研究生: |
Diego Vazquez Gonzalez Diego Vazquez Gonzalez |
---|---|
論文名稱: |
Binary Space : Application of the Family of Complementary Curves Binary Space : Application of the Family of Complementary Curves |
指導教授: |
鮑興國
Hsing-Kuo Pao |
口試委員: |
黃毅青
Ngai-Ching 楊傳凱 Chuan-Kai Yang 鮑興國 Hsing-Kuo Pao |
學位類別: |
碩士 Master |
系所名稱: |
電資學院 - 資訊工程系 Department of Computer Science and Information Engineering |
論文出版年: | 2024 |
畢業學年度: | 112 |
語文別: | 英文 |
論文頁數: | 47 |
外文關鍵詞: | Binary Space, Circular Projections, Dataset Summarization, Space Filling Curves |
相關次數: | 點閱:132 下載:0 |
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這項在計算機科學領域的研究基於將位元視為方向的觀點。這種對位元的看法產生了一個我們稱之為二進位空間(BS)的空間。
首先解釋了二進位空間的一些屬性以及如何解釋它。然後介紹了一個函數,該函數將點從一個BS投影到另一個更大的BS上。然後使用該函數作為基礎製作了算法FCC。最後,介紹了圓形投影,它允許我們將點從一個BS映射到圓內的唯一位置,以及半徑為1的球體。
在以下內容中,以FCC算法為基礎,將介紹兩種應用:
這個算法可以將數據集的內容總結為單一的n維物體(取決於數據集是圖像、體積、向量還是其他東西)。
密碼系統:這個密碼系統作為一種演示創建,以展示算法的工作方式並利用BS的分形特性。
This research in computer science is based on the view of bits as directions. This view of the bits produces a space that we call Binary Space (BS).
First are explained some properties of the Binary Space and how to interpret it. Then is introduced the function that project points from a BS onto another larger BS. Then using that function as base is made the algorithm FCC. Finally, are introduced the circular projections that allow us to map points from a BS in to unique positions contained in a circle and a sphere or radius 1.
In the following, using the FCC algorithm as a basis, two applications will be presented:
This algorithm can summarize the contents of a dataset into a single n-dimensional object (depending on whether the datasets are images, volumes, vectors, or something else).
Cryptographic system: This cryptographic system is created as a demonstration to show how the algorithm works and exploit the fractal properties of the BS.
[1] D. Hilbert, “Ueber die stetige abbildung einer linie auf ein flächenstück,” Mathematische Annalen, vol. 38, no. 3, pp. 459–460, 1891.
[2] G. M. Morton, “A computer oriented geodetic data base and a new technique in file sequencing,” IBM Canada, Ottawa, Ontario, 1966.
[3] M. F. Mokbel and W. G. Aref, “Space-filling curves,” Encyclopedia of GIS, 2008.
[4] B. Moon, H. Jagadish, C. Faloutsos, and J. H. Saltz, “Analysis of the clustering properties of the hilbert space-filling curve,” IEEE Transactions on Knowledge and Data Engineering, vol. 13, no. 1, pp. 124–141, 2001.
[5] Z. Song and N. Roussopoulos, “Using hilbert curve in image storing and retrieving,”
[6] W. Chen, X. Zhu, G. Chen, and B. Yu, “Efficient point cloud analysis using hilbert curve,” pp. 730–747, 2022.
[7] D. Zhang, Y. Wang, Z. Liu, and S. Dai, “Improving nosql storage schema based on z-curve for spatial vector data,” IEEE Access, vol. 7, pp. 78817–78829, 2019.
[8] T. Sivakumar and R. Venkatesan, “A novel image encryption method with z-ordering based scan and random number,” International Journal of Computer Applications, vol. 103, Oct 2014.
[9] T. Sivakumar and R. Venkatesan, “A novel image encryption method with z-order curve and random number,” International Journal of Computer Applications, p. 17, 2014.
[10] “An image encryption technique using logistic map and z-order curve,” 2018 International Conference on Emerging Trends and Innovations In Engineering And Technological Research (ICETIETR), 2018.
[11] Z. Liu, P. Luo, X. Wang, and X. Tang, “Deep learning face attributes in the wild,” December 2015.