Non-linear dimensionality reduction using fuzzy lattices

Rajiv Kapoor; Rashmi Gupta

Non-linear dimensionality reduction using fuzzy lattices

View Fulltext

Author(s): Rajiv Kapoor ¹ and Rashmi Gupta ²
- Affiliations: 1: Delhi Technological University (Formerly Delhi College of Engineering), Delhi, India;
  2: Ambedkar Institute of Advanced Communication Technologies and Research (Affiliated to Guru Gobind Singh Indraprastha University), Delhi, India
Source: Volume 7, Issue 3, June 2013, p. 201 – 208
DOI: 10.1049/iet-cvi.2012.0097 , Print ISSN 1751-9632, Online ISSN 1751-9640

Received 21/05/2012, Accepted 29/01/2013, Revised 02/01/2013, Published

The proposed method is based on extraction of non-linearity from the nearest neighbourhood elements of image. To detect non-linearity, relation between the nearest neighbourhood elements of the image, have been expressed in terms of Gaussian membership functions. All the elements of the image are connected with the nearest neighbourhood elements with some membership degree of the Gaussian functions. It results in the formation of number of fuzzy lattices. The lattices have been expressed in the form of Schrödinger equation, to find the kinetic energy (KE) used, corresponding to change occurring in the facial activity of a person. Finally, the KE embedded in three dimension space is used to distinguish non-linear changes during occurrence of various facial activities. Experimental results show that proposed method is effective in recognition of facial expression as it focuses on extracting the non-linear features corresponding to contours of maximum energy which are appearing because of different expressions.

References

1. 1)
  - 21. Edmonds, E.A.: ‘Lattice Fuzzy Logics’, Int. J. Man-Mach. Stud., 1980, 13, (4), pp. 455–465 (doi: 10.1016/S0020-7373(80)80006-X).
2. 2)
  - 23. Kotsia, I., Pitas, I.: ‘Facial expression recognition in image sequences using geometric deformation features and support vector machines’, IEEE Trans. Image Process., 2007, 16, (1), pp. 172–187 (doi: 10.1109/TIP.2006.884954).
3. 3)
  - 18. Yang, J., Zhang, D., Frangi, A., Yang, J.: ‘Two-dimensional PCA: a new approach to appearance-based face representation and recognition’, IEEE Trans. Pattern Anal. Mach. Intell., 2004, 26, (1), pp. 131–137 (doi: 10.1109/TPAMI.2004.1261097).
4. 4)
  - 16. Tian, Y., Kanade, T., Cohn, J.F.: ‘Recognizing action units for facial expression analysis’, IEEE Trans. Pattern Anal. Mach. Intell., 2001, 23, pp. 97–115 (doi: 10.1109/34.908962).
5. 5)
  - 11. Khurd, P., Davatzikos, C.: ‘On analyzing diffusion tensor images by identifying manifold structure using isomaps’, IEEE Trans. Med. Imaging, 2007, 26, (6), pp. 772–778 (doi: 10.1109/TMI.2006.891484).
6. 6)
  - 13. Vizireanu, D.N., Udrea, R.M.: ‘Visual-oriented morphological foreground content grayscale frames interpolation method’, J. Electron. Imaging, 2009, 18, (2), pp. 1–3 (doi: 10.1117/1.3134142).
7. 7)
  - 17. Buciu, I., Kotropoulos, C., Pitas, I.: ‘ICA and Gabor representation for facial expression recognition’, Proc. IEEE Int. Conf. on Image Process., 2003, 2, (3), pp. 855–858.
8. 8)
  - 6. Dacheng Tao, S.S., Chan, K.P.: ‘Evolutionary cross-domain discriminative Hessian eigenmaps’, IEEE Trans. Image Process., 2010, 19, (4), pp. 1075–1086 (doi: 10.1109/TIP.2009.2035867).
9. 9)
  - 1. Tenenbaum, J.B., Silva, V. de, Langford, J.C.: ‘A global geometric framework for nonlinear dimensionality reduction’, Science, 2000, 290, (5500), pp. 2319–2323 (doi: 10.1126/science.290.5500.2319).
10. 10)
  - 30. Zhu, X., Ramanan, D.: ‘Face detection, pose estimation and landmark localization in the wild’. Computer Vision and Pattern Recognition, Providence, Rhode Island, June 2012, pp. 1–8.
11. 11)
  - 27. http://www.kasrl.org/jaffe.html.
12. 12)
  - 8. Feng, X., Pietikäinen, M., Hadid, A.: ‘Facial expression recognition with local binary patterns and linear programming’, Pattern Recognit. Image Anal., 2005, 15, (2), pp. 546–548.
13. 13)
  - 19. Kong, H., Teoh, E., Wang, J., Venkateswarlu, R.: ‘Two dimensional Fisher discriminant analysis: forget about small sample size problem’. Proc. IEEE Conf. on Acoustics Speech Signal Processing, March 2005, pp. 761–764.
14. 14)
  - 25. Kanade, T., Cohn, J., Tian, Y.: ‘Comprehensive database for facial expression analysis’. Proc. IEEE Int. Conf. on Face and Gesture Recognition, 2000, pp. 46–53.
15. 15)
  - 9. Shan, C., Gong, S., McOwan, P.W.: ‘Facial expression recognition based on local binary patterns: a comprehensive study’, Image Vis. Comput., 2009, 27, (6), pp. 803–816 (doi: 10.1016/j.imavis.2008.08.005).
16. 16)
  - 22. Petridis, V., Kaburlasos, V.G.: ‘Learning in the framework of fuzzy lattices’, IEEE Trans. Fuzzy Syst., 1999, 7, (4), pp. 422–440 (doi: 10.1109/91.784201).
17. 17)
  - 20. Kapoor, R., Gupta, R.: ‘Fuzzy Lattice based technique for classification of power quality disturbances’ European Trans. Electrical Power, (Wiley online library, 2011) DOI: 10.1002/etep.624.
18. 18)
  - 2. Lee, M.D.: ‘Determining the dimensionality of multidimensional scaling models for cognitive modeling’, J. Math. Psychol., 2001, 45, (1), pp. 149–166 (doi: 10.1006/jmps.1999.1300).
19. 19)
  - 28. Martinez, A.M., Benavente, R.: ‘The AR Face Database’. CVC Technical Report #24, June1998.
20. 20)
  - 24. Guiling, Li., Zhao, Hui.: ‘Facial expression recognition based on the second feature selection and support vector machines’, Comput. Knowl. Technol., 2008, 1, pp. 2700–2702.
21. 21)
  - 7. Lyons, M.J., Akamatsu, S., Kamachi, M., Gyoba, J.: ‘Coding facial expressions with Gabor wavelets’. IEEE Int. Conf. on Automatic Face and Gesture Recognition, Nara, Japan, April 1998, pp. 200–205.
22. 22)
  - 26. http://vasc.ri.cmu.edu//idb/html/face/facial_expression/index.html.
23. 23)
  - 3. Roweis, S.T., Saul, L.K.: ‘Nonlinear dimensionality reduction by locally linear embedding’, Science, 2000, 290, (5500), pp. 2323–2326 (doi: 10.1126/science.290.5500.2323).
24. 24)
  - 15. He, Li., Buenaposada, J.M., Baumela, L.: ‘An empirical comparison of graph-based dimensionality reduction algorithms on facial expressions recognition tasks’. Int. Conf. on Pattern Recognition, Tampa, Florida, December 2008, pp. 1–4.
25. 25)
  - 4. Huang, M.W., Wang, Z.W., Ying, Z.L.A.: ‘Novel method of facial expression recognition based on GPLVM plus SVM’. Proc. Int. Conf. Signal Processing, Beijing, October 2010, pp. 916–919.
26. 26)
  - 5. Cai, D., He, X.F., Han, J.W., Zhang, H.J.: ‘Orthogonal Laplacian faces for face recognition’, IEEE Trans. Image Process., 2006, 15, (11), pp. 3608–3614 (doi: 10.1109/TIP.2006.881945).
27. 27)
  - 12. Qinggang, W., Jianwei, L.: ‘Combining local and global information for nonlinear dimensionality reduction’, J. Neurocomput., 2009, 72, (10–12), pp. 2235–2241 (doi: 10.1016/j.neucom.2009.01.006).
28. 28)
  - 14. Udrea, R.M., Vizireanu, D.N.: ‘Iterative generalization of morphological skeleton’, J. Electron. Imaging, 2007, 16, (1), pp. 1–3 (doi: 10.1117/1.2713739).
29. 29)
  - 29. Dhall, A., Goecke, R., Lucey, S., Gedeon, T.: ‘Static facial expression analysis in tough conditions: data, evaluation protocol and benchmark’. IEEE Int. Conf. on Computer Vision, Workshop BEFIT, Barcelona, Spain, November 2011, pp. 6–13.
30. 30)
  - 10. Yeh, Y.R., Huang, S.Y., Lee, Y.J.: ‘Nonlinear dimension reduction with Kernel sliced inverse regression’, IEEE Trans. Knowl. Data Eng., 2009, 21, (11), pp. 1590–1603 (doi: 10.1109/TKDE.2008.232).

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Non-linear dimensionality reduction using fuzzy lattices

References

Related content