本研究探討基於雙層濾波器與高斯混合模型分群的影像抽象化方法，改善兩種方法在影像抽象化上參數最佳化與影像品質的問題。在使用雙層濾波器的研究中，我們提出根據影像亂度決定濾波器參數組合的方法，以此可自動找出有較佳抽象化效果之影像。另外，我們提出隨各像素與其最近邊跡點距離而動態調整色彩變異度的方法，用以改善不同顏色區塊邊界的色彩混合現象。處理結果顯示，此方法有不錯的抽象化效果，可以保留影像細節並且避免色彩混合。
在基於GMM分群之影像抽象化方法上，我們先探討了不同色彩特徵組合對影像抽象化之影響。進一步，我們提出以色彩誤差決定GMM群數的影像抽象化之方法；此方法可以自動找到失真較少且能夠涵蓋主要色彩之群數，可應用於圖像簡化或是檢索。最後，我們提出模糊分群方法來改善原始GMM分群方法所產生的影像破碎問題，結果顯示，此方法可以改進群集邊界的顏色自然度，提升抽象化影像的視覺品質。

This paper discussed image abstraction based on bilateral filter and Gaussian mixture model (GMM), respectively, and proposed methods for optimizing the parameters and improving image quality. As regard the methods based on bilateral filter, the entropy of the image is proposed as an indicator for determining the color variance of bilateral filtering, though which better abstraction results could be obtained. In addition, the color variance of the bilateral filter could be further tuned dynamically according to the distance between each pixel and its closest edge point. This may alleviate effectively the problem of color mixing, that the colors around the boundaries of adjacent areas tend to be mixed during bilateral filtering and improve the quality of abstracted image. For the methods based on GMM clustering, the combinations of color features and spatial features are studied first. Furthermore, a method of selecting the number of clusters according to the average quantization error of color was proposed. It was shown that this method can achieve better abstraction results because the clusters may contain the major colors of the image with fewer distortions. Finally, a fuzzy clustering approach was utilized to eliminate the unnatural breaks around the boundaries of the clusters, and the results with better visual quality can be obtained.

[ 1 ]
阮喬愷、施仁忠。影像式漫畫肖像生成之研究(碩士論文，國立交通大學，新竹，台灣)。國立交通大學博碩士論文系統。2009。
[ 2 ]
邱義欽、林伯慎。文本無關之語者驗證方法研究(碩士論文，國立台灣科技大學，台北，台灣)。國立台灣科技大學圖書館。2014。
[ 3 ]
A. A. Efros and W. T. Freeman, “Image Quilting for Texture Synthesis and Transfer,” ACM SIGGRAPH, p.p. 341-346, 2001.
[ 4 ]
C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” IEEE International Conference on Computer Vision, p.p. 839-846, 1998.
[ 5 ]
D. Marr and E. Hildreth, “Theory of edge detection,” Proceeding of the Royal Society, B 207, p.p. 187-217, 1980.
[ 6 ]
H. Chen, N. N. Zheng, L. Liang, and Y. Q. Xu, “PicToon: A Personalized Image-based Cartoon System,” ACM International Conference of Multimedia, p.p. 171-178, 2002.
[ 7 ]
H. Kang, S. Lee, and C. K. Chui, “Flow-Based Image Abstraction,” IEEE Transaction on Visualization and Computer Graphics, vol. 15, no. 1, p.p. 62-76, 2009.
[ 8 ]
H. Lee, S. Kwon and S. Lee, “Real-Time Pencil Rendering,” ACM Proceeding of the 4th international symposium on Non-photorealistic animation and rendering, p.p. 37-45, 2006.
[ 9 ]
H. Winnemöller, S. C. Olsen, and B. Gooch, “Real-time video abstraction,” ACM Transactions on Graphics, vol. 25, no. 3, p.p. 1221-1226, 2006.
[ 10 ]
I. Sobel, “An Isotropic 3 3 Image Gradient Operator,” Presentation at Stanford A.I. Project, 1986.

[ 11 ]
J. Bilmes. “A gentle tutorial on the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden markov models,” Technical Report ICSI-TR-97-02, University of Berkeley, 1997.
[ 12 ]
J. Canny, “A Computational Approach to Edge Detection,” IEEE Transaction on Pattern Analysis and Machine Intelligence, vol. 9, no. 6, p.p. 679-698, 1986.
[ 13 ]
J. Lai and J. Z. Wang, “Studying Digital Imagery of Ancient Paintings by Mixtures of Stochastic Model,” IEEE Transaction on Image Proceeding, vol. 13, no. 3, p.p. 340-353, 2004.
[ 14 ]
J. Lansdown and S. Schofiel, “Expressive Rendering: A Review of Nonphotorealistic Techniques,” IEEE Computer Graphics and Applications, vol.15, no. 3, p.p. 29-37, 1995.
[ 15 ]
J. Kyprianidis, J. Collomosse, T. Wang, and T. Isenberg, “State Of the ‘Art’: A Taxonomy of Artistic Stylization Techniques for Images and Video,” IEEE Transactions on Visualization and Computer Graphics,” vol. 19, no. 5, p.p. 866-885, 2013.
[ 16 ]
J. E. Kyprianidis, H. Kang, and J. Döllner, “Image and Video Abstraction by Anisotropic Kuwahara Filtering,” Pacific Graphics Computer Graphics Forum, vol. 28, no. 7, 2009.
[ 17 ]
J. E. Kyprianidis and J. Döllner, “Image Abstraction by Structure Adaptive Filtering,” Theory and Practice of Computer Graphics, UK, 2008.
[ 18 ]
M. M. Cheng, J. Warrell, W. Y. Lin, S. Zheng, V. Vineet and N. Crook, “Efficient Salient Region Detection with Soft Image Abstraction,” IEEE International Conference on Computer Vision, p.p. 1529-1536, 2013.
[ 19 ]
Q. Yang, K. H. Tan, and N. Ahuja, “Real-Time O(1) Bilateral Filtering,” IEEE Conference on Computer Vision and Pattern Recognition,” p.p. 557-564, 2009.
[ 20 ]
S. Brooks, “Mixed-Media Painting and Portraiture,” IEEE Transactions on Visualization and Computer Graphics, vol. 13, no. 5, p.p. 1041-1054, 2007.

[ 21 ]
T. M. Nguyen and Q. M. J. Wu, “A fuzzy logic model based markov random field for medical image segmentation,” Springer Evolving System, vol. 4, no.3, p.p 171-181,2013.
[ 22 ]
Y. Z. Song, D. Pickup, C. Li, P. Rosin, and P. Hall, “Abstract Art by Shape Classification,” IEEE Transaction on Visualization and Computer Graphics, vol. 19, no. 8, p.p. 1252-1263, 2013.
[ 23 ]
Z. Fu and L. Wang, “Color Image Segmentation Using Gaussian Mixture Model and EM Algorithm,” Springer Multimedia and Signal Processing, vol. 346, p.p. 61-66, 2012.