本研究主要於構成影像基本單位的像素格子，以數個矩形格子做為重新取樣模擬，創造出一個新的像素格子:類旋轉六角格，來與傳統矩形格以及垂直排列的六角格來進行解析度的比較。
研究過程中，我們以直接的矩形格子來重新取樣模擬六角格以及類旋轉六角格，並將也以小格子模擬而成的矩形格子進行比較。因為要在一定的範圍裡進行比較，我們採取了取樣定理的觀念，將影像格子的取樣轉換到頻率域上，建立一套Nyquist 頻率系統。而因為像素格子的形狀與排列會影響到視覺的判定，稱之為像素結構干擾，所以在建立好的系統中，用主觀判定的影像測試實驗，找出各像素所組成的影像的視覺解析度極限，進而可以判定何種像素格子所組成的影像其解析度的優劣，並在最後得到結論，且有著未來的展望可以應用。

In this study, we focus on the method which is simulated resembled by many rectangular grids to create the new pixel grid on images: rotation type hexagonal grids. We compared this new generated grid to traditional rectangular grid and hexagonal grid arranged by vertical direction.
In the processing, we used rectangular grids to simulated hexagonal grids and rotation type hexagonal grids. We also simulated new rectangular grids and compared these three types’ grids to know which is better or not. We used the concept of sampling theorem to transform pixels from time domain to frequency domain for the comparison in a fixed arrangement. Then we created the Nyquist frequency diagrams. Since noises by shapes and arrangements of pixels called pixel structure noise will affect the visual resolution, we needed to establish the subjective evaluation to find out the visual resolution limits on this system to know which resolution of pixels is better or not. We also had the conclusion and hope this research could have more application at future.

摘要 i
Abstract ii
目錄 iii
圖次 v
表次 viii
第一章 緒論 1
1-1 背景介紹 1
1-2 研究方法 4
1-3 論文架構 5
第二章 類旋轉六角像素排列 6
2-1 對稱六角座標系統 6
2-2 六角格子的顯示方式 8
2-3 類旋轉六角格子的顯示方式 10
2-4類旋轉六角格子的排列方式 11
2-5旋轉影像效果最佳之角度與長度 20
第三章 取樣定裡以及Nyquist頻率系統 24
3-1取樣定裡 24
3-2 Nyquist頻率系統 26
第四章 頻率域上的轉換 31
4-1 三種格子像素的顯示及轉換 31
4-2 頻率域上的比較及討論 36
4-3 像素格子排列的誤差 38
第五章 視覺主觀性判定實驗 40
5-1 視覺實驗的架構 40
5-1-1訊號圖的變化 40
5-1-2訊號圖重新取樣以及頻率的變化 49
5-2 主觀判定實驗 56
5-3 VRL的範圍大小 67
第六章 結論與討論 71
參考文獻 73

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