資料壓縮與重建在科學和工程領域一向扮演重要的角色，其中影像的壓縮主要在減少影像的資料量以便於資料儲存或傳遞，而重建的目的是為了還原影像並儘可能避免失真，其方法和技術仍值得大力研發。本研究特別針對二維和三維數值高程模型的地形輪廓和地表資料的壓縮和重建提出一些新的改良方法，來加快計算速度和提高資料重建的效果。相較於著名的IDP方法運用在二維地形輪廓的特徵點萃取，本研究設計了一個新的萃取法，至於如何從萃取出的資料點重建該地形輪廓，現行的碎形內插方法已被廣泛使用，本研究進一步在碎形內插方法中提出基於機率和輪廓曲線的運算模式，有效地改善運算速度及重建的擬真程度，其中基於機率的運算模式也適用於三維地表的資料重建。三維地表資料重建的效果因所使用的壓縮資料而異，本研究採用幾種不同幾何形狀的壓縮資料點分佈如：正方形、矩行、平行四邊形、梯形、任意四邊形和特徵四邊形，來作實驗及分析，並獲得一致的結論。最後，本研究也檢視了碎形維度和裂隙度(Lacunarity)之間的關係並導出如何利用裂隙度的計算結果來增加碎形維度計算的準確度。

Data compression and reconstruction have been playing important roles in information science and engineering. As part of them, image compression and reconstruction that mainly deal with image data set reduction for storage or transmission and data set restoration with least loss is still a topic deserved a great deal of works to focus on. In this study, several methods are proposed to improve the fractal reconstruction on 2-Dimensional Digital Elevation Model (2-D DEM) terrain profile or 3-D DEM terrain surface with the computation efficiency and the reconstruction performance. For 2-D profile a new scheme is proposed in comparison with the well-known Improved Douglas-Peucker (IDP) method to extract the characteristic or feature points to compress data set. As for the reconstruction of the compressed data set in use of fractal interpolation, a probability-based method is proposed to speed up the fractal interpolation execution. The probability-based method is also applicable to 3-D surface. In addition, a curve-based method is proposed to determine the vertical scaling factor that much affects the generation of the interpolated data points to significantly improve the reconstruction performance of 2-D profile. On 3-D surfaces the performance of fractal reconstruction depends on the compressed data set whose elements are extracted from the original data points on the surface. In the study various geometric shapes of the extracted data set, such as square, rectangle, parallelogram, trapezoid, random quadrilateral and characteristic quadrilateral are tested and compared to carry out a conclusion. Finally, an investigation is made to show the advantage of employing lacunarity to help with linear regression analysis in the computation of 3-D DEM surface fractal dimension.

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