angle subtended by edge at origin arccos( 5)
A= = 5
然後這 12 個頂點的三維座標為：
( 0,± ±a, b) (±b, 0,±a) (± ±a, b, 0)
圖 C.1、正 20 面體
接下來我們針對正二十面體的正三角形面作子分割，以每個邊的中點為分割 點，將邊分成兩個等長的邊，再使兩兩中點之間連線，如此一來，每個正三角面 被分割成四個正三角面。重覆此步驟兩次(共三次)，此時的正二十面體變成了 320 面(即 20*4*4*4)、642 個頂點的多面體。之後，我們將每個新產生的頂點到中心 距離作正規化，使其到中心距離為單位距離，正規下後結果如圖 C.2。雖然正規 化後的每個面並不是正三角形，此方法但提供了一個頂點分佈較均勻的分割方 式，這也是我們為何使用此方法作為球面分割的原因。
圖 C.2、球面分割後的多面體
投影攝影機，鏡頭對準中間的人物模型，即可作二維投影。
參考文獻：
[Alb01] A. Albiol, I. Mora ,and V. Naranjo, “Real-time high density people counter using morphological tools,” IEEE Trans. on Intelligent Transportation Systems, Vol.
2 , No. 4 , pp.204 – 218, 2001.
[Bes03] J. Bescos, J.M. Menendez ,and N. Garcia, “DCT based segmentation applied to a scalable zenithal people counter,” Proc. International Conference on Image Processing, Vol. 3, pp. III - 1005-8 vol.2, 2003.
[Bro00] A. Broggi, M. Bertozzi, A. Fascioli ,and M. Sechi, "Shape-based pedestrian detection," Proc. the IEEE on Intelligent Vehicles Symposium IV, pp.215 - 220, 2000.
[Che03] Thou-Ho Chen, ” An Automatic Bi-Directional Passing-People Counting Method Based on Color Image Processing,” Proc. IEEE 2003 International Carnahan Conference on Security Technology , pp.200 – 207,2003.
[Che05] Maolin Chen, Gengyu Ma ,and Seokcheol Kee, ” Pixels Classification for Moving Object Extraction,” IEEE Workshop on Motion and Video Computing, WACV/MOTIONS '05, Vol. 2, pp.44 – 49 ,2005.
[Che06] Thou-Ho Chen, Tsong-Yi Chen ,and Zhi-Xian Chen, “An Intelligent People-Flow Counting Method for Passing Through a Gate,” IEEE Conference on Robotics, Automation and Mechatronics , pp.1 – 6, 2006.
[Che07]Ming-Hsu Cheng, Meng-Fen Ho ,and Chung-Lin Huang, “Gait Analysis for
Symposium on Circuits and Systems ,ISCAS 2007, pp. 969 – 972,2007.
[Cho06] Jung-Uk Cho, Seung-Hun Jin, Xuan-Dai Pham, Jae-Wook Jeon, Jong-Eun Byun ,and Hoon Kang, “A Real-Time Object Tracking System Using a Particle Filter,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems pp.2822 – 2827,2006.
[Dai00] D. J. Dailey, F. W. Cathey ,and S. Pumrin, "An Algorithm to Estimate Mean Traffic Speed Using Un-Calibrated Cameras," IEEE Trans. on Intelligent Transportation Systems, vol. 1, no. 2, pp. 98–107, 2000.
[Fou03] C.Fouard, "Automatic Calculation of Chamfer Mask Coefficients for Large Masks and Anisotropic Images," INRIA, pp.7-10 , 2003.
[Har99] I. Haritaoglu, D. Harwood ,and L.S. Davis, “Hydra: multiple people detection and tracking using silhouettes,” Proc. International Conference on Image Analysis and Processing, pp.280 – 285, 1999.
[Hua02] D. Huang, T.W.S. Chow ,and W.N. Chau, “Neural network based system for counting people,” IECON 02 [Industrial Electronics Society, IEEE 2002 28th Annual Conference] , Vol. 3 , pp. 2197 - 2201,2002.
[Hsi07]Jun-Wei Hsieh, Chuang-Yu Huang, Cheng-Shuang Peng ,and Kuo-Chin Fan
“GRID-BASED TEMPLATE MATCHING FOR PEOPLE COUNTING,” Proc. of the 20th IPPR Conf. on CVGIP, Mauli, Taiwan, 2007.
[Isa96]Michael Isard ,and Andrew Blake ”Contour tracking by stochastic propagation of conditional density,” Proc. European Conference on Computer Vision, vol. 1, pp.
343--356, 1996.
[Jae] Ae-Won Kim, Kang-Sun Choi, Byeong-Doo Choi ,and Sung-Jea Ko, “Real-time Vision-based People Counting System for the Security Door,” Department of Electronics Engineering,Korea University, Anam-dong, Sungbuk-ku, Seoul,pp.
136-701, Korea.
[Jam99] Sethian, and James “A Level Set Methods and Fast Marching Methods : Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science,” (2nd ed.). Cambridge University Press. ISBN 0-521-64557-3.4., 1999.
[Kom00] I. Kompatsiaris, G. Mantzaras ,and M.G. Strintzis, “Spatiotemporal segmentation and tracking of objects in color image sequences”, Proc. ISCAS 2000 Geneva. The 2000 IEEE International Symposium on Circuits and Systems, vol.5 , pp.29 - 32, 2000.
[Lai98] A.H.S. Lai ,and N.H.C Yung, “A fast and accurate scoreboard algorithm for estimating stationary backgrounds in an image sequence,” ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, Vol. 4 , pp.241 - 244 , 1998.
[Lin01] G. Linda Shapiro ,and C. George Stockman, “Computer Vision” by Prentice Hall Chap.10.1.1 Clustering Methods ,pp.281-282,2001
[Mag07] E. Maggio, F. Smerladi, and A. Cavallaro, “Adaptive Multifeature Tracking in a Particle Filtering Framework,” IEE Trans. On Circuits and Systems for Video Technology, vol. 17, no. 10, pp. 1348-1359, 2007
[Mas01] Masoud, O., Papanikolopoulos, and N.P.”A novel method for tracking and counting pedestrians in real-time using a single camera,” IEEE Transactions on Vehicular Technology, vol. 50, no. 5, pp. 1267 – 1278, 2001.
[Ter99]K.Terada, ” A Method of Counting the Passing People by Using the Stereo Images,” Proc. 1999 International Conference on Image Processing,
vol.2, pp.:338 – 342, 1999.
[Tan07]Yu-Gin Tang, Jiann-der Lee ,and Li-Chang Liu “AN EMBEDDED SYSTEM FOR VEHICLE TYPE RECOGNITION” Proc. of the 20th IPPR Conf. on CVGIP, Mauli, Taiwan, 2007.
[Wan07] J. M. Wang, S. W. Chen, S. Cherng , and C. S. Fuh, “People Counting Using Fisheye Camera,” Proceeding. of the 20th IPPR Conf. on CVGIP, Mauli, Taiwan, 2007.
[Xia95] Xiaowei Zhang ,and G. Sexton, “A new method for pedestrian counting,”
Fifth International Conference on Image Processing and its Applications , pp. 208 – 212, 1995.
[Xia97] Xiaowei Zhang ,and G. Sexton, “Automatic human head location for pedestrian counting,” Sixth International Conference on Image Processing and Its Applications, vol.2, pp.535 – 540, 1997.
[Yan03] Yang, D.B., Gonzalez-Banos, H.H., Guibas, and L.J. “Counting people in crowds with a real-time network of simple image sensors,” Proc. Ninth IEEE International Conference on Computer Vision, vol.1, pp. 122 - 129 ,2003.
[Zha95] X. Zhang, and G. Sexton, “Automatic pedestrian counting using image processing techniques” Electronics Letters , vol. 31 , no. 11 , pp.863 – 865, 1995.
[陳 03] 陳重傑 “高層辦公建築火災避難安全評估之研究”中華大學 建築與都市 計畫學系碩士班 國家圖書館全國博碩士論文 系統編號：92CHPI0224013,2003
[沈 93] 沈東石 “建築物內部人員交通系統緊急疏散效率之評估模型與應用”國 立台灣大學 土木工程研究所 國家圖書館全國博碩士論文 系統編號：
82NTU00015075,1993.
[張 05] 張厥煒、張傑閔 “運動視訊場景中動態物件搜尋與追蹤方法”國立台北科 技大學資訊工程系 臺北科技大學學報第四十之一期,2005.
[鄭 05] 鄭皓盈 “使用Particle Filter之物體追蹤技術”工業技術研究院資訊與通 訊研究所 第112期 電腦與通訊(CCL),2005.