The authors propose two equations based on the pixel geometry and connectivity properties, which can be used to compute, efficiently, the Euler number of a binary digital image with either thick or thin boundaries. Although computing this feature, the authors’ technique extracts the underlying topological information provided by the shape pixels of the given image. The correctness of computing the Euler number using the new equations is also established theoretically. The performance of the proposed method is compared against other available alternatives. Experimental results on a large image database demonstrate that the authors technique for computing the Euler number outperforms the earlier approaches significantly in terms of the number of basic arithmetic operations needed per pixel. Both equations are specialised only for 4-connectivity cases.

References

1. 1)
  - 21. Sossa, H., Cuevas, E., Zaldivar, D.: ‘Computation of the Euler number of a binary image composed of hexagonal cells’, J. Appl. Res. Technol., 2010, 8, (3), pp. 340–351.
2. 2)
  - 11. Díaz de León Santiago, J.L., Sossa, J.H.: ‘On the computation of the Euler number of a binary object’, Pattern Recognit., 1996, 29, (3), pp. 471–476 (doi: 10.1016/0031-3203(95)00098-4).
3. 3)
  - 17. Kiderlen, M.: ‘Estimating the Euler characteristic of a planar set from a digital image’, J. Vis. Commun. Image Represent., 2006, 17, (6), pp. 1237–1255 (doi: 10.1016/j.jvcir.2006.05.001).
4. 4)
  - 1. Yang, H.S., Sengupta, S.: ‘Intelligent shape recognition for complex industrial tasks’, IEEE Control Syst. Mag., 1988, 8, (3), pp. 23–29 (doi: 10.1109/37.473).
5. 5)
  - 4. Bribiesca, E.: ‘Measuring 2d shape compactness using the contact perimeter’, Comput. Math. Appl., 1997, 33, (11), pp. 1–9 (doi: 10.1016/S0898-1221(97)00082-5).
6. 6)
  - 6. Dyer, Ch.R.: ‘Computing the Euler number of an image from its quadtree’, Comput. Vis. Graph. Image Process., 1980, 13, pp. 270–276 (doi: 10.1016/0146-664X(80)90050-7).
7. 7)
  - 4. Al Faqheri, W., Mashohor, S.: ‘A real-time Malaysian automatic license plate recognition (M-ALPR) using hybrid fuzzy’, Int. J. Comput. Sci. Netw. Sec., 2009, 9, (2), pp. 333–340.
8. 8)
  - 10. Chiavetta, F., Di Gesú, V.: ‘Parallel computation of the Euler number via connectivity graph’, Pattern Recognit. Lett., 1993, 14, (11), pp. 849–859 (doi: 10.1016/0167-8655(93)90148-7).
9. 9)
  - 14. Sossa, H., Cuevas, E., Zaldivar, D.: ‘Computation of the Euler number of a binary image composed of hexagonal cells’, J. Appl. Res. Technol., 2010, 8, (3), pp. 340–351.
10. 10)
  - 9. Chen, M.H., Yan, P.F.: ‘A fast algorithm to calculate the Euler number for binary images’, Pattern Recognit. Lett., 1988, 8, (12), pp. 295–297 (doi: 10.1016/0167-8655(88)90078-5).
11. 11)
  - 26. Bishnu, A., Bhattacharya, B.B., Kundu, M.K., Murthy, C.A., Acharya, T.: ‘A pipeline architecture for computing the Euler number of a binary image’, J. Syst. Archit. Euromicro J., 2005, 51, (8), pp. 470–487 (doi: 10.1016/j.sysarc.2004.12.001).
12. 12)
  - 15. Sossa, H., Cuevas, E., Zaldivar, D.: ‘Alternative way to compute the Euler number of a binary image’, J. Appl. Res. Technol., 2011, 9, (3), pp. 335–341.
13. 13)
  - 22. Samet, H., Tamminen, M.: ‘Computing geometric properties of images represented by linear quadtrees’, IEEE Trans. Pattern Anal. Mach. Intell., 1985, 7, (2), pp. 229–240 (doi: 10.1109/TPAMI.1985.4767646).
14. 14)
  - 24. Rosenfeld, A., Kak, A.: ‘Digital picture processing’ (Academic Press, New-York, 1976), pp. 449–350.
15. 15)
  - 8. Beri, H.: ‘Computing the Euler characteristic and related additive functionals of digital objects from their beentree representation’, Comput. Vis. Graph. Image Process., 1987, 40, pp. 115–126 (doi: 10.1016/0734-189X(87)90059-4).
16. 16)
  - 16. Imiya, A., Eckhardt, U.: ‘The Euler characteristics of discrete objects and discrete quasi-objects’, Comput. Vis. Image Underst., 1999, 75, (3), pp. 307–318 (doi: 10.1006/cviu.1999.0791).
17. 17)
  - 25. Dey, S., Bhattacharya, B.B., Kundu, M.K., Acharya, T.: ‘A fast algorithm for computing the Euler number of an image and its VLSI implementation’. Proc. 13th Int. Conf. VLSI Design, 2000, pp. 330–335.
18. 18)
  - L. Snidaro , G. Foresti . Real-time thresholding with Euler numbers. Pattern Recognit. Lett. , 1533 - 1544
19. 19)
  - 18. Nonato, L.G., CasteloFilho, A., Minghim, R., Batista, J.: ‘Morse operators for digital planar surfaces and their application to image segmentation’, IEEE Trans. Image Process., 2004, 13, (2), pp. 216–227 (doi: 10.1109/TIP.2003.819908).
20. 20)
  - 3. Lin, X., Ji, J., Gu, G.: ‘The Euler number study of image and its application’. Proc. Second IEEE Conf. Industrial Electronics and Applications (ICIEA 2007), 2007, pp. 910–912.
21. 21)
  - 7. Beri, H., Nef, W.: ‘Algorithms for the Euler characteristic and related additive functionals of digital objects’, Comput. Vis. Graph. Image Process., 1984, 28, pp. 166–175 (doi: 10.1016/S0734-189X(84)80019-5).
22. 22)
  - 13. Bribiesca, E.: ‘Computation of the Euler number using the contact perimeter’, Comput. Math. Appl., 2010, 60, pp. 1364–1373 (doi: 10.1016/j.camwa.2010.06.018).
23. 23)
  - 12. Serra, J.: ‘Image analysis and mathematical morphology’ (Academic Press, 1982).
24. 24)
  - 19. Di Zenzo, S., Cinque, L., Levialdi, S.: ‘Run-based algorithms for binary image analysis and processing’, IEEE Trans. Pattern Anal. Mach. Intell., 1996, 18, (1), pp. 83–89 (doi: 10.1109/34.476016).
25. 25)
  - 20. Feng He, L., Yan Chao, Y., Susuki, K.: ‘An algorithm for connected-component labeling, hole labeling and Euler number computing’, J. Comput. Sci. Technol., 2013, 28, (3), pp. 468–478 (doi: 10.1007/s11390-013-1348-y).
26. 26)
  - 27. Dey, S., Bhattacharya, B.B., Kundu, M.K., Bishnu, A., Acharya, T.: ‘A co-processor for computing Euler number of a binary image using divide-and-conquer strategy’, Fundam. Inform., 2007, 76, pp. 75–89.
27. 27)
  - 5. Gray, S.B.: ‘Local properties of binary images in two dimensions’, IEEE Trans. Comput., 1971, 20, (5), pp. 551–561 (doi: 10.1109/T-C.1971.223289).

Alternative formulations to compute the binary shape Euler number

References

Related content