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標題: 奇異吸引子的應用----碎形影像壓縮
An Application of Strange Attractors----Fractal Image Compression
作者: 洪嘉祥
Hung, Chia-Hsiang
關鍵字: fractal;碎形;attractor;chaos;dimension;ifs;encode;self-similarity;classification;吸引子;混沌;維度;疊代函數系統;編碼;自我相似性;分類
出版社: 物理學系
The study of Fractals has been developed and evolved for at least 10 years. Its study has been the vogue in the present world. In this research, we first discuss the phenomenon that is produced in the attractors because of the dynamical system in Chaos, the dimension problem in fractal structure, and the ways attractors are automatically produced. We then set our hand on image compression utilizing attractors.
In 1985, Barnsley and his colleagues' proposal that image compression make use of the global Iterated Function System(IFS)failed finally. In 1993, Jacquin, a post-graduate student of Barnsley, published Partitioned Iterated Function System(PIFS)for image compression encoding theorem in his doctoral thesis that leading to image compression succeed. Image compression utilizing the property of fractals accomplished an impossible mission in the ultimate.
Fractal patterns can be reconstructed using simple IFS because they have the global self-similarity. An ordinary picture has no property of self-similarity, but it can be reconstructed using local block of itself patterns. After Jacquin's proposal, Fisher and other researchers make a study and apply progressively for fractal encoding that make fast development in fractal image compression. Yuval Fisher put his C program on the World Wide Web site, let the study of fractal image compression grow up fast.
In the 90's, some new better methods were proposed. Based on the earlier studies on the fractal image compression, we find that changing the number of Domains does affect the compressive quality. For this reason, we propose the factor that changes the number of Domain in Domain pool, so as to reduce the compressive time. At the same time, we use Isometry Classified for each Range and Domain beforehand. In the last, to keep the quality of compression and further reduce the compressive time, we propose the classification of features that can automatically change the range in Domain search. The classification of features not only diminishes the compressive time but also raises the quality of compression.

碎形(Fractals)經過了十幾年來的發展與開創,其研究在當今已形成了一股熱潮。本研究從吸子(Attractor)的動力系統所產生的混沌(Chaos)現象、吸子碎形結構的維度(Dimension)問題,以及如何自動(Automatic)產生吸子開始,後來我們著手研究吸子在圖形壓縮(Image Compression)上的應用。
碎形圖像因為它們具有全域的自我相似性(Self-similarity),所以可用簡單的IFS呈現出來,而一張不具有全域的自相似的生活圖像,得經由它本身的部分(Local)區域的影像重建整張圖像,Jacquin之後碎形編碼由Fisher和其他研究人員進一步研究與應用,加速了這門學科的進展,Yuval Fisher並將C程式放在全球網路上,使碎形影像壓縮,隨之快速發展,我們也由此出發提出新改進方法。
90年代起有很多人提出一些改進的方法。我們在針對初期的碎形影像壓縮作研究之後,發現改變定義域塊(Domain)的數量影響壓縮品質,因而提出參l數調整Domain pool中Domain的數目以縮短壓縮時間,並事先對每個Range和Domain作變換矩陣(Isometry)的分類,在不影響壓縮品質下,進一步縮短壓縮時間,配合利用特性(Feature)分類的原則,使搜尋Domain的範圍自動化調整,更進一步縮短了壓縮時間,並能夠提高壓縮的品質的目標,最後我們再利用碎形壓縮進一步補償碎形壓縮的失真度,使得兩次碎形壓縮的品質超越一次碎形壓縮品質的極限。
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