Skip to main content

Advertisement

SpringerLink
Log in

Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Shape analysis techniques such as geometric moment descriptors, Fourier descriptors, wavelet descriptors etc. have been used commercially in the fields of biometrics for finger print matching, iris matching and facial recognition for almost over a decade. These techniques are capable of decomposing high resolution images with 105 to 106 pixels into only a few hundred unique shape descriptors which are a true representation of the features in the corresponding images thus tremendously reducing the computational data and time required for image analysis and comparison. This paper explores the possibility of employing shape analysis techniques to facilitate the comparison of full-field data obtained from techniques such as digital image correlation, thermoelasticity and photoelasticity for the purpose of validation of computational models and damage assessment. A new shape descriptor is introduced which combines Fourier decomposition with Zernike moments. The Fourier-Zernike descriptor is shown to be capable of decomposing full-field strain distributions containing engineering features and discontinuities arising from damage by combining the desirable properties of its parent shape descriptors while eliminating their individual limitations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Pavladis T (1978) A review of algorithms for shape analysis. Comput Graphics Image Process 7:243–258

    Article  Google Scholar 

  2. Pavladis T (1980) Algorithms for shape analysis of contours and waveforms. IEEE Trans Pattern Anal Mech Intell 2:301–321

    Article  Google Scholar 

  3. Young I, Walker J, Bowie J (1974) An analysis technique for biological shape. Comput Graphic Image Processing 25:357–370

    MathSciNet  MATH  Google Scholar 

  4. Kashyap R, Chellappa R (1981) Stochastic models for closed boundary analysis: representation and reconstruction. IEEE Trans Inform Theory 27:627–637

    Article  MathSciNet  MATH  Google Scholar 

  5. Kartikeyan B, Sarkar A (1989) Shape description by time series. IEEE Trans Pattern Anal Mech Intell 11:977–984

    Article  Google Scholar 

  6. Goshtasby A (1985) Description and discrimination of planar shapes using shape matrices. IEEE trans Patterns Anal Mach Intell 7:738–743

    Article  Google Scholar 

  7. Taza A, Suen C (1989) Discrimination of planar shapes using shape matrices. IEEE Trans SMC 19:1281–1289

    Google Scholar 

  8. Zahn C, Roskies R (1972) Fourier descriptors for plane closed curves. Comput Graphics Image Process 21:261–281

    MathSciNet  Google Scholar 

  9. Granlund GH (1972) Fourier processing for handprint character recognition. IEEE Trans Comput 21:195–201

    Article  MathSciNet  MATH  Google Scholar 

  10. Richards CW, Hemami H (1974) Identification of three-dimensional objects using Fourier descriptors of the boundary curve. IEEE Trans SMC 4:371–378

    Google Scholar 

  11. Persoon E, Fu K (1977) Shape discrimination using Fourier descriptors. IEEE Trans SMC 7:170–179

    MathSciNet  Google Scholar 

  12. Wallace T, Wintz P (1980) An efficient three-dimensional aircraft recognition algorithm using normalized Fourier descriptors. Comput Graphics Image Process 13:99–126

    Article  Google Scholar 

  13. Blum H (1973) Biological shape and visual science. J Theoret Biol 38:205–287

    Article  Google Scholar 

  14. Peleg S, Rosenfeld A (1981) A min-max medial axis transformation. IEEE Trans Pattern Anal Mech Intell 3:208–210

    Article  Google Scholar 

  15. Blum H, Nagel R (1978) Shape description using weighted symmetric axis feature. Pattern Recognition 10:167–180

    Article  MATH  Google Scholar 

  16. Wang W, Mottershead J and Mares C (2009) Shape descriptors for mode-shape recognition and model updating. Proc. of 7th International Conf. on Modern Practice in Stress and Vibration Analysis, Cambridge, United Kingdom, J. Physics: Conference Series 181(1):012004

  17. Wang W, Mottershead J, Mares C (2009) Vibration mode shape recognition using image processing. Journal of Sound and Vibration 326(3–5):909–938

    Article  Google Scholar 

  18. Hu MK (1962) Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory, IT-8, 179–187

  19. Teague MR (1980) Image analysis via the general theory of moments. Optical Society of America 70:920–930

    Article  MathSciNet  Google Scholar 

  20. Belkasim SO, Sridhar M, Ahmadi M (1991) Pattern recognition with moment invarients: a comparative study and new results. Pattern Recognition 24:1117–1138

    Article  Google Scholar 

  21. Prakop RJ, Reves AP (1992) A survey of moment based techniques for for unoccluded object representation and recognition. CVGIP: Graphical Models Image Process 54:438–460

    Article  Google Scholar 

  22. Wang W, Mottershead J, Mares C (2009) Mode shape recognition and finite element model updating the Zernike moment descriptors. Mechanical Systems and Signal Processing 23:2088–2112

    Article  Google Scholar 

  23. Peura M and Iivarinen J (1997) Effeciency of simple shape descriptors. In Proceedings of the Third International Workshop on Visual form, Capri, Italy, pp 443–451

  24. Cosgriff RG (1960) Identification of shape, Report No. 820–11 of the Ohio State University Research Foundation

  25. Kennedy RL, Lee Y, Roy BV, Reed CD, Lippman RP (1998) Solving data mining problems through pattern recognition. Prentice-Hall, Upper Saddle River, NJ

    Google Scholar 

  26. Taubin G and Cooper DB (1992) Recognition and positioning of rigid objects using algebraic moment invariants. In Proceedings of SPIE Conference on Geometric Methods in Computer Vision, Florida, USA, 1570, 175–186

  27. Taubin G, Cooper DB (1992) Object recognition based on moment. Geometric Invariance in Computer Vision, MIT Press, MA, pp 375–397

    Google Scholar 

  28. Scassellati B, Slexopoulos S and Flickner M (1994) Retriving images by two-dimensional shapes:a comparison of computation methods with human perceptual judgment. In SPIE Proceedings on Storage and Retrieval for Image and video Databases II, San Jose, CA, USA, 2185, 2–14

  29. Teh C-H, Chin RT (1988) On image analysis by the methods of moments. IEEE Trans Pattern Anal Mach Intell 10(4):496–513

    Article  MATH  Google Scholar 

  30. Liao SX, Pawlak M (1996) On image analysis by moments. IEEE Trans Pattern Anal Mach Intell 70(8):254–266

    Article  Google Scholar 

  31. Zhang D S and Lu G (2002) Generic Fourier descriptors for shape-based image retrival. In Proceedings of IEEE International Conference on Multimedia and Expo, Lausanne, Switzerland, 1:425–428

  32. Zhang DS and Lu G (2002), Enhanced generic Fourier descriptors for shape-based image retrival. In Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, Orlando, Fl, USA, 4:3668–3671

  33. Dudani SA, Breeding KJ, McGhee RB (1977) Aircraft identification by moment invariants. IEEE Trans Comput C-26(1):39–46

    Article  Google Scholar 

  34. Bhanu B (1986) Automatic target recognition: state of the art survey. IEEE Trans on Aerospace and Electronic Systems 4:364–379

    Article  Google Scholar 

  35. Bhanu B and Jones TL (1993) Image understanding research for automatic target recognition. IEEE Aerospace and Electronic Systems Magazine, pp 15–22

  36. Pizarro O, Singh H (2003) Towards large area mosaicing for underwater scientific applications. IEEE Journal of Ocean Engineering 28(4):651–672

    Article  Google Scholar 

  37. Iscan Z, Dokur Z, Olmez T (2010) Tumor detection using Zernike moments on segmented magnetic resonance brain images. Expert Syst Appl 37:2540–2549

    Article  Google Scholar 

  38. Li B, Fan Y, Meng Q-H and Qi L (2009) Intestinal polyp recognition in capsule endoscopy images using color and shape features. In Proceedings of the IEEE International Conference on Robotics and biomimetics Guilin China, pp 1490–1494

  39. Grandison S, Roberts C, Morris RJ (2009) An application of three-dimensional Zernike moments for “Model-Free” molecular structure, functional motion and structural reliability. J of Computational Biology 16(3):487–500

    Article  MathSciNet  Google Scholar 

  40. Faez K and Farajzadeh N (2006) A performance comparison of ZM, PZM and LM in a face recognition system in presence of salt-pepper noise. IEEE International Conference on Systems, Man and Cybernetics, Taipei, Taiwan, pp 4197–4201

  41. Nabatchian A, Makaremi I, Abdel-Raheem E and Ahmadi M (2008) Pseudo-Zernike moments invariants for the recognition of faces using different classifiers in FERET database. In Proceedings of 3rd International Conference on Convergence and Hybrid Information Technology, pp 933–936

  42. Nabatchian A, Abdel-Raheem E and Ahmadi M (2008) Human face recognition using different moment invariants: a comparative review. Congress on Image and Signal Processing, pp 661–666

  43. Kong J, Lu Y, Wang S, Qi M, Li H (2008) A two-stage neural network based personal identification system using handprint. Neurocomputing 71:641–647

    Article  Google Scholar 

  44. Yau WC, Kumar DK, Arjunan SP and Kumar S (2006) Visual speech recognition using image moments multi-resolution wavelet images. In Proceedings of the International Conference on Computer Graphics, Imaging and Visualization, pp.194–199

  45. Hengzhuo Z, Yanping W (1998) Recognition of three-dimensional aircrafts by Fourier descriptors with fast and efficient library search. Wuhan University of Natural Sciences 3(2):169–174

    Article  Google Scholar 

  46. Shen L, Rangayyan RM, Desautels JEL (1994) Application of Shape descriptors to mammographic calcifications. IEEE Trans On Medical Imaging 13(2):236–274

    Google Scholar 

  47. Ahmad WSHMW and Fauzi MFA (2008) Comparison of different feature extraction techniques in content based image retrieval for CT brain images. IEEE 10th workshop on multimedia signal processing, Cairns, Qld, pp 503–508

  48. Ismail RA, Ramadan MA, Danf TE and Samak AH (2008) Multi-resolution Fourier-Wavelet descriptors for fingerprint recognition. International Conference on Computer Science and Information Technology, pp 951–955

  49. Abate AF, Nappi M, Riccio D and Sabatino G (2006) Three-dimensional face recognition using normal spheres and general Fourier descriptors. In the Proceedings of the 18th International Conference on Pattern Recognition, pp 1183–1186

  50. Nomir O, Abdel-Mottaleb (2007) Human identification from dental X—ray images based on the shape and appearance of the teeth. IEEE Trans on Information Forensics and Security 2(2):188–197

    Article  Google Scholar 

  51. Gurbuz S, Tufekci Z, Patterson E, Gowdy JN (2001) Application of affine-invariant Fourier descriptors to lipreading for audio-visual speech recognition. In Proc Int Conf Acoust Speech Signal Processing 1:177–180

    Google Scholar 

  52. Patki AS, Patterson EA (2010) Structural damage assessment in fiber-reinforced composites using image decomposition. Proc. of SEM2010 Annual Conference & Exposition on Experimental & Applied Mechanics, Indianapolis, #265

  53. Mottershead JE, Friswell MI (1993) Model updating in structural dynamics: A Survey. Journal of Sound and Vibration 167(2):347–375

    Article  MATH  Google Scholar 

  54. Friswell MI, Mottershead JE, Ahmadian H (2001) Finite-element model updating using experimental test data: parameterization and regularization. Phil Trans R Soc Lond A 359:169–186

    Article  MATH  Google Scholar 

  55. Patki A, Weizhuo W, Mottershead J and Patterson E (2010) Image decomposition as a tool for validating stress analysis models. In Proceedings of the 14th International Conference on Experimental Mechanics, Poitiers, France, #271

  56. Zernike F (1934) Beugungstheorie des schneidenverfahrens und seiner verbesserten form, der phasenkontrastmethode (diffraction theory of the cut procedure and its improved form, the phase contrast method). Physica 1:689

    Article  MATH  Google Scholar 

  57. Zhang D, Lu G (2002) Shape-based image retrieval using generic Fourier descriptor. Signal Processing: Image Communication 17:825–848

    Article  Google Scholar 

  58. Kuntuu I, Lepisto L, Visa A (2005) Enhanced Fourier shape descriptor using zero-padding. Image Analysis: Lecture Notes in Computer Science. Springer Berlin / Heidelberg 3540(2005):892–900

    Google Scholar 

  59. Patki AS (2010) Advances in structural damage assessment using strain measurements and invariant shape descriptors. Doctoral Dissertation, Department of Mechanical Engineering, Michigan State University

Download references

Acknowledgements

The authors gratefully acknowledge contributions from members of the EU FP7 project ADVISE (Advanced Dynamic Validation using Integrated Simulations and Experimentation) consortium which is funded by through Grant no. 218595. EAP is a Royal Society Wolfson Research Merit Award holder. The authors are grateful for the financial support of the College of Engineering, Michigan State University. The authors had many helpful discussions with Dr W. Wang and Professor J.E Mottershead, which are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, 2555 Engineering Building, East Lansing, MI, 48824, USA

    A. S. Patki & E. A. Patterson

  2. School of Engineering, University of Liverpool, The Quadrangle, Brownlow Hill, Liverpool, L69 3GH, UK

    E. A. Patterson

Authors
  1. A. S. Patki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. A. Patterson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. S. Patki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Patki, A.S., Patterson, E.A. Decomposing Strain Maps Using Fourier-Zernike Shape Descriptors. Exp Mech 52, 1137–1149 (2012). https://doi.org/10.1007/s11340-011-9570-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-011-9570-4

Keywords

Search

Navigation