模糊集合論在影像處理上之應用

Abstract

影像處理在近三十年來快速的發展，而因影像處理的發展及好處引發了在 人工智慧，心理學、心理物理學、計算機結構、電腦圖學上的研究，其應 用的範圍廣泛地包括了文件處理、藥學及生理學、遙測、工業上的自動化 等等。影像處理有各種不同的運算來處理影像資料；這些運算有濾波器， 影像強化，特徵偵測，影像壓縮及影像還原等等，然而不確定性卻充斥在 影像處理中，所以很自然且適合的用模糊集理論去定義影像處理的基本要 素及關係。模糊集合理論已廣泛地應用在科學及工業上因為它處理不精確 性的能力，近年來在控制等方面更是有不凡的表現。傳統分析系統的量化 技術不適合處理人類語意的或較複雜的系統，因為當系統的複雜度增加時 我們要求精準的能力在達到某一定水準後會慢慢消失，所以複雜度與要求 精準度幾乎具有互斥的特性。在此，我們注重在利用模糊集合理論於影像 強化、邊線偵測及紋理分析等方面的研究。影像強化(Image Enhancement) 的技術包括影像平滑 (Image Smoothing)，影像內插( Image Interpolation) 及影像尖銳化 (Image Sharpening)，而邊線偵 測 (Edge detection)亦是影像處理中基本且重要的一環，紋理分析( Texture Analysis)的技術更提供了各種不同的應用；從醫學影像至遙測 的應用。這些都是利用模糊不確定性(Fuzzy Uncertainty) 及模糊推理 (Fuzzy Reasoning) 的技術來完成。我們亦使用目前大家常用的遺傳演算 法則(Genetic Algorithms) 來得到更具彈性的隸屬函數(Membership Functions)；以避免不好的隸屬函數定義而使得我們的模糊推理系統無法 達到滿意的結果。 Image processing has been a fast-growing field for the last thirty years. Influence for its growth and advancement has arisen from studies in artificial intelligence, psychology, psychophysics, computer architecture and computer graphics. Application area for image processing includes document processing, medicine and physiology, remote sensing, industrial automation and surveillance amongst many others. Image process- ing involves various operations on image data. These operations include preprocessing, spatial filtering, image enhancement, feature detection, image compression, image restoration, and so on. However, uncertainty abounds in most phases of image processing. It is natural and also appropriate to define primitives and relation among them using labels of fuzzy set. Fuzzy set theory has been widely used in science and industry because of its capability to model nonstatistical imprecision. The conventional quantitative techniques of system analysis are unsuited for dealing with humanistic systems and other compar- able complex systems, because, as the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics [Zadeh 1973]. In this thesis, we focus on the image enhancement, edge detection and texture analysis by using fuzzy uncertainty and fuzzy logic methods. The techniques of image enhancement include smoothing, interpolation and sharpening. Edge detection the fundamental importance task in image processing. Texture analysis is an import technique in image processing because plays a critical role in inspecting surfaces and provides important techniques in a variety of applications ranging from medical imaging to remote sensing. We also use the popular method of genetic algorithms to obtain more flexible membership functions to avoid the ill-defined membership