簡易檢索 / 詳目顯示
| 研究生： |
喻世文 Yu, Shih-Wen |
|---|---|
| 論文名稱： |
多影像曲體的次數 Degrees of Multi-Image Varieties |
| 指導教授： |
卓士堯
Jow, Shin-Yao |
| 口試委員: |
蔡孟傑
Chuah, Meng-Kiat 陳正傑 Chen, Jheng-Jie |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2022 |
| 畢業學年度： | 110 |
| 語文別： | 英文 |
| 論文頁數： | 37 |
| 中文關鍵詞： | 代數幾何 、多視圖幾何 、電腦視覺 |
| 外文關鍵詞： | Multiple View Geometry, Algebraic Geometry, Computer Vision |
| 相關次數： | 點閱：3 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本論文主軸為推廣 EK17 中所定義的幾何相機模型與多影像曲體。此外，本論文也將計算多影像曲體在 G(1,n)^m 中 的周類，以及其在 Plucker 嵌入映射下作為一射影乘積空間 (P^n)^m 中射影曲體的次數。
Our work extends the definitions of multi-image variety and geometric cameras defined in \cite{EK17}, and computes its Chow class in G(1,n)^m and its multidegree as a subvariety of $(P^n)^m$ via the Plucker embedding.
[DPM88] P. De Poi and E. Mezzetti. On Congruences of Linear Spaces of Order One, volume XXXIX. Rend. Istit. Mat. Univ. Trieste, 1988.
[DPM09] P. De Poi and E. Mezzetti. On a Class of First Order Congruences of Lines, volume 16. Bull. Belg. Math. Soc. Simon Stevin, 2009.
[EH16] D. Eisenbud and J. Harris. 3264 and All That: A Second Course in Algebraic Geometry. Cambridge University Press, 1st edition, 2016.
[EK17] L. Escobar and A. Knutson. The multidegree of the multi-image variety, 2017. arXiv:1701.03852.
[Ful98] W. Fulton. Intersection Theory. Springer, Berlin, 2nd edition, 1998.
[GH78] P. Griffiths and J. Harris. Principles of Algebraic Geometry. Wiley, New York, 1978.
[Har77] R. Hartshorne. Algebraic Geometry. Springer, New York, 1977. GTM 52.
[HP52] W. V. D. Hodge and D. Pedoe. Methods of Algebraic Geometry, volume 2. Cambridge University Press, 1952.
[HZ00] R. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000.
[PST16] J. Ponce, B. Sturmfels, and M. Trager. Congruences and concurrent lines in multi-view geometry, 2016. arXiv:1608.05924v1.
[Sha94] I. R. Shafarevich. Basic Algebraic Geometry, volume I, II. Springer, Berlin, 2nd edition, 1994.
[Tot14] B. Totaro. Chow groups, chow cohomology, and linear varieties. For. Math. Sigma, 2(e17), 2014.