本研究應用碎形理論實施碎形壓縮，由於碎形理論具有「自我
相似性」的優點，因此只要能找到影像的碎形轉換函數及碎形轉換
碼，不論使用任何初始影像均能利用其碎形轉換函數及碎形轉換碼
將初使影象迭代為原始影像。
碎形壓縮的限制為所有的值域區塊必須透過碎形轉換函數在廣
大的定義域區域中找到其最相似的區塊，以取得該值域區塊之碎形
轉換碼，其龐大的相似區塊比對計算量使得碎形壓縮無法應用在真
實的世界。因此，亟須改進其壓縮效率。
本研究本提出二個減少值域區塊與定義域區塊之間相似性比對
計算時間的方法：
一、 重覆使用的資料先行計算並儲存。因為在相似區塊比對
的過程中，要取得每一個值域區塊的碎形轉換碼都必須計算某些定
義塊參數，因此我們先將每次相似轉換所用到的數值先計算並儲存，
爾後在相似比對過程使用到這些參數時就不需再行計算。
二、 使用多重解析空間分解原始影像。碎形影像的計算量大
部份來自相似區塊比對，本論文利用多重解析空間將原始影像依其
頻率特性分解成為四個子影像，每一子影像大小是原始影像的四分
之一，在對每一個子影像進行碎形壓縮，以減少相似區塊比對時間。
根據模擬結果此二種減少碎形壓縮時間的方法，在PSNR相差有限
的情況下，確能使碎形壓縮的時間從2000多秒下降到600多秒。

The purpose of this study was to improve the effect of fractal-based image compression. By taking advantage of the feature of "Self- assimilation" in fractal image processing, any image can be compressed and decompressed through the iteration of transformation and reverse transformation.
In order to improve the efficiency of image compression, the time of finding the most similar block within a vast range block correspondent to the domain block should be reduced. Two steps of fractal image compression were developed in this study for reducing the time of image block comparison. The first step was to search and encode the iterated data of an image. Then the input image was compressed through checking the input data with encoded data. The second step was carried out through the multi-resolution analysis of an image. The image was divided into four sub-images according to their spatial frequency and was compressed with 4*4 resolution blocks.. The experiment results showed that the time spent of this method was reduced to one-third of general fractal method. And the PSNR was also improved a little with this multi- resolution method.