有鑑於碎形內插可有效減少二維DEM在斷面重建時所遇到的邊緣平滑問題，在資料點數減少後以碎形內插，將資料增補回原始資料所得到的地形斷面可相似於原始的地形斷面。本文探討碎形內插對自然界不規則邊緣現象的模擬程度，在資料經過不等程度的壓縮及碎形重建後與2D及3D數值高程模型資料之間的各項變化。同時為了探討一般影像資料型態利用碎形內插處理的重建效果，將原始資料經過不等程度的壓縮後做為初始資料，進行碎形重建，而灰階影像圖的碎形維度則可表現出影像的複雜度及灰階分佈程度的特徵，透過首四階動差統計量、PSNR及SNR來比較灰階值的變化、紋理特徵的保留及碎形重建程度等各方面的差異。
在本研究中我們討論了以下幾個問題：(1)選用兩個實測的二維DEM資料以探討二維DEM資料型態在經過Douglas-Peucker線性簡化法的壓縮處理後，以碎形內插呈現出原始地貎重建的壓縮率探討；(2)選用兩個實測的三維DEM資料，進行隨機壓縮，再以碎形內插重建DEM，以討論DEM資料在資料量大小與經壓縮重建的壓縮率關係；(3)選用一張灰階衛星影像，利用碎形內插方法直接對其進行碎形內插，在欲觀察區域的局部可視化放大處理後，經局部放大處理後可將原始影像的馬賽克現象減緩同時呈現出細節；(4)對於三維碎形內插方法應用於影像資料重建的探討，目的是為了解當資料來源為不可再取得時，使用碎形內插為資料進行重建的成效如何。
研究結果顯示出：(1)實際斷面高程資料經不同程度的壓縮處理後，藉由碎形技術進行內插，可使重建後之斷面形體趨於自然且真實，呈現出更多的細部紋理結構；(2)應用碎形內插重建DEM，在保留地貌整體結構的原則下，DEM的原始資料量愈多的-其壓縮率較資料較少的壓縮率高；(3)在低解析度的情況下進行碎形內插，可減緩影像直接放大時的邊緣鋸齒與馬賽克情況；(4)當影像資料在高解度的情況下進行碎形內插，可有效提升資料邊緣輪廓的清晰程度，同時提高區域內物件特徵的可辨識度。

3D fractal reconstruction can efficiently address the edge smoothing problem of 2D DEM in sectional reconstruction, and the topographic section obtained by adding supplementary data to the original data with 3D fractal reconstruction may be similar to the original topographic section. In this study, we discuss the use of a data reduction method along with a fractal interpolation method to supplement data into 2D and 3D DEM, thus exploring the feasibility of 2D and 3D global data reduction and fractal reconstruction.
To study general image data patterns, source data are compressed to various extents to serve as irreproducible source data, and are then reconstructed by fractal interpolation, among which the grayscale image fractal dimension can show both image complexity and gray scale distribution features. Various differences in gray scale, texture feature retention, and the extent of fractal reconstruction are compared through statistics of the first four-order moments, PSNR and SNR.
The work covers the following issues: (1) 2D DEM data of measured geographic profiles is taken as the study object, and the major objective is to study the reduction ratio of the data profile after data reduction by the Douglas-Peucker (DP) linear simplification method and by fractal interpolation to show the original terrain reconstruction. (2) We adopt two sets of 3D terrain profile data to proceed with the data reduction, i.e. random data sampling, then reconstruct them through 3D fractal reconstruction in order to discuss DEM data with respect to the relationship between the original data size and data reduction rate. (3) Gray image data is taken as the study object, and the fractal interpolation method is used to improve it. The aim is to retain image textures, in order to reconstruct lost data, and to compare the experimental data with direct zoom in the data. (4) We also discuss the application of the 3D fractal interpolation method to satellite image data reconstruction, in order to examine its efficiency when the data source is no longer available.
The results of this study indicate that: (1) If real profile elevation data is manipulated with various reduction approaches, and then reconstructed by means of fractal interpolation, then the reconstructed profile has more natural and realistic details. (2) If the 3D fractal interpolation method is applied to DEM reconstruction, a higher reduction rate can be obtained for DEM with a larger data size compared to that with smaller data size under the assumption that the entire terrain structure is still maintained. (3) Fractal interpolation under an insufficient image resolution can reduce edge alias and mosaic when enlarging the image, as well as improving the visibility of object features in the region. It can thus be used as a tool for surface analysis. (4) Fractal interpolation of high-resolution image data can effectively improve the sharpness of data border contours.

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