臺灣博碩士論文加值系統

在對比增強的這塊領域中，許多主要的方法是將柱狀圖切分成許多的子區域來做柱狀圖等化法。在此論文中提出在柱狀圖中用混合高斯模型來做新的對比增強法。我們的方法中提出了五個主要的步驟，第一步，我們利用成本方程式計算出混合高斯模型需要幾個群組，計算出群組參數主要是於圖片的柱狀圖中能夠用混合高斯模型來逼近，之後使用二分搜尋法找出彼此兩個鄰近高斯的交點，針對柱狀圖的各個子區域做傳統的柱狀圖等化法來達成對比增強，最後利用保亮度機制將整張圖片做處理。在論文中利用三張實驗結果圖證明此方法優於十二種方法。

The current major theme in contrast enhancement is to partition the input histogram into multiple sub-histograms before final equalization of each sub-histogram is performed. This paper presents a novel contrast enhancement method based on Gaussian mixture modeling of image histograms, which provides a sound theoretical underpinning of the partitioning process. Our method comprises five major steps. First, the number of Gaussian functions to be used in the model is determined using a cost function of input histogram partitioning. Then the parameters of a Gaussian mixture model are estimated to find the best fit to the input histogram under a threshold. A binary search strategy is then applied to find the intersection points between the Gaussian functions. The intersection points thus found are used to partition the input histogram into a new set of sub-histograms, on which the classical histogram equalization (HE) is performed. Finally, a brightness preservation operation is performed to adjust the histogram produced in the previous step into a final one. Based on three representative test images, the experimental results demonstrate the contrast enhancement advantage of the proposed method when compared to twelve state-of-the-art methods in the literature.

Contents
List of Figures……………………………………………………ii
List of Tables…………………………………………………… iv
1. Introduction....................................... 1
2. The Proposed Method................................ 5
2.1. Determination of the Number of Gaussian Functions in the Mixture ................. 5
2.2. Estimating the Parameters of the Gaussian Mixture Model (GMM)................... 8
2.3. Determination of Intersection Points Between Adjacent Gaussian Functions .. 10
2.4. Application of HE to Each Sub-histogram for Contrast Enhancement ............. 14
2.5 Brightness Preservation Operation ..................................................................... 15
3. Experimental results ............................. 15
3.1. Objective Comparison of all the Methods ..... 18
3.2. Subjective Comparison of Non-brightness Preserving Methods....................... 19
3.3. Subjective Comparison of Brightness Preserving Methods....................... 20
3.4. Impact of the Threshold Parameter.............. 23
4. Conclusions........................................ 26
References............................................ 28

List of Figures
Figure 1: Two cases for determining intersection points between two adjacent Gaussian functions. (a) Case 1: non-covering case, (b) Case 2: two covering sub-cases, b1 and b2. ..................... 11
Figure 2: Segmented histogram with four sub-histograms. ............................................. 14
Figure 3: For image “Putrajaya”, the results by using non-mean preserving-based methods. (a) Original image (b) HE (c) DSIHE (d) RSIHE (e) DHE (f) GHE (g) FHE (h) SRHE (i) The proposed EMCE. ................................................................ 20
Figure 4: For image “Castle”, the results by using non-mean preserving-based methods. (a) Original image (b) HE (c) DSIHE (d) RSIHE (e) DHE (f) GHE (g) FHE (h) SRHE (i) The proposed EMCE................................................................................ 21
Figure 5: For image “Aircraft”, the results by using non-mean preserving-based methods. (a) Original image (b) HE (c) DSIHE (d) RSIHE (e) DHE (f) GHE (g) FHE (h) SRHE (i) The proposed EMCE................................................................................ 22
Figure 6: For image “Putrajaya”, the results by using mean preserving-based methods. (a) Original image (b) BBHE (c) RMSHE (d) BPDHE (e) RSWHE (f) BPWCHE (g) Our proposed EMCE+BP. ....................................................................................... 24
Figure 7: For image “Castle”, the results by using mean preserving-based methods. (a) Original image (b) BBHE (c) RMSHE (d) BPDHE (e) RSWHE (f) BPWCHE (g) Our proposed EMCE+BP. ....................................................................................... 25
Figure 8: For image “Aircraft”, the results by using mean preserving-based methods. (a) Original image (b) BBHE (c) RMSHE (d) BPDHE (e) RSWHE (f) BPWCHE (g) Our proposed EMCE+BP. ....................................................................................... 25
Figure 9: For image “Putrajaya”, four intersection points of the histogram is dependent onthe threshold Tip....................................................................................... 26

List of Tables
Table 1: For three test images, the comparison of all concerned methods in terms of EME................................................................................................................................. 17
Table 2: The execution time requirement in terms of seconds. ........................................ 18

[1] R. C. Gonzalez and R. E. Woods, Digital image processing, 2nd edition, Upper Saddle River, NJ: Prentice Hall (2002).
[2] S. C. Pei, Y. C. Zeng, and C. H. Chang, “Virtual restoration of ancient Chinese paintings using color contrast enhancement and lacuna texture synthesis,” IEEE Transactions on Image Processing, vol. 13, no. 3, pp. 416-429 (2004).
[3] U. Ghanekar, A. K. Singh, and R. Pandey, “A contrast enhancement-based filter for removal of random valued impulse noise,” IEEE Signal Processing Letters, vol. 17, no. 1, pp. 47-50 (2010).
[4] J. Zimmerman, S. Pizer, E. Staab, E. Perry, W. McCartney, and B. Brenton, “An evaluation of the effectiveness of adaptive histogram equalization for contrast enhancement,” IEEE Transactions on Medical Imaging, vol. 7, no. 4, pp. 304-312 (1988).
[5] Y. Li, W. Wang, and D. Y. Yu, “Application of adaptive histogram equalization to x-ray chest image,” Proc. of the SPIE, vol. 2321, pp. 513-514 (1994).
[6] S. M. Pizer, “The medical image display and analysis group at the University of North Carolina: Reminiscences and philosophy,” IEEE Transactions on Medical Imaging, vol. 22, no. 1, pp. 2-10 (2003).
[7] A. Wahab, S. H. Chin, and E. C. Tan, “Novel approach to automated fingerprint recognition,” Proc. of IEE Visual Image Signal Processing, vol. 145, no. 3, pp. 160-166 (1998).
[8] A. Torre, A. M. Peinado, J. C. Segura, J. L. Perez-Cordoba, M. C. Benitez, and A. J. Rubio, “Histogram equalization of speech representation for robust speech recognition,” IEEE Transactions on Speech Audio Processing, vol. 13, no. 3, pp. 355-366 (2005).
[9] W. C. Kao, J. A. Ye, M. I. Chu, and C. Y. Su, “Image quality improvement for electrophoretic displays by combining contrast enhancement and halftoning techniques,” IEEE Transactions on. Consumer Electronics, vol. 55, no. 1, pp. 15-19 (2009).
[10] M. Kang, B. Kim, and K. Sohn, “CIECAM02-based tone mapping technique for color image contrast enhancement,” Optical Engineering, vol. 48, no. 8, pp. 087001 (2009).
[11] Y. T. Kim, “Contrast enhancement using brightness preserving bi-histogram equalization,” IEEE Transactions on Consumer Electronics, vol. 43, no. 1, pp. 1-8 (1997).
[12] Y. Wang, Q. Chen, and B. Zhang “Image enhancement based on equal area dualistic sub-image histogram equalization method,” IEEE Transactions on Consumer Electronics, vol. 45, no. 1, pp. 68-75 (1999).
[13] S. D. Chen and A. R. Ramli, “Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation,” IEEE Transactions on Consumer Electronics, vol. 49, no. 4, pp. 1301-1309 (2003).
[14] S. D. Chen and A. R. Ramli, “Minimum mean brightness error bi-histogram equalization in contrast enhancement,” IEEE Transactions on Consumer Electronics, vol. 49, no. 4, pp. 1310-1319 (2003).
[15] K. S. Sim, C. P. Tso, and Y. Y. Tan, “Recursive sub-image histogram equalization applied to gray scale images,” Pattern Recognition Letters, vol. 28, no. 10, pp. 1209-1221 (2007).
[16] M. A. A. Wadud, M. H. Kabir, M. A. A. Dewan, and O. Chae, “A dynamic histogram equalization for image contrast enhancement,” IEEE Transactions on Consumer Electronics, vol. 53, no. 2, pp. 593-600 (2007).
[17] H. Ibrahim and N. S. P. Kong, “Brightness preserving dynamic histogram equalization for image contrast enhancement,” IEEE Transactions on Consumer Electronics, vol. 53, no. 4, pp. 1752-1758 (2007).
[18] N. Sengee and H. K. Choi, “Brightness preserving weight clustering histogram equalization,” IEEE Transactions on Consumer Electronics, vol. 54, no. 3, pp. 1329-1337 (2008).
[19] M. Kim and M. G. Chung, “Recursively separated and weighted histogram equalization for brightness preservation and contrast enhancement,” IEEE Transactions on Consumer Electronics, vol. 54, no. 3, pp. 1389-1397 (2008).
[20] H. Ibrahim and N. S. P. Kong, “Image sharpening using sub-regions histogram equalization,” IEEE Transactions on Consumer Electronic, vol. 55, no. 2, pp. 891-895 (2009).
[21] S. Hashemi, S. Kiani, N. Noroozi, and M. E. Moghaddam, “An image contrast enhancement method based on genetic algorithm,” Pattern Recognition Letters, vol. 31, no. 13, pp. 1816-1824 (2010).
[22] H. D. Cheng, M. Xue, X. Shi, and M. Zhang, “Novel contrast enhancement approach based on fuzzy homogeneity,” Optical Engineering, vol. 46, no. 4, pp. 047002 (2007).
[23] L. Xu and M. I. Jordan, “On convergence properties of the EM algorithm for Gaussian mixtures,” Neural Computation, vol. 8, no. 1, pp. 129-151 (1996).
[24] H. O. Hartley, “Maximum likelihood estimation from incomplete data,” Biometrics, vol. 14, no. 2, pp. 174-194 (1958).
[25] S. S. Agaian, K. Panetta, and A. M. Grigoryan, “A new measure of image enhancement,” Int. Conf. Signal Processing Communication, pp. 19-22 (2000).