org/10.1016/j.bspc.2018.10.004
  15. You L, Man J, Yan K, Wang D, Li H. Combined Fourier-wavelet transforms for studying dynamic response of anisotropic multi-layered flexible pavement with linear-gradual interlayers. Applied Mathematical Modelling. 2020;81:559-81. https://doi.org/10.1016/j.apm.2020.01.031
  16. Biglari M, Mirzaei F, Hassanpour H. Feature selection for small sample sets with high dimensional data using heuristic hybrid approach. International Journal of Engineering, Transactions B: Applications. 2020;33(2):213-20. https://doi.org/10.5829/IJE.2020.33.02B.05
  17. Fattahzadeh M, Saghaei A. A statistical method for sequential images–based process monitoring. International Journal of Engineering, Transactions A: Basics. 2020;33(7):1285-92. https://doi.org/10.5829/IJE.2020.33.07A.15
  18. Santosh NK, Barpanda SS. Wavelet and PCA-based glaucoma classification through novel methodological enhanced retinal images. Machine Vision and Applications. 2022;33(1):11. https://doi.org/10.1007/s00138-021-01263-w
  19. Abdul-Kareem AA, & Al-Jawher, W. A. M. ‏. A Hybrid Domain Medical Image Encryption Scheme Using URUK and WAM Chaotic Maps with Wavelet–Fourier Transform. Journal of Cyber Security and Mobility. 2023:435-64.
  20. Reynolds Jr MR, Lou J. An evaluation of a GLR control chart for monitoring the process mean. Journal of quality technology. 2010;42(3):287-310. https://doi.org/10.1080/00224065.2010.11917825
  21. Wirsing K. Time frequency analysis of wavelet and Fourier transform. Wavelet theory. 2020.
  22. Stein EM, Weiss G. Introduction to Fourier Analysis on Euclidean Spaces (PMS-32). Introduction to Fourier Analysis on Euclidean Spaces (PMS-32).32.
  23. Zhang Z, Jing Z, Wang Z, Kuang D. Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase calculation at discontinuities in fringe projection profilometry. Optics and Lasers in Engineering. 2012;50(8):1152-60. https://doi.org/10.1016/j.optlaseng.2012.03.004
  24. Lin L, Feng L. Comparative analysis of image denoising methods based on wavelet transform and threshold functions. International Journal of Engineering. 2017;30(2):199-206. https://doi.org/10.5829/idosi.ije.2017.30.02b.06
  25. Kunttu I, Lepistö L, Rauhamaa J, Visa A. Multiscale Fourier descriptors for defect image retrieval. Pattern Recognition Letters. 2006;27(2):123-32. https://doi.org/10.1016/j.patrec.2005.08.022
  26. Mallat S. A wavelet tour of signal processing: Elsevier; 1999.
  27. Shen D IH. Discriminative wavelet shape descriptors for recognition of 2-D patterns. Pattern recognition. 1999;32(2):151-65.
  28. Illanes A, Esmaeili N, Poudel P, Balakrishnan S, Friebe M. Parametrical modelling for texture characterization—A novel approach applied to ultrasound thyroid segmentation. PloS one. 2019;14(1):e0211215. https://doi.org/10.1371/journal.pone.0211215
  29. Matuszewski DJ, Hast A, Wählby C, Sintorn I-M. A short feature vector for image matching: The Log-Polar Magnitude feature descriptor. Plos one. 2017;12(11):e0188496. https://doi.org/10.1371/journal.pone.0188496
  30. Bishop CM, Nasrabadi NM. Pattern recognition and machine learning: Springer; 2006.
  31. Rao RM. Wavelet transforms: Introduction to theory and applications: Pearson Education India; 1998.
  32. Haar A. Zur theorie der orthogonalen funktionensysteme: Georg-August-Universitat, Gottingen.; 1909.
  33. Kumar S, Bhandari AK, Raj A, Swaraj K. Triple clipped histogram-based medical image enhancement using spatial frequency. IEEE Transactions on NanoBioscience. 2021;20(3):278-86. https://doi.org/10.1109/TNB.2021.3064077
  34. Wang J, Cui L, Xu Y. Quantitative and localization fault diagnosis method of rolling bearing based on quantitative mapping model. Entropy. 2018;20(7):510. https://doi.org/10.3390/e20070510