## Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms

Optics Express, Vol. 18, Issue 12, pp. 12992-13005 (2010)

http://dx.doi.org/10.1364/OE.18.012992

Acrobat PDF (1207 KB)

### Abstract

A novel method for evaluation of bacterial colonies number (Colony Forming Units - CFU), is described. Proposed algorithm, based on the Mellin transform, allows the CFU evaluation, invariant for the spatial orientation and scale changes. The proposed method involves image recording of bacteria grown in Petri dishes, calculation of the Fourier spectrum followed by coordinates transformation, and determination of the Mellin transform. It was proved that there is a high correlation between CFU and maxima of Mellin spectra. The method was practically implemented for evaluation of antibacterial activity of silver-based nanomaterials and the effect of an additional laser light irradiation.

© 2010 OSA

## 1. Introduction

1. M. Putman, R. Burton, and M. H. Nahm, “Simplified method to automatically count bacterial colony forming unit,” J. Immunol. Methods **302**(1-2), 99–102 (2005). [CrossRef] [PubMed]

2. D. Mukherjee, A. Pal, S. Sarma, and D. Majumder, “Bacterial colony counting using distance transform,” Int. J. Biomed. Comput. **38**(2), 131–140 (1995). [CrossRef] [PubMed]

3. M. Masuko, S. Hosoi, and T. Hayakawa, “A novel method for detection and counting of single bacteria in a wide field using an ultra-high-sensitivity TV camera without a microscope,” FEMS Microbiol. Lett. **81**(3), 287–290 (1991). [CrossRef]

7. X. Liu, S. Wang, L. Sendi, and M. J. Caulfield, “High-throughput imaging of bacterial colonies grown on filter plates with application to serum bactericidal assays,” J. Immunol. Methods **292**(1-2), 187–193 (2004). [CrossRef] [PubMed]

8. K. H. Kim, J. Yu, and M. H. Nahm, “Efficiency of a pneumococcal opsonophagocytic killing assay improved by multiplexing and by coloring colonies,” Clin. Diagn. Lab. Immunol. **10**(4), 616–621 (2003). [PubMed]

6. J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant recognition of polychromatic image of Vibrio Cholerae O1,” Opt. Eng. **41**(4), 827–833 (2002). [CrossRef]

## 2. Influence of objects number on Fourier spectrum

*x*) (

_{i}, y_{i}*i = 1, 2, …, n*, where

*n*is a number of apertures) and the object is illuminated by a monochromatic, coherent plane wave of an unit amplitude, propagating perpendicularly to the (

*x*,

*y*) plane, then the total optical field

*U*(

_{n}*x,y*) in object plane can be described by the convolution of the amplitude transmittance of single aperture with the localization function

*n*objects

*n*and modulation factor

*m(f*, which represents phase relationship associated with mutual spatial configuration of analyzed objects. The modulation factor can be expressed as a sum of

_{x}, f_{y})*N*can be considered as a constant component of

*S*while the factor

_{output}(f_{x}, f_{y}),*m(f*is an additional cosinusoidal modulation. It should be pointed out that determination of

_{x}, f_{y})*S*is possible only for set of objects with the same size and shape. In the case of an unknown number of objects in the input plane, the modulation background may be exploited for determination of the objects number. Furthermore, this approach may be used to perform comparative analysis of samples with various objects numbers, like e.g. bacteria colonies. It based on correlation between Fourier spectrum properties and number of analyzed objects.

_{output}(f_{x}, f_{y})## 3. Verification of the theoretical considerations by numerical simulations

*S*(Eq. (8)). As an example, the function

_{output}(f_{x}, f_{y})*S*for

_{output}(f_{x}, f_{y})*n*= 5 objects is presented on Fig. 2 . In order to estimate the modulation background value

*N,*we will define it as a mean value of maxima and minima of

*S*:The parameter

_{output}(f_{x}, f_{y})*N*can be considered as a constant component of the modulation.

*S*was calculated. Then, the modulation background

_{output}(f_{x}, f_{y})*N*was estimated by use of Eq. (9). The high correlation between the modulation background and the number of apertures was stated (see Fig. 3 ).

*n*and calculated

*N*value by using proposed approach. This value is increasing, when the number of objects increases. The relationship between modulation background value

*N*and number of objects

*n*is expressed as follows:

*error(n)*between

*N*and

*n*described by Eq. (10) is caused by the limited bandwidth of Discrete Fourier Transform (DFT). The Fourier transform of the analyzed objects limited by the window can be considered as a convolution of the Fourier transforms of the objects and the window. It is known that convolution result is depending on the shape of both convoluted functions. When the window size is infinite, then the object space is unlimited and the Fourier transform of the window takes a form of a Dirac delta function. Therefore the final Fourier transform of the analyzed objects and the window is equal to the Fourier transform of the object itself according to the “sifting” properties of Dirac delta function. The finite size of the window causes smoothing and spreading of the original Fourier spectrum of the objects. When the size of the window decreases this effects are more significant. In our analysis the size of the window limiting the object space is constant. Therefore the increasing number of analyzed objects in input space decreases the area of the windows causing the spreading and smoothing of the analyzed objects Fourier spectrum. This effect affects the proposed approach by occurring the difference

*error(n)*between the modulation background and the number of analyzed objects.

*N*for various configurations of apertures is equal to 0.036 [a.u.] Therefore, the proposed method might be used to evaluate objects number with the significant accuracy, providing that the objects have the same shape and size.

## 4. Application of Mellin transform for scale invariant analysis

24. R. J. Sasiela and J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A **10**(4), 646–660 (1993). [CrossRef]

25. B. L. Ellerbroek, “Including outer scale effects in zonal adaptive optics calculations,” Appl. Opt. **36**(36), 9456–9467 (1997). [CrossRef]

26. E. Kolenović, E. Kolenović, T. Kreis, Ch. von Kopylow, and W. Jüptner, “Determination of large-scale out-of-plane displacements in digital Fourier holography,” Appl. Opt. **46**(16), 3118–3125 (2007). [CrossRef] [PubMed]

27. Y. K. Tung, “Mellin transform applied to uncertainty analysis in hydrology/ hydraulics,” J. Hydraul. Eng. **116**(5), 659–674 (1990). [CrossRef]

28. Ch. Zoppou, “Review of urban storm water models,” Environ. Model. Softw. **16**(3), 195–231 (2001). [CrossRef]

6. J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant recognition of polychromatic image of Vibrio Cholerae O1,” Opt. Eng. **41**(4), 827–833 (2002). [CrossRef]

*s*is a complex variable. If the complex variable

*s*associated with imaginary axis equals

37. T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging **18**(11), 1049–1075 (1999). [CrossRef]

38. L. Yaroslavsky, “Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling,” Appl. Opt. **42**(20), 4166–4175 (2003). [CrossRef] [PubMed]

39. C. Y. Wu, A. R. D. Somervell, T. G. Haskell, and T. H. Barnes, “Optical Mellin transform through Haar wavelet transformation,” Opt. Commun. **227**(1-3), 75–82 (2003). [CrossRef]

20. Q. Yin, L. Shen, J. N. Kim, and Y. J. Jeong, “Scale-invariant pattern recognition using a combined Mellin radial harmonic function and the bidimensional empirical mode decomposition,” Opt. Express **17**(19), 16581–16589 (2009). [CrossRef] [PubMed]

22. D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. **15**(7), 1795–1799 (1976). [CrossRef] [PubMed]

*ρ*- ln

*m*,

*θ*)|

^{2}, so the scale change is now represented by the shift along

*ρ*coordinate, what causes log-polar transformation of the input Fourier spectrum. So, one-dimensional (1D) Mellin transform described by Eq. (11) (see Fig. 6 ) can be expressed by:where

## 5. Practical implementation of Mellin transform for evaluation of the antibacterial activity of some agents

*in vitro*, were performed. The problem of growing bacteria resistance to various antibacterial agents and sterilization methods, is known worldwide. Many laboratories are working towards elaboration of new methods and materials for combating pathogens. Recently, antibacterial features of nanomaterials are examined and it was proved that e.g. silver based nanomaterials exhibit certain antimicrobial activity [40

40. M. Kawashita, S. Toda, H.-M. Kim, T. Kokubo, and N. Masuda, “Preparation of Antibacterial Silver-Doped Silica Glass Microspheres,” J. Biomed. Mater. Res. **66**(2), 266–274 (2003). [CrossRef]

41. J. S. Kim, E. Kuk, K. N. Yu, J. H. Kim, S. J. Park, H. J. Lee, S. H. Kim, Y. K. Park, Y. H. Park, C. Y. Hwang, Y. K. Kim, Y. S. Lee, D. H. Jeong, and M. H. Cho, “Antimicrobial effects of silver nanoparticles,” Nanomedicine **3**(1), 95–101 (2007). [PubMed]

### 5.1 Material and methods

### 5.2 Correlation between Mellin spectrum properties and CFU

^{th}order polynomial expressed by the following formula:where polynomial coefficients are equal to:

*a*= 1.321 x 10

_{2}^{−14};

*a*= −1.0166 x 10

_{1}^{−5};

*a*= 2397.5. The R

_{0}^{2}value, describing how good is the fitting of provided experimental data by 2

^{th}order polynomial, is equal 0.9963.

## 6. Discussion

^{TM}2 duo, 1GB RAM). This time can be extended for the images recorded with higher resolution. The performance speed and accuracy of proposed algorithm can be increased by achieving higher contrast between bacteria colonies and agar background, for example by using dyes to color colony or by using appropriate image processing algorithm to obtain binary mask of examined samples on Petri dish. It should be mentioned as well, that any defect of medium, possible structural and optical non-homogeneities may affect the described above analysis. Proposed approach was considered the case of bacteria colonies with the same shape, therefore the analysis of samples containing bacteria colonies with different shapes by proposed method can lead to significant errors. It should be pointed out as well, that all bacteria sample images should be recorded in the same illumination conditions.

## 7. Conclusion

## Acknowledgement

## References and links

1. | M. Putman, R. Burton, and M. H. Nahm, “Simplified method to automatically count bacterial colony forming unit,” J. Immunol. Methods |

2. | D. Mukherjee, A. Pal, S. Sarma, and D. Majumder, “Bacterial colony counting using distance transform,” Int. J. Biomed. Comput. |

3. | M. Masuko, S. Hosoi, and T. Hayakawa, “A novel method for detection and counting of single bacteria in a wide field using an ultra-high-sensitivity TV camera without a microscope,” FEMS Microbiol. Lett. |

4. | A. Robinson, N. Sadr-kazemi, G. Dickason, and S. T. L. Harrison, “Morphological characterization of yeast colonies growth on solid media using image processing,” Biotechnol. Tech. |

5. | J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant optical color correlation for recognition of Vibrio cholerae O1,” in |

6. | J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant recognition of polychromatic image of Vibrio Cholerae O1,” Opt. Eng. |

7. | X. Liu, S. Wang, L. Sendi, and M. J. Caulfield, “High-throughput imaging of bacterial colonies grown on filter plates with application to serum bactericidal assays,” J. Immunol. Methods |

8. | K. H. Kim, J. Yu, and M. H. Nahm, “Efficiency of a pneumococcal opsonophagocytic killing assay improved by multiplexing and by coloring colonies,” Clin. Diagn. Lab. Immunol. |

9. | E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. |

10. | E. Bae, A. Aroonnual, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “System automation for a bacterial colony detection and identification instrument via forward scattering,” Meas. Sci. Technol. |

11. | P. P. Banada, S. Guo, B. Bayraktar, E. W. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. |

12. | M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. |

13. | B. Rajwa, M. Venkatapathi, K. Ragheb, P. P. Banada, E. D. Hirleman, T. Lary, and J. P. Robinson, “Automated classification and recognition of bacterial particles in flow by multi-angle scatter measurement and a support-vector machine classifier,” Cytometry A |

14. | E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Analysis of time – resolved scattering from macroscale bacterial colonies,” J. Biomed. Opt. |

15. | R. N. Bracewell, |

16. | H. Stark, ed., |

17. | M. Nieto-Vesperinas, |

18. | J. W. Goodman, |

19. | N. Götz, S. Drüe, and G. Hartmann, “Invariant object recognition with discriminant features based on local fast-Fourier Mellin transform, “in |

20. | Q. Yin, L. Shen, J. N. Kim, and Y. J. Jeong, “Scale-invariant pattern recognition using a combined Mellin radial harmonic function and the bidimensional empirical mode decomposition,” Opt. Express |

21. | F. S. Roux, “Rotation- and scale – invariant feature extraction by diffractive optical inner – product transform,” Appl. Opt. |

22. | D. Casasent and D. Psaltis, “Position, rotation, and scale invariant optical correlation,” Appl. Opt. |

23. | D. Casasent, and D. Psaltis, “New optical transforms for pattern recognition,” in |

24. | R. J. Sasiela and J. D. Shelton, “Transverse spectral filtering and Mellin transform techniques applied to the effect of outer scale on tilt and tilt anisoplanatism,” J. Opt. Soc. Am. A |

25. | B. L. Ellerbroek, “Including outer scale effects in zonal adaptive optics calculations,” Appl. Opt. |

26. | E. Kolenović, E. Kolenović, T. Kreis, Ch. von Kopylow, and W. Jüptner, “Determination of large-scale out-of-plane displacements in digital Fourier holography,” Appl. Opt. |

27. | Y. K. Tung, “Mellin transform applied to uncertainty analysis in hydrology/ hydraulics,” J. Hydraul. Eng. |

28. | Ch. Zoppou, “Review of urban storm water models,” Environ. Model. Softw. |

29. | J. Dongmei, and Z. Rongchun, “Speaker normalization based on the generalized time - frequency representation and Mellin transform”, in |

30. | J. Chen, B. Xu, and T. Huang, “A novel robust feature of speech signal based on Mellin transform for speaker – independent speech recognition,” in |

31. | T. Irino and R. D. Patterson, “Segregating information about the size and the shape of the vocal tract using a time domain auditory model: The stabilized wavelet-Mellin transform,” Speech Commun. |

32. | A. De Sena, and D. Rocchesso, “A Fast Mellin transform with applications in DAFX,” |

33. | Z. Sun, and Ch. Han, “Parameter estimation of non-Rayleigh RCS models for SAR images based on the Mellin transformation,” in |

34. | A. Derbel, F. Kalel, A. Ben Hamida, and M. Samet, “Wavelet filtering based on Mellin transform dedicated to Cochlear Prostheses”, in |

35. | Z. Tong, Y. Fusheng, and T. Qingyu, “A fast algorithm of continuous wavelet transform based on Mellin transform with biomedical application,” in |

36. | I. Buzalewicz, K. Wysocka, and H. Podbielska, “Exploiting of optical transforms for bacteria evaluation in vitro,” Proc. SPIE |

37. | T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging |

38. | L. Yaroslavsky, “Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling,” Appl. Opt. |

39. | C. Y. Wu, A. R. D. Somervell, T. G. Haskell, and T. H. Barnes, “Optical Mellin transform through Haar wavelet transformation,” Opt. Commun. |

40. | M. Kawashita, S. Toda, H.-M. Kim, T. Kokubo, and N. Masuda, “Preparation of Antibacterial Silver-Doped Silica Glass Microspheres,” J. Biomed. Mater. Res. |

41. | J. S. Kim, E. Kuk, K. N. Yu, J. H. Kim, S. J. Park, H. J. Lee, S. H. Kim, Y. K. Park, Y. H. Park, C. Y. Hwang, Y. K. Kim, Y. S. Lee, D. H. Jeong, and M. H. Cho, “Antimicrobial effects of silver nanoparticles,” Nanomedicine |

42. | K. Wysocka, I. Buzalewicz, A. Wieliczko, K. Kowal, W. Stręk, and H. Podbielska, “Biomaterials with antibacterial activity,” Engin. Biomaterials |

**OCIS Codes**

(100.2960) Image processing : Image analysis

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: April 2, 2010

Revised Manuscript: May 8, 2010

Manuscript Accepted: May 11, 2010

Published: June 2, 2010

**Virtual Issues**

Vol. 5, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Igor Buzalewicz, Katarzyna Wysocka-Król, and Halina Podbielska, "Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms," Opt. Express **18**, 12992-13005 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-12-12992

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### References

- M. Putman, R. Burton, and M. H. Nahm, “Simplified method to automatically count bacterial colony forming unit,” J. Immunol. Methods 302(1-2), 99–102 (2005). [CrossRef] [PubMed]
- D. Mukherjee, A. Pal, S. Sarma, and D. Majumder, “Bacterial colony counting using distance transform,” Int. J. Biomed. Comput. 38(2), 131–140 (1995). [CrossRef] [PubMed]
- M. Masuko, S. Hosoi, and T. Hayakawa, “A novel method for detection and counting of single bacteria in a wide field using an ultra-high-sensitivity TV camera without a microscope,” FEMS Microbiol. Lett. 81(3), 287–290 (1991). [CrossRef]
- A. Robinson, N. Sadr-kazemi, G. Dickason, and S. T. L. Harrison, “Morphological characterization of yeast colonies growth on solid media using image processing,” Biotechnol. Tech. 12(10), 763–767 (1998). [CrossRef]
- J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant optical color correlation for recognition of Vibrio cholerae O1,” in Proceedings of International IEEE Conference on Pattern Recognition, vol. 2, (IEEE, 2000), pp. 2283.
- J. Alvarez-Borrego, R. Mouriño-Pérez, G. Cristóbal, and J. Pech-Pacheco, “Invariant recognition of polychromatic image of Vibrio Cholerae O1,” Opt. Eng. 41(4), 827–833 (2002). [CrossRef]
- X. Liu, S. Wang, L. Sendi, and M. J. Caulfield, “High-throughput imaging of bacterial colonies grown on filter plates with application to serum bactericidal assays,” J. Immunol. Methods 292(1-2), 187–193 (2004). [CrossRef] [PubMed]
- K. H. Kim, J. Yu, and M. H. Nahm, “Efficiency of a pneumococcal opsonophagocytic killing assay improved by multiplexing and by coloring colonies,” Clin. Diagn. Lab. Immunol. 10(4), 616–621 (2003). [PubMed]
- E. Bae, P. P. Banada, K. Huff, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “Biophysical modeling of forward scattering from bacterial colonies using scalar diffraction theory,” Appl. Opt. 46(17), 3639–3648 (2007). [CrossRef] [PubMed]
- E. Bae, A. Aroonnual, A. K. Bhunia, J. P. Robinson, and E. D. Hirleman, “System automation for a bacterial colony detection and identification instrument via forward scattering,” Meas. Sci. Technol. 20(1), 1–9 (2009). [CrossRef]
- P. P. Banada, S. Guo, B. Bayraktar, E. W. Bae, B. Rajwa, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, “Optical forward-scattering for detection of Listeria monocytogenes and other Listeria species,” Biosens. Bioelectron. 22(8), 1664–1671 (2007). [CrossRef]
- M. Venkatapathi, B. Rajwa, K. Ragheb, P. P. Banada, T. Lary, J. P. Robinson, and E. D. Hirleman, “High speed classification of individual bacterial cells using a model-based light scatter system and multivariate statistics,” Appl. Opt. 47(5), 678–686 (2008). [CrossRef] [PubMed]
- B. Rajwa, M. Venkatapathi, K. Ragheb, P. P. Banada, E. D. Hirleman, T. Lary, and J. P. Robinson, “Automated classification and recognition of bacterial particles in flow by multi-angle scatter measurement and a support-vector machine classifier,” Cytometry A 73A(4), 369–379 (2008). [CrossRef]
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- B. L. Ellerbroek, “Including outer scale effects in zonal adaptive optics calculations,” Appl. Opt. 36(36), 9456–9467 (1997). [CrossRef]
- E. Kolenović, E. Kolenović, T. Kreis, Ch. von Kopylow, and W. Jüptner, “Determination of large-scale out-of-plane displacements in digital Fourier holography,” Appl. Opt. 46(16), 3118–3125 (2007). [CrossRef] [PubMed]
- Y. K. Tung, “Mellin transform applied to uncertainty analysis in hydrology/ hydraulics,” J. Hydraul. Eng. 116(5), 659–674 (1990). [CrossRef]
- Ch. Zoppou, “Review of urban storm water models,” Environ. Model. Softw. 16(3), 195–231 (2001). [CrossRef]
- J. Dongmei, and Z. Rongchun, “Speaker normalization based on the generalized time - frequency representation and Mellin transform”, in Proceedings of 5th International Conference on Signal Processing Proceedings2, (IEEE, 2000), pp. 782–785.
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- T. Irino and R. D. Patterson, “Segregating information about the size and the shape of the vocal tract using a time domain auditory model: The stabilized wavelet-Mellin transform,” Speech Commun. 36(3), 181–203 (2002). [CrossRef]
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- Z. Sun, and Ch. Han, “Parameter estimation of non-Rayleigh RCS models for SAR images based on the Mellin transformation,” in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2009), pp. 1081–1084.
- A. Derbel, F. Kalel, A. Ben Hamida, and M. Samet, “Wavelet filtering based on Mellin transform dedicated to Cochlear Prostheses”, in Proceedings of 29th Annual International Conference of the IEEE on Engineering in Medicine and Biology Society3 (IEEE, 2007), pp. 1990–1903.
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- I. Buzalewicz, K. Wysocka, and H. Podbielska, “Exploiting of optical transforms for bacteria evaluation in vitro,” Proc. SPIE 7371, 73711H–73711H–6 (2009).
- T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999). [CrossRef]
- L. Yaroslavsky, “Boundary effect free and adaptive discrete signal sinc-interpolation algorithms for signal and image resampling,” Appl. Opt. 42(20), 4166–4175 (2003). [CrossRef] [PubMed]
- C. Y. Wu, A. R. D. Somervell, T. G. Haskell, and T. H. Barnes, “Optical Mellin transform through Haar wavelet transformation,” Opt. Commun. 227(1-3), 75–82 (2003). [CrossRef]
- M. Kawashita, S. Toda, H.-M. Kim, T. Kokubo, and N. Masuda, “Preparation of Antibacterial Silver-Doped Silica Glass Microspheres,” J. Biomed. Mater. Res. 66(2), 266–274 (2003). [CrossRef]
- J. S. Kim, E. Kuk, K. N. Yu, J. H. Kim, S. J. Park, H. J. Lee, S. H. Kim, Y. K. Park, Y. H. Park, C. Y. Hwang, Y. K. Kim, Y. S. Lee, D. H. Jeong, and M. H. Cho, “Antimicrobial effects of silver nanoparticles,” Nanomedicine 3(1), 95–101 (2007). [PubMed]
- K. Wysocka, I. Buzalewicz, A. Wieliczko, K. Kowal, W. Stręk, and H. Podbielska, “Biomaterials with antibacterial activity,” Engin. Biomaterials 81–84, 117–119 (2008).

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