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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
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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.

    Abstract in Chinese ............................................ iii Abstract in English ............................................ iv Acknowledgements ................................................ v Contents ........................................................ vi List of Figures ................................................. viii List of Tables .................................................. xi List of Algorithms .............................................. xii 1 Introduction .................................................. 1 2 Previous Work ................................................. 3 3 Methodology ................................................... 5 3.1 The Binary Space ......................................... 5 3.2 Construction of the Binary Space ......................... 11 3.3 Equivalent position ...................................... 17 3.4 Family of Complementary Curves ........................... 21 3.5 Circular Projections ..................................... 26 4 Experiments and Results ....................................... 34 4.1 Cryptographic System ..................................... 35 5 Conclusions ................................................... 44 5.1 Future Work .............................................. 44 References ...................................................... 46 Letter of Authority ............................................. 47

    [1] D. Hilbert, “Ueber die stetige abbildung einer linie auf ein flächenstück,” Mathematische Annalen, vol. 38, no. 3, pp. 459–460, 1891.
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    [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.
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    [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.

    無法下載圖示 全文公開日期 2029/02/16 (校內網路)
    全文公開日期 2029/02/16 (校外網路)
    全文公開日期 2029/02/16 (國家圖書館:臺灣博碩士論文系統)
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