Skip to main content
SpringerLink
Log in

A pseudo-parabolic diffusion model to enhance deep neural texture features

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this work, we propose a methodology for texture recognition. The combination of deep learning with texture encoding techniques has demonstrated to be a powerful strategy to solve this problem. However, one of such encoding classically used in texture images, which are PDE operators, has not been explored in deep learning frameworks. Based on that, here we introduce a pseudo-parabolic diffusion operator to the pipeline of a convolutional neural network (CNN). The method is divided into 4 major stages: 1) application of the pseudo-parabolic operator to the image; 2) use of the resulting image as input to a pre-trained CNN; 3) extraction of local features from the last convolutional layer and pooling by Fisher vectors; 4) classification of the pooled features. Our approach is compared in a texture classification task and outperforms, in terms of classification accuracy, several state-of-the-art solutions. For example, in the challenging benchmark datasets KTH2b and FMD, the proposed method achieves classification accuracy of 79% and 81.8%, respectively. From the numerical viewpoint, we also highlight the key approximation and algorithmic aspects of our computational pseudo-parabolic diffusion modeling into the pipeline of a CNN to enhance deep neural texture features. In particular, the advantage over the plain CNN architecture is substantial. Such interesting performance can be justified by the capacity of the pseudo-parabolic operator to remove spurious noise while preserving important discontinuity information on the texture. The results also suggest the potential of our approach in real-world application, as attested on a practical application to the identification of plant species. In this specific task, our method achieves an accuracy of 94% and outperforms the state-of-the-art results. This is especially the case when we do not have access to a large amount of data for training and when the computational resources are limited, as our method do not involve any fine tuning.

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

Similar content being viewed by others

Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Abreu E, Durán A (2021) Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models. Comput Math Appl 102:15–44

    MathSciNet  Google Scholar 

  2. Abreu E, Ferraz P, Vieira J (2020) Numerical resolution of a pseudo-parabolic buckley-leverett model with gravity and dynamic capillary pressure in heterogeneous porous media. J Comput Phys 411:109395

    MathSciNet  Google Scholar 

  3. Abreu E, Vieira J (2017) Computing numerical solutions of the pseudo-parabolic buckley-leverett equation with dynamic capillary pressure. Mathematics and Computers in Simulation 137:29–48, mAMERN VI-2015: 6th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources

  4. Akiva P, Purri M, Leotta M (2022) Self-supervised material and texture representation learning for remote sensing tasks. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition (CVPR), pp 8203–8215

  5. Alkhatib M, Hafiane A (2019) Robust adaptive median binary pattern for noisy texture classification and retrieval. IEEE Trans Image Process 28(11):5407–5418

    MathSciNet  Google Scholar 

  6. Barros Neiva M, Guidotti P, Bruno OM (2018) Enhancing lbp by preprocessing via anisotropic diffusion. Int J Mod Phys C 29(08):1850071

    Google Scholar 

  7. Bishop CM (2006) Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag, Berlin, Heidelberg

    Google Scholar 

  8. Boudra S, Yahiaoui I, Behloul A (2022) Tree trunk texture classification using multi-scale statistical macro binary patterns and cnn. Appl Soft Comput 118:108473

    Google Scholar 

  9. Bruna J, Mallat S (2013) Invariant scattering convolution networks. IEEE Trans Pattern Anal Mach Intell 35(8):1872–1886

    Google Scholar 

  10. Bu X, Wu Y, Gao Z, Jia Y (2019) Deep convolutional network with locality and sparsity constraints for texture classification. Pattern Recog 91:34–46

    Google Scholar 

  11. Casanova D, de Mesquita Sá Junior JJ, Bruno OM (2009) Plant leaf identification using gabor wavelets. Int J Imaging Syst Technol 19(3):236–243

    Google Scholar 

  12. Chan T, Jia K, Gao S, Lu J, Zeng Z, Ma Y (2015) PCANet: A simple deep learning baseline for image classification? IEEE Trans Image Process 24(12):5017–5032

    MathSciNet  Google Scholar 

  13. Cimpoi M, Maji S, Kokkinos I, Vedaldi A (2016) Deep filter banks for texture recognition, description, and segmentation. Int J Comput Vision 118(1):65–94

    MathSciNet  Google Scholar 

  14. Cimpoi M, Maji S, Kokkinos I, Mohamed S, Vedaldi A (2014) Describing textures in the wild. In: Proceedings of the 2014 IEEE conference on computer vision and pattern recognition, IEEE Computer Society, Washington, DC, USA, CVPR ’14, pp 3606–3613

  15. Csurka G, Perronnin F (2011) Fisher vectors: Beyond bag-of-visual-words image representations. In: Richard P, Braz J (eds) Computer vision, imaging and computer graphics. Theory and Applications, Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 28–42

    Google Scholar 

  16. Deepalakshmi P, Lavanya K, Srinivasu PN et al (2021) Plant leaf disease detection using cnn algorithm. Int J Inf Sys Model Des (IJISMD) 12(1):1–21

    Google Scholar 

  17. Donahue J, Jia Y, Vinyals O, Hoffman J, Zhang N, Tzeng E, Darrell T (2014) Decaf: A deep convolutional activation feature for generic visual recognition. In: Proceedings of the 31st international conference on international conference on machine learning - Volume 32, JMLR.org, ICML’14, pp I-647-I-655

  18. Düll WP (2006) Some qualitative properties of solutions to a pseudoparabolic equation modeling solvent uptake in polymeric solids. Commun Partial Differ Equat 31(8):1117–1138

    MathSciNet  Google Scholar 

  19. Florindo JB (2020) DSTNet: Successive applications of the discrete schroedinger transform for texture recognition. Inf Sci 507:356–364

    Google Scholar 

  20. Florindo JB, Abreu E (2021) An application of a pseudo-parabolic modeling to texture image recognition. In: Paszynski M, Kranzlmüller D, Krzhizhanovskaya VV, Dongarra JJ, Sloot PMA (eds) Computational Science - ICCS 2021. Springer International Publishing, Cham, pp 386–397

    Google Scholar 

  21. Florindo JB, Metze K (2021) A cellular automata approach to local patterns for texture recognition. Expert Syst Appl 179:115027

    Google Scholar 

  22. Florindo JB, Lee YS, Jun K, Jeon G, Albertini MK (2021) Visgraphnet: A complex network interpretation of convolutional neural features. Inf Sci 543:296–308

    Google Scholar 

  23. Géron A (2019) Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow: Concepts, tools, and techniques to build intelligent systems.“O’Reilly Media, Inc.”

  24. Gonçalves WN, da Silva NR, da Fontoura Costa L, Bruno OM (2016) Texture recognition based on diffusion in networks. Inf Sci 364(C):51–71

    Google Scholar 

  25. Guidotti P (2015) Anisotropic diffusions of image processing from perona-malik on. In: AIP Conference Proceeding, pp 46

  26. Guo Z, Zhang L, Zhang D (2010) A completed modeling of local binary pattern operator for texture classification. Trans Img Proc 19(6):1657–1663

    MathSciNet  Google Scholar 

  27. Guo Z, Zhang L, Zhang D (2010) Rotation invariant texture classification using lbp variance (lbpv) with global matching. Pattern Recog 43(3):706–719

    Google Scholar 

  28. Hayman E, Caputo B, Fritz M, Eklundh JO (2004) On the significance of real-world conditions for material classification. In: Pajdla T, Matas J (eds) Computer Vision - ECCV 2004. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 253–266

    Google Scholar 

  29. Hazgui M, Ghazouani H, Barhoumi W (2022) Genetic programming-based fusion of hog and lbp features for fully automated texture classification. Vis Comput 38(2):457–476

    Google Scholar 

  30. Kannala J, Rahtu E (2012) Bsif: Binarized statistical image features. In: ICPR, IEEE Computer society, pp 1363–1366

  31. Keys R (1981) Cubic convolution interpolation for digital image processing. IEEE Trans Acoust Speech Sig Process 29(6):1153–1160

    MathSciNet  Google Scholar 

  32. Koenderink JJ (1984) The structure of images. Biol Cybern 50(5):363–370

    MathSciNet  Google Scholar 

  33. Kuznetsov I, Sazhenkov S (2022) Strong solutions of impulsive pseudoparabolic equations. Nonlinear Anal Real World Appl 65:103509

    MathSciNet  Google Scholar 

  34. Lazebnik S, Schmid C, Ponce J (2005) A sparse texture representation using local affine regions. IEEE Trans Pattern Anal Mach Intell 27(8):1265–1278

    Google Scholar 

  35. LeVeque RJ (2007) Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM

  36. Liu S, Deng W (2015) Very deep convolutional neural network based image classification using small training sample size. In: 2015 3rd IAPR Asian conference on pattern recognition (ACPR), pp 730–734

  37. Mao S, Rajan D, Chia LT (2021) Deep residual pooling network for texture recognition. Pattern Recog 112:107817

    Google Scholar 

  38. Mikelić A (2010) A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure. J Differ Equ 248(6):1561–1577

    MathSciNet  Google Scholar 

  39. Ojala T, Pietikäinen M, Mäenpää T (2002) Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans Pattern Anal Mach Intell 24(7):971–987

    Google Scholar 

  40. Pan Z, Wu X, Li Z (2019) Central pixel selection strategy based on local gray-value distribution by using gradient information to enhance lbp for texture classification. Expert Syst Appl 120:319–334

    Google Scholar 

  41. Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639

    Google Scholar 

  42. Ranganath A, Sahu PK, Senapati MR (2022) A novel approach for detection of coronavirus disease from computed tomography scan images using the pivot distribution count method. Comput MethodsBiomech Biomed Eng Imaging Vis 10(2):145–156

    Google Scholar 

  43. Saad Y (2003) Iterative methods for sparse linear systems. SIAM

  44. Seam N, Vallet G (2011) Existence results for nonlinear pseudoparabolic problems. Nonlinear Anal Real World Appl 2(5):2625–2639

    MathSciNet  Google Scholar 

  45. Sharan L, Rosenholtz R, Adelson EH (2009) Material perceprion: What can you see in a brief glance? J Vis 9(8):784

    Google Scholar 

  46. Showalter RE (2010) Hilbert space methods in partial differential equations. Cour Corp

  47. Showalter R (1970) Well-posed problems for a partial differential equation of order 2m+1. SIAM J Math Anal 1(2):214–231

    MathSciNet  Google Scholar 

  48. Showalter R (1975) A nonlinear parabolic-sobolev equation. J Math Anal Appl 50(1):183–190

    MathSciNet  Google Scholar 

  49. Showalter RE, Ting TW (1970) Pseudoparabolic partial differential equations. SIAM J Math Anal 1(1):1–26

    MathSciNet  Google Scholar 

  50. Shu X, Pan H, Shi J, Song X, Wu XJ (2022) Using global information to refine local patterns for texture representation and classification. Pattern Recog 131:108843

    Google Scholar 

  51. Singh C, Walia E, Kaur KP (2018) Color texture description with novel local binary patterns for effective image retrieval. Pattern Recog 76:50–68

    Google Scholar 

  52. Song T, Li H, Meng F, Wu Q, Cai J (2018) Letrist: Locally encoded transform feature histogram for rotation-invariant texture classification. IEEE Trans Circ Syst Video Technol 28(7):1565–1579

    Google Scholar 

  53. Song T, Xin L, Gao C, Zhang G, Zhang T (2018) Grayscale-inversion and rotation invariant texture description using sorted local gradient pattern. IEEE Signal Process Lett 25(5):625–629

    Google Scholar 

  54. Song T, Feng J, Wang S, Xie Y (2020) Spatially weighted order binary pattern for color texture classification. Expert Syst Appl 147:113167

    Google Scholar 

  55. Song T, Feng J, Wang Y, Gao C (2021) Color texture description based on holistic and hierarchical order-encoding patterns. In: 2020 25th International conference on pattern recognition (ICPR), pp 1306–1312

  56. Song Y, Zhang F, Li Q, Huang H, O’Donnell LJ, Cai W (2017) Locally-transferred fisher vectors for texture classification. In: 2017 IEEE International conference on computer vision (ICCV), pp 4922–4930

  57. Srinivasu PN, JayaLakshmi G, Jhaveri RH, Praveen SP (2022) Ambient assistive living for monitoring the physical activity of diabetic adults through body area networks. Mob Inf Syst 2022:1–18

    Google Scholar 

  58. Van Duijn C, Peletier LA, Pop IS (2007) A new class of entropy solutions of the buckley-leverett equation. SIAM J Math Anal 39(2):507–536

    MathSciNet  Google Scholar 

  59. Varma M, Zisserman A (2005) A statistical approach to texture classification from single images. Int J Comput Vis 62(1):61–81

    Google Scholar 

  60. Varma M, Zisserman A (2009) A statistical approach to material classification using image patch exemplars. IEEE Trans Pattern Anal Mach Intell 31(11):2032–2047

    Google Scholar 

  61. Vieira J, Abreu E, Florindo JB (2022) Texture image classification based on a pseudo-parabolic diffusion model. Multimedia Tools Appl 1–24

  62. Wang G, Bo F, Chen X, Lu W, Hu S, Fang J (2022) A collaborative despeckling method for sar images based on texture classification. Remote Sens 14(6)

  63. Witkin AP (1983) Scale-space filtering. In: Proceedings of the eighth international joint conference on artificial intelligence - Volume 2, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, IJCAI’83, pp 1019–1022

  64. Xiao B, Wang K, Bi X, Li W, Han J (2019) 2d-lbp: An enhanced local binary feature for texture image classification. IEEE Trans Circ Syst Video Technol 29(9):2796–2808

    Google Scholar 

  65. Xu Y, Ji H, Fermüller C (2009) Viewpoint invariant texture description using fractal analysis. Int J Comput Vis 83(1):85–100

    Google Scholar 

  66. Xue J, Zhang H, Dana K (2018) Deep texture manifold for ground terrain recognition. In: Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR), pp 558–567

  67. Yang Z, Lai S, Hong X, Shi Y, Cheng Y, Qing C (2022) Dfaen: Double-order knowledge fusion and attentional encoding network for texture recognition. Expert Syst Appl 209:118223

    Google Scholar 

  68. Zhai W, Cao Y, Zhang J, Zha ZJ (2019) Deep multiple-attribute-perceived network for real-world texture recognition. In: Proceedings of the IEEE/CVF international conference on computer vision (ICCV), pp 3612–3621

  69. Zhang H, Xue J, Dana K (2017) Deep ten: Texture encoding network. In: 2017 IEEE Conference on computer vision and pattern recognition (CVPR), pp 2896–2905

  70. Zhou Y, Wu W, Wang H, Zhang X, Yang C, Liu H (2022) Identification of soil texture classes under vegetation cover based on sentinel-2 data with svm and shap techniques. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing pp 1–1

Download references

Acknowledgements

J. B. Florindo gratefully acknowledges the financial support of São Paulo Research Foundation (FAPESP) (Grants #2020/01984-8 and #2020/09838-0) and from National Council for Scientific and Technological Development, Brazil (CNPq) (Grants #306030/2019-5 and #423292/2018-8). E. Abreu gratefully acknowledges the financial support from National Council for Scientific and Technological Development - Brazil (CNPq) (Grant 306385/2019-8).

Author information

Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing - University of Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária “Zeferino Vaz” - Distr. Barão Geraldo, CEP 13083-859, Campinas, SP, Brasil

    Joao B. Florindo & Eduardo Abreu

Authors
  1. Joao B. Florindo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eduardo Abreu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joao B. Florindo.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Florindo, J.B., Abreu, E. A pseudo-parabolic diffusion model to enhance deep neural texture features. Multimed Tools Appl 83, 11507–11528 (2024). https://doi.org/10.1007/s11042-023-15886-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-15886-w

Keywords

Search

Navigation