## Three-dimensional identification of biological microorganism using integral imaging

Optics Express, Vol. 14, Issue 25, pp. 12096-12108 (2006)

http://dx.doi.org/10.1364/OE.14.012096

Acrobat PDF (549 KB)

### Abstract

In this paper, we address the identification of biological microorganisms using microscopic integral imaging (II). II senses multiview directional information of 3D objects illuminated by incoherent light. A micro-lenslet array generates a set of elemental images by projecting a 3D scene onto a detector array. In computational reconstruction of II, 3D volumetric scenes are numerically reconstructed by means of a geometrical ray projection method. The identification of the biological samples is performed using the 3D volume of the reconstructed object. In one approach, the multivariate statistical distribution of the reference sample is measured in 3D space and compared with an unknown input sample by means of statistical discriminant functions. The multivariate empirical cumulative density of the 3D volume image is determined for classification. On the other approach, the graph matching technique is applied to 3D volumetric images with Gabor feature extraction. The reference morphology is identified in unknown input samples using 3D grids. Experimental results are presented for the identification of sphacelaria alga and tribonema aequale alga. We present experimental results for both 3D and 2D imaging. To the best of our knowledge, this is the first report on 3D identification of microorganisms using II.

© 2006 Optical Society of America

## 1. Introduction

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**, 4492–4506 (2005), http://www.opticsinfobase.org/abstract.cfm?id=84327. [CrossRef] [PubMed]

5. A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. **40**, 837–850 (2004). [CrossRef]

2. B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, “Real-time automated 3D sensing, detection, and recognition of dynamic biological micro-organic events,” Opt. Express **14**, 3806–3829 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-9-3806. [CrossRef] [PubMed]

14. H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction”, Opt. Lett. **26**, 157–159 (2001). [CrossRef]

16. A. Stern and B. Javidi, “3D image sensing and reconstruction with time-division multiplexed computational integral imaging (CII),” Appl. Opt. **42**, 7036–7042 (2003). [CrossRef] [PubMed]

19. A. L. Amaral, M. da Motta, M. N. Pons, H. Vivier, N. Roche, M. Moda, and E. C. Ferreira, “Survey of protozoa and metazoa populations in wastewater treatment plants by image analysis and discriminant analysis,” Environmentrics **15**, 381–390 (2004). [CrossRef]

23. A. C. Rencher, *Methods of multivariate analysis*, (Wiley, 2002). [CrossRef]

3. S. Yeom, I Moon, and B. Javidi, “Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms,” Proceedings of IEEE **94**, 550–566 (2006). [CrossRef]

24. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. **2**, 1160–1169 (1985). [CrossRef]

25. T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern. Anal. Mach. Intell. **18**, 959–971 (1996). [CrossRef]

26. M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, and W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. **42**, 300–311 (1993). [CrossRef]

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**, 4492–4506 (2005), http://www.opticsinfobase.org/abstract.cfm?id=84327. [CrossRef] [PubMed]

## 2. Overview of integral imaging (II) recording and reconstruction

15. S. Hong, J. Jang, and B. Javidi, “Three-dimensional volulmetric object reconstruction using computational integral imaging,” Opt. Express **12**, 483–491 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-483. [CrossRef] [PubMed]

27. Y. Frauel, O. Matoba, E. Tajahuerce, and B. Javidi, “Comparison of passive ranging integral imaging and active imaging digital holography for 3D object recognition,” Appl. Opt. **43**, 452–462 (2004). [CrossRef] [PubMed]

15. S. Hong, J. Jang, and B. Javidi, “Three-dimensional volulmetric object reconstruction using computational integral imaging,” Opt. Express **12**, 483–491 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-483. [CrossRef] [PubMed]

27. Y. Frauel, O. Matoba, E. Tajahuerce, and B. Javidi, “Comparison of passive ranging integral imaging and active imaging digital holography for 3D object recognition,” Appl. Opt. **43**, 452–462 (2004). [CrossRef] [PubMed]

## 3. Microorganism recognition using the multivariate statistical method

*p*section images by the geometrical ray projection method. Let the multidimensional data set be described by

**X**

^{p}, which is a combination of feature vectors [

*X*

^{1}…

*X*

^{p}]. We randomly select

*n*test pixel points from a well-focused one section image of the reconstructed volumetric 3D image, where we choose enough samples to use in estimating a reference population distribution [28]. For classification of biological microorganisms based on multi-dimensional data sets, reference M-ECDF

*F*

_{ref}can be obtained by extracting

*n*pixel values from each section image at the same test pixel points. It is also possible to analyze the variation of the data in the longitudinal direction at the fixed test pixel points. Given

*n*ordered data points

*X*

^{p}(1),

*X*

^{p}(2),

*X*

^{p}(3), …

*X*

^{p}(

*n*), the reference M-ECDF of the section images can be represented as follows:

*X*

^{p}is the randomly selected pixel value in the

*p*

^{th}section image and #{A} is the number of times the event A occurs. In order to obtain the statistical distribution of the criterion discriminant function of the reference data set for a statistical decision rule, we define the following criterion discriminant function for the null hypothesis:

*F′*

_{ref}is obtained by generating

*n*′×

*p*random sample data distributed according to the reference M-ECDF

*F*

_{ref}. We can obtain the statistical sampling distribution for the criterion discriminant functions by generating multiple

*F′*

_{ref}and substituting the resulting values in Eq. (2). The test statistics Λˆ enables us to convert a multi-dimensional data set into a one dimensional distribution and obtain the statistical sampling distribution for the null hypothesis. We then define the following discriminant function for comparing two multidimensional data sets:

*F*

_{input}is obtained by randomly extracting

*n*′ pixel values from each section image of a unknown input microorganism at the same test pixel points. The values of Λ will lie between 0 and 1. We can obtain the statistical distribution for the discriminant functions by generating multiple

*F*

_{input}of the unknown input data set and substituting the resulting values into Eq. (3).

*F*

_{ref}and

*F*

_{input}, are similar, the statistical distribution of Λ has sharp and peak points close to Λ=0.5. The statistical distribution of the criterion discriminant functions for the null hypothesis Λˆ has its highest value at Λˆ=0.5. Finally, we calculate the mean-square-distance (MSD) for comparing the actual multi-dimensional discriminant functions Λwith the criterion discriminant functions Λˆ:

*E*{·} is expectation operator. The statistical decision for identification of biological microorganisms can be achieved with a hypothesis test on the criterion discriminant function. This statistical approach for 3D recognition is suitable for recognizing the microorganisms, such as bacteria and biological cells, which do not have well defined shapes or profiles. Therefore, it allows our 3D recognition system to be robust to variations in the shape of the microorganisms.

## 4. Morphology-based recognition using Gabor-based wavelets and the RGM technique

24. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. **2**, 1160–1169 (1985). [CrossRef]

25. T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern. Anal. Mach. Intell. **18**, 959–971 (1996). [CrossRef]

**x**is a 2D discrete position vector,

**k**

_{uv}is a wave number vector, and

*σ*is proportional to the standard deviation of the Gaussian envelope.

**k**

^{uv}is defined as

**k**

_{uv}=

*k*

_{0u}[cos

*ϕ*

_{ν}sin

*ϕ*

_{ν}]

^{t}, where

*k*

_{0u}=

*k*

_{0}/

*δ*

^{u-1},

*ϕ*

_{ν}=[(

*ν*-1)/

*V*]π,

*u*=1, …,

*U*, and

*ν*=1, …,

*V*.

*k*

_{0u}is the magnitude of the wave number vector,

*ϕ*

_{ν}is the azimuth angle of the wave number vector,

*k*

_{0}is the maximum carrier frequency of the Gabor kernels,

*δ*is the spacing factor in the frequency domain,

*U*and

*V*are the total number of decompositions along the radial and tangential directions, respectively, and superscript

*t*denotes transpose.

**k**

_{uv}. By changing the magnitude and direction of the vector

**k**

_{uv}, we can scale and rotate the Gabor kernel to make self-similar forms, so that each Gabor kernel covers the frequency range selectively. The parameterization of 2D Gabor-based wavelets has been investigated in [24

24. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. **2**, 1160–1169 (1985). [CrossRef]

25. T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern. Anal. Mach. Intell. **18**, 959–971 (1996). [CrossRef]

*σ*=π,

*k*

_{0}=π/8,

*δ*=√2,

*U*=6, and

*V*=12.

*y*

_{uv}be the filtered output of the image

*o*after it is convolved with the Gabor kernel g

_{uv}:

*y*

_{uv}is referred to as the Gabor coefficient. The rotation-invariant property can be achieved by adding up all of the Gabor coefficients along the tangential directions of the frequency domain. Therefore, we can define a rotation-invariant node vector at

**x**

_{i}, which is the location of pixel

*i*, as

**v**(

**x**

_{i}) is a

*U*-dimensional complex vector.

1. B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express **13**, 4492–4506 (2005), http://www.opticsinfobase.org/abstract.cfm?id=84327. [CrossRef] [PubMed]

26. M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, and W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. **42**, 300–311 (1993). [CrossRef]

*R*and

*S*be two identical and rigid 3D grids placed on the 3D reference image set Ω

_{r}and the unknown 3D input image set Ω

_{s}, respectively. The reference image set Ω

_{r}and the input image set Ω

_{s}are composed of images reconstructed at different depths:

*o*

_{r}and

*o*

_{s}are the reference and input images, respectively;

*D*is the number of depth levels. The location of the reference graph in each reference image

*o*

_{r}is predetermined by a translation vector

**p**

_{r}, and a counter clock-wise rotation angle

*θ*

_{r}. Position vectors of nodes in each reference image can be computed as

*k*and the center of the grid without any translation and rotation, respectively; and

*K*

_{grid}is the number of nodes in the grid for one reconstructed image.

*R*covers a designated shape representing the geometrical characteristics of the reference microorganism, we search the similar local shape by translating and rotating the graph S in the unknown input image set, which has arbitrary depth levels. A similarity function between the graph

*R*and

*S*is defined as

**v**

_{r}[

**x**

_{k}(

**p**

_{r},

*θ*

_{r};

**v**

_{s}[

**x**

_{k}(

**p**

_{s},

*θ*

_{s};

*R*in the reference image set and the graph

*S*in the unknown input image set, respectively. The local area, which is covered by the graph

*S*, is identified with the reference shape if the following condition is satisfied:

*α*

_{Γ}is a threshold for the similarity function; and

*θˆ*

_{s}is obtained by searching the best matching angle to maximize the similarity function at the position vector

**p**

_{s}as

## 5. Experimental results

*d*=300, 306, …, 366 µm for each microorganism, where

*d*is the distance between the lens array and the reconstructed plane of the object. In II, a micro-lenslet array captures light rays as shown in Fig. 2. The light sources that are diffused from the 3D objects pass through each micro-lenslet and are recorded on a 2D imaging sensor, such as a CCD detector. Each microlenslet generates a 2D elemental image containing directional information of the 3D object. In the microscope system, to get magnified elemental images of object, an objective lens is used between the lens array and the CCD. The minimum distance of the reconstructed object is the same as the thickness of the cover glass of the slide.

### 5.1 3D II recognition using the multivariate statistical method

15. S. Hong, J. Jang, and B. Javidi, “Three-dimensional volulmetric object reconstruction using computational integral imaging,” Opt. Express **12**, 483–491 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-483. [CrossRef] [PubMed]

*F*′

_{ref}by selecting 500×15 random data samples distributed according to the reference M-ECDF and generate

*F*′

_{ref}500 times to construct statistical sampling distribution of the criterion discriminant function Λˆ for the null hypothesis (

*F*

_{ref}=

*F*

_{input}). As we expected, the value of the criterion discriminant function has a peak value at 0.5.

*F*

_{input}200 times and substituting the resulting values into Eq. (3), where this procedure can be repeated more often to obtain the precise statistical sampling distribution for the test statistics, Λ.

*x*

^{1}, …,

*x*

^{p})> and the actual discriminant function Λ(

*x*

^{1}, …,

*x*

^{p}) of the true class and false classes, respectively. We obtain the statistical distribution of the MSD for the null hypothesis by calculating the MSD between <Λˆ(

*x*

^{1}, …,

*x*

^{p})> and Λˆ (

*x*

^{1}, …,

*x*

^{p}) to make a statistical decision rule. As shown in Fig. 6, the maximum value of the MSD for the null hypothesis is 0.0003 and the mean values of the MSD for the true and false class are 0.00026 and 0.0016, respectively. It is noted that all of the false classes over 200 trial data sets are above the maximum value of the MSD for the null hypothesis. To compare the value of the calculated MSD using only one section image (a well focused image), we also calculate the MSD between the averaged criterion discriminant function <Λˆ(

*x*)> and the actual discriminant function Λ(

*x*) using the data set that consisted of only one section 2D image.

*x*)> and Λ(

*x*) for the true and the false classes, respectively. As shown in Fig. 7, the maximum value of the MSD for the null hypothesis is 0.0033 and the mean values of MSD for the true and false classes are 0.0005 and 0.0006, respectively. It is noted that all of the 200 trial data sets for true and false classes are below the maximum value of the MSD for the null hypothesis. In this case, it is difficult to measure the similarity or dissimilarity between two data sets using only one section image. Thus, preliminary experimental results indicate that it may be possible to classify microorganisms using volumetric 3D images obtained by II and the multivariate statistical method.

### 5.2 3D II recognition using the morphology-based method

**12**, 483–491 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-3-483. [CrossRef] [PubMed]

*R*and

*S*are composed of 5×5×3 nodes and the distance between nodes is 10 pixels in both the

*x*and

*y*directions. In the

*z*direction, the reference grid is superimposed on a reference image set, which is composed of 3 reconstructed images at depths of 324, 330, and 336 µm. Therefore, the number of depths (

*D*) is 3, and the number of nodes in one image (

*K*

_{grid}) is 25. The reference grid is placed with

**p**

_{r}=[116, 75]

^{t}and

*θ*

_{r}=30° in each reconstructed image. The location and orientation of the reference grid is manually decided in the experiments.

*d*=330 µm and one layer of the reference graph and the input graphs at the image. The threshold

*Γ*

_{α}in Eq. (12) is set at 0.995. The input graph is translated every two pixels in the

*x*and

*y*directions. To search the orientation angle, the input graph is rotated from 0° to 180° by 7.5° at every translated location, that is, the searching intervals for position and angle are set at 2 pixels and 7.5°, respectively. When the positions of the rotated nodes are not integers, they are replaced with the nearest neighbor nodes. We may improve the system performance by finer searching steps and/or high-order interpolation methods for the sake of computational complexity. However, as shown in the experimental results, the scheme presented in this paper can effectively recognize two different microorganisms illustrating the robustness of the system.

## 7. Conclusions

## Acknowledgments

## References and links

1. | B. Javidi, I. Moon, S. Yeom, and E. Carapezza, “Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography,” Opt. Express |

2. | B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, “Real-time automated 3D sensing, detection, and recognition of dynamic biological micro-organic events,” Opt. Express |

3. | S. Yeom, I Moon, and B. Javidi, “Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms,” Proceedings of IEEE |

4. | T. Kreis, ed., |

5. | A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, “Design and application of quadratic correlation filters for target detection,” IEEE Trans. Aerosp. Electron. Syst. |

6. | H. Kwon and N. M. Nasrabadi, “Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. |

7. | P. Refregier, |

8. | F. Sadjadi, ed., |

9. | B. Javidi and F. Okano eds, Three dimensional television, video, and display technologies, (Springer, Berlin, 2002). |

10. | T. Okoshi, “Three-dimensional displays,” Proceedings of IEEE |

11. | M. G. Lippmann, “Epreuves reversibles donnant la sensation du relief,” J. Phys. |

12. | R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral, and B. Javidi, “Enhanced depth of field integral imaging with sensor resolution constraints,” Opt. Express |

13. | J. Jang and B. Javidi, “Three-dimensional integral imaging of micro-objects,” Opt. Lett. |

14. | H. Arimoto and B. Javidi, “Integral three-dimensional imaging with digital reconstruction”, Opt. Lett. |

15. | S. Hong, J. Jang, and B. Javidi, “Three-dimensional volulmetric object reconstruction using computational integral imaging,” Opt. Express |

16. | A. Stern and B. Javidi, “3D image sensing and reconstruction with time-division multiplexed computational integral imaging (CII),” Appl. Opt. |

17. | S. Kishk and B. Javidi, “Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging,” Opt. Express |

18. | S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express |

19. | A. L. Amaral, M. da Motta, M. N. Pons, H. Vivier, N. Roche, M. Moda, and E. C. Ferreira, “Survey of protozoa and metazoa populations in wastewater treatment plants by image analysis and discriminant analysis,” Environmentrics |

20. | S.-K. Treskatis, V. Orgeldinger, H. wolf, and E. D. Gilles, “Morphological characterization of filamentous microorganisms in submerged cultures by on-line digital image analysis and pattern recognition,” Biotechnol. Bioeng. |

21. | J. M. S. Cabral, M. Mota, and J. Tramper eds., |

22. | M. Hollander and D. A. Wolfe, |

23. | A. C. Rencher, |

24. | J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. |

25. | T. S. Lee, “Image representation using 2D Gabor wavelets,” IEEE Trans. Pattern. Anal. Mach. Intell. |

26. | M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, and W. Konen, “Distortion invariant object recognition in the dynamic link architecture,” IEEE Trans. Comput. |

27. | Y. Frauel, O. Matoba, E. Tajahuerce, and B. Javidi, “Comparison of passive ranging integral imaging and active imaging digital holography for 3D object recognition,” Appl. Opt. |

28. | C. E. Lunneborg, |

29. | R. C. Gonzalez and R. E. Woods, |

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(110.6880) Imaging systems : Three-dimensional image acquisition

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: June 22, 2006

Revised Manuscript: October 2, 2006

Manuscript Accepted: October 12, 2006

Published: December 11, 2006

**Virtual Issues**

Vol. 2, Iss. 1 *Virtual Journal for Biomedical Optics*

**Citation**

Bahram Javidi, Inkyu Moon, and Seokwon Yeom, "Three-dimensional identification of biological microorganism using integral imaging," Opt. Express **14**, 12096-12108 (2006)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-25-12096

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### References

- B. Javidi, I. Moon, S. Yeom, and E. Carapezza, "Three-dimensional imaging and recognition of microorganism using single-exposure on-line (SEOL) digital holography," Opt. Express 13, 4492-4506 (2005). [CrossRef] [PubMed]
- B. Javidi, S. Yeom, I. Moon, and M. Daneshpanah, "Real-time automated 3D sensing, detection, and recognition of dynamic biological micro-organic events," Opt. Express 14, 3806-3829 (2006). [CrossRef] [PubMed]
- S. Yeom, I Moon, and B. Javidi, "Real-time 3D sensing, visualization and recognition of dynamic biological micro-organisms," Proceedings of IEEE 94, 550-566 (2006). [CrossRef]
- T. Kreis, ed., Handbook of holographic interferometry, (Wiley, VCH, 2005).
- A. Mahalanobis, R. R. Muise, S. R. Stanfill, and A. V. Nevel, "Design and application of quadratic correlation filters for target detection," IEEE Trans. Aerosp. Electron. Syst. 40, 837-850 (2004). [CrossRef]
- H. Kwon and N. M. Nasrabadi, "Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 43, 388-397 (2005). [CrossRef]
- P. Refregier, Noise theory and application to physics, (Springer, 2003).
- F. Sadjadi, ed., Selected papers on automatic target recognition, (SPIE-CDROM, 1999).
- <bok>. B. Javidi and F. Okano eds, Three dimensional television, video, and display technologies, (Springer, Berlin, 2002).</bok>
- T. Okoshi, "Three-dimensional displays," Proceedings of IEEE 68, 548-564 (1980). [CrossRef]
- M. G. Lippmann, "Epreuves reversibles donnant la sensation du relief," J. Phys. 7, 821-825 (1908).
- R. Martínez-Cuenca, G. Saavedra, M. Martínez-Corral and B. Javidi, "Enhanced depth of field integral imaging with sensor resolution constraints," Opt. Express 12, 5237-5242 (2004). [CrossRef] [PubMed]
- J. Jang and B. Javidi, "Three-dimensional integral imaging of micro-objects," Opt. Lett. 29, 1230-1232 (2004). [CrossRef] [PubMed]
- H. Arimoto and B. Javidi, "Integral three-dimensional imaging with digital reconstruction", Opt. Lett. 26, 157-159 (2001). [CrossRef]
- S. Hong, J. Jang, and B. Javidi, "Three-dimensional volulmetric object reconstruction using computational integral imaging," Opt. Express 12, 483-491 (2004), [CrossRef] [PubMed]
- A. Stern and B. Javidi, "3D image sensing and reconstruction with time-division multiplexed computational integral imaging (CII)," Appl. Opt. 42, 7036-7042 (2003). [CrossRef] [PubMed]
- S. Kishk and B. Javidi, "Improved resolution 3D object sensing and recognition using time multiplexed computational integral imaging," Opt. Express 11, 3528-3541 (2003). [CrossRef] [PubMed]
- S. Yeom, B. Javidi, and E. Watson, "Photon counting passive 3D image sensing for automatic target recognition," Opt. Express 13, 9310-9330 (2005), http://www.opticsexpress.org/abstract.cfm?id=86216. [CrossRef] [PubMed]
- A. L. Amaral, M. da Motta, M. N. Pons, H. Vivier, N. Roche, M. Moda, and E. C. Ferreira, "Survey of protozoa and metazoa populations in wastewater treatment plants by image analysis and discriminant analysis," Environmentrics 15, 381-390 (2004). [CrossRef]
- S.-K. Treskatis, V. Orgeldinger, H. wolf, and E. D. Gilles, "Morphological characterization of filamentous microorganisms in submerged cultures by on-line digital image analysis and pattern recognition," Biotechnol. Bioeng. 53, 191-201 (1997). [CrossRef] [PubMed]
- J. M. S. Cabral, M. Mota, and J. Tramper eds., Multiphase bioreactor design: chap2 image analysis and multiphase bioreactor, (London, Taylor & Francis, 2001). [CrossRef]
- M. Hollander and D. A. Wolfe, Nonparametric statistical methods, (Wiley, 1999).
- A. C. Rencher, Methods of multivariate analysis, (Wiley, 2002). [CrossRef]
- J. G. Daugman, "Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters," J. Opt. Soc. Am. 2, 1160-1169 (1985). [CrossRef]
- T. S. Lee, "Image representation using 2D Gabor wavelets," IEEE Trans. Pattern. Anal. Mach. Intell. 18, 959-971 (1996). [CrossRef]
- M. Lades, J. C. Vorbruggen, J. Buhmann, J. Lange, C. v.d. Malsburg, R. P. Wurtz, and W. Konen, "Distortion invariant object recognition in the dynamic link architecture," IEEE Trans. Comput. 42, 300-311 (1993). [CrossRef]
- Y. Frauel, O. Matoba, E. Tajahuerce, and B. Javidi, "Comparison of passive ranging integral imaging and active imaging digital holography for 3D object recognition," Appl. Opt. 43, 452-462 (2004). [CrossRef] [PubMed]
- C. E. Lunneborg, Data analysis by resampling: concepts and applications, (Duxbury Press, 1999).
- R. C. Gonzalez and R. E. Woods, Digital imaging processing, (Prentice Hall, 2002).

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