## How to optimize OCT image

Optics Express, Vol. 9, Issue 1, pp. 24-35 (2001)

http://dx.doi.org/10.1364/OE.9.000024

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### Abstract

Quantization, which maps real values of raw data to a series of fixed gray levels, is an inevitable step in Optical Coherence Tomography (OCT) image formation. Three new quantization methods, Minimum Distortion, Information Expansion and Maximum Entropy are applied in the specific problem. Quantization results of a capillary with milk and the femoralis of rabbit are shown in this paper. Comparisons with the present log-based methods show that a suitable quantization method significantly increases contrast, SNR and visual fineness of the final image and reduces quantization error effectively. Applicability of different quantization methods is also discussed.

© Optical Society of America

## 1. Introduction

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J.G. Fujimoto, “Optical Coherence Tomography,” Science **254**, 1178(1991) [CrossRef] [PubMed]

2. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron **5**, 1205(1999) [CrossRef]

## 2. Quantization methods commonly used in digital image processing and in OCT image formation

7. W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Graph. Image Process. , **6**, 286(1977) [CrossRef]

6. J. P. Dunkers, R. S. Parnas, C. G. Zimba, R. C. Peterson, K. M. Flynn, J. G. Fujimoto, and B. E. Bouma, “Optical coherence tomography of glass reinforced polymer composites,” Compos. Pt. A: Appl. Sci. and Mfg. **30**, 139 (1999) [CrossRef]

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J.G. Fujimoto, “Optical Coherence Tomography,” Science **254**, 1178(1991) [CrossRef] [PubMed]

*t*, based on a predetermined dynamic range. All values less than

*t*are set to

*t*.

*t*, 1

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J.G. Fujimoto, “Optical Coherence Tomography,” Science **254**, 1178(1991) [CrossRef] [PubMed]

## 3. Applying new quantization methods in OCT image formation

## 3.1 Minimum Distortion (MD) and Truncation MD (TMD) Methods

*x*with probability density function

*p*(

*x*), the optimal quantization output levels

*q*,…,

_{1}*q*and the internal breakpoints

_{N}*Z*,…,

_{1}*Z*

_{N+1}of minimum distortion are subject to the following formula [11

11. J. Max, “Quantizing for minimum distortion,” IEEE Trans. Inf. Theory **IT-6**, 7 (1960) [CrossRef]

*N*is the number of the output levels,

*k*is from

*1*to

*N*for

*q*while

_{k}*2*to

*N*+

*1*for

*Z*. Typically, endpoints

_{k}*Z*and

_{1}*Z*

_{N+1}are known

*a priori*.

*N*usually equals

*256*. Despite the real value

*q*, each output level is mapped to a fixed gray level sequentially after quantization, i.e., the smallest output level is mapped to gray level 0, the second smallest to gray level 1, and so on. This is different from the common quantization procedure and is a particularity of OCT data quantization.

_{k}11. J. Max, “Quantizing for minimum distortion,” IEEE Trans. Inf. Theory **IT-6**, 7 (1960) [CrossRef]

*a*and

_{i}*a*

_{i+1}the

*i*th and the (

*i*+

*1*)th internal breakpoints of the raw data. The number of output levels is

*256*and

*i*is set from

*0*to

*255*. The

*i*th output level

*d*and the distortion function

_{i}*J*can be defined as following:

_{e}*y*is the value of the raw data.

*n*(

*y*) is the number of raw data with value

*y*.

*a*and

_{0}*a*-

_{256}*1*are the minimum value and the maximum value of the raw data respectively.

*d*can be determined by minimizing the distortion function, which is similar to that of the c-means clustering method in pattern recognition [12]. Since

_{i}*y*is scalar, it is not necessary to examine all clusters to decide whether

*J*is reduced, a comparison between adjacent clusters should be sufficient. All data with the same value y should be moved between clusters simultaneously. Therefore the common c-means algorithm can be modified and employed to execute MD method as the following [13

_{e}13. M. Friedman and K. Abraham, *Introduction to pattern recognition: statistical, structural, neural, and fuzzy logic approaches*, (River Edge, NJ: World scientific, 1999) [CrossRef]

*y*are in

*γ*’ and

_{i}*γ*is the

_{i}*i*th cluster in which all data will be mapped to the

*i*th image gray level (

*i*=0,…,255). Calculate

*ρ*as the following:

_{j}*m*is the center of the

_{j}*j*th cluster,

*n*(

*y*) is the number of samples whose value is

*y*,

*N*is the total number of samples in

_{j}*j*th cluster.

*ρ*≤

_{i}*ρ*, move

_{j}*y*from

*γ*to

_{i}*γ*.

_{j}*m*,

_{i}*m*and

_{j}*J*

_{e}*J*is small enough or

_{e}*J*remains unchanged.

_{e}## 3.2 Information Expansion (IE) Method

7. W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Graph. Image Process. , **6**, 286(1977) [CrossRef]

## 3.3 Maximum Entropy (ME) Method

## 4. Experiments and Results

*µ*is the mean value of the object region,

_{o}*µ*is the mean value of the background region,

_{b}*σ*is the standard deviation of the noise in the background region.

_{n}*S*is the mean energy of the object region,

_{e}*n*is the mean energy of the background region.

_{e}*N*and

_{o}*N*are numbers of pixels in the object region and the background region respectively,

_{b}*pixel*(

*i*,

*j*) is the gray value of the point (

*i*,

*j*). In our experiments, object region and background region were determined manually, since the sample shape are known in advance.

## 5. Conclusion and Discussion

## Acknowledgement

## Reference and links

1. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J.G. Fujimoto, “Optical Coherence Tomography,” Science |

2. | J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron |

3. | K. R. Castleman, |

4. | J. S. Lim, |

5. | R. M. Haralick and L. G. Shapiro, |

6. | J. P. Dunkers, R. S. Parnas, C. G. Zimba, R. C. Peterson, K. M. Flynn, J. G. Fujimoto, and B. E. Bouma, “Optical coherence tomography of glass reinforced polymer composites,” Compos. Pt. A: Appl. Sci. and Mfg. |

7. | W. Frei, “Image enhancement by histogram hyperbolization,” Comput. Graph. Image Process. , |

8. | Y. Tao, |

9. | H. Ishikawa, R. Gurses-Ozden, S. T. Hoh, H. L. Dou, J. M. Liebmann, and R. Ritch, “Grayscale and proportion-corrected optical coherence tomography images,” Ophthal. Surg. and Lasers |

10. | Jan C.A. Van der Lubbe, |

11. | J. Max, “Quantizing for minimum distortion,” IEEE Trans. Inf. Theory |

12. | R. O. Duda and P. E. Hart, |

13. | M. Friedman and K. Abraham, |

**OCIS Codes**

(100.0100) Image processing : Image processing

(100.2980) Image processing : Image enhancement

(110.4500) Imaging systems : Optical coherence tomography

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 10, 2001

Published: July 2, 2001

**Citation**

Kai Yu, Liang Ji, Lei Wang, and Ping Xue, "How to optimize OCT image," Opt. Express **9**, 24-35 (2001)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-1-24

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### References

- D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J.G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178 (1991). [CrossRef] [PubMed]
- J. M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE J. Sel. Top. Quantum Electron 5, 1205 (1999). [CrossRef]
- K. R. Castleman, Digital Image Processing, (Prentice Hall, Inc., 1996).
- J. S. Lim, Two-Dimensional Signal and Image Processing, (Englewood Cliffs, NJ: Prentice Hall, 1990).
- R. M. Haralick, L. G. Shapiro, Computer and Robot Vision, (Reading Press: Addison-Wesley, 1993).
- J. P. Dunkers, R. S. Parnas, C. G. Zimba, R. C. Peterson, K. M. Flynn, J. G. Fujimoto and B. E. Bouma, "Optical coherence tomography of glass reinforced polymer composites," Compos. Pt. A: Appl. Sci. and Mfg. 30, 139 (1999). [CrossRef]
- W. Frei, "Image enhancement by histogram hyperbolization," Comput. Graph. Image Process. 6, 286 (1977). [CrossRef]
- Y. Tao, Experimental Research of OCT System, MA's thesis of Tsinghua University, (1998).
- H. Ishikawa, R. Gurses-Ozden, S. T. Hoh, H. L. Dou, J. M. Liebmann, R. Ritch, "Grayscale and proportion-corrected optical coherence tomography images," Ophthal. Surg. and Lasers 31, 223 (2000).
- Jan C. A. Van der Lubbe, Information theory, (English translation Cambridge University Press, 1997).
- J. Max, "Quantizing for minimum distortion," IEEE Trans. Inf. Theory IT-6, 7 (1960). [CrossRef]
- R.O. Duda, P.E. Hart, Pattern Classification and Scene Analysis, (New York: Wiley, 1973).
- M. Friedman, K.Abraham, Introduction to pattern recognition: statistical, structural, neural, and fuzzy logic approaches, (River Edge, NJ, World scientific, 1999). [CrossRef]

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