劉長遠臺灣大學：資訊工程學研究所鄭為正Cheng, Wei-ChenWei-ChenCheng2007-11-262018-07-052007-11-262018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/53888Morphological associative memory 在 17 年前被提出。W 只能處理 erosive 的 noisy pattern 而 M 只能處理 dilative 的 noisy pattern。而 G. X. Ritter 提出的 morphological kernel 的方法露出一道曙光，他提出使用兩步 associative memory 的方法來解決 lattice 的 associative memory 在 random noise 上的缺陷。但他們只展示解的樣子，但沒有提出方法，只單純用嘗試錯誤法來找解，日本人 M. Hattori 找到了解法，先找出各 patterns 間最小重疊的 bits 來做 kernel patterns 的初始值，再檢查是否可以滿足可正確被回憶，如不行則調整 Z 直到滿足，最後再修正 Z 使其更精簡。此論文對 lattice 的 associative memory 做了dynamics 的分析並提出當尋找 kernel 時，滿足特定條件的 bit 才需被計算。這 樣可以使原來的程式增快三倍以上的速度，未來大型orphological associative memory 的應用計算將可獲益。 本論文取材自國科會計畫編號 NSC 94-2213-E-002-105。論文題目為指導教授所教，相關智慧財產權依照國科會計畫與本校規定。Morphological associative memory was proposed around seventeen years. The defect is that W only can address erosive noisy patterns and M can only address dilative noisy patterns. The kernel of morphological associative memory shows a clue for real mankind associative memory. G. X. Ritter proposed using two step associative memory to address the defect of error tolerance of lattice based associative. They use trail and error to find the kernel Z and try to work out a way to find kernel in mathematics. Japanese M. Hattori find out a solution. The solution is that find the smallest overlap bit as initial kernel patterns, than adjust Z to satisify perfect recall condition, and try to check each bit in Z to see whether it can be removed or not without affecting the recall result. We propose that when calculating kernel, only those bits satisfying certain condition need to be checked. We consider binary case only. This finding can benefit the application of large scale data processing with morphological assocaitive memory.Contents 1 Introduction 1 1.1 The History of Morphological Neural Network . . . . . . . . . . . . . . . . . 1 1.2 The Biological Evidence of Morphological Neurons . . . . . . . . . . . . . . 14 1.3 Endmember Detection with Morphological Associative Memory . . . . . . . 18 2 Investigation of Morphological Associative Memory 20 2.1 The Drawback of Mophological Associative Memory . . . . . . . . . . . . . 20 2.2 The Advantage of Morphological Associative Memory . . . . . . . . . . . . 21 2.3 The Trajectory of Morphological Associative Memory . . . . . . . . . . . . 23 2.4 The Condition of Stable Points . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5 Perfect Recall Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 The Condition of Dilative Noise Patterns . . . . . . . . . . . . . . . . . . . 30 2.7 Error Tolerance Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3 Logical Operation of Morphological Associative Kernel 35 3.1 The property of kernel patterns . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Transformation from Binary Lattice Structure to Boolean Logic . . . . . . . 39 3.3 Speed the Algorithm Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Algorithm for Finding Binary Morphological Model Kernel . . . . . . . . . 44 3.5 Experimental Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4 Conclusion 48620641 bytesapplication/pdfen-US類神經網路關聯式記憶Lattice Theoryneural networkassociative memorymorphological associative memoriesmorphological kernelmorphological neural networksthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53888/1/ntu-95-R93922108-1.pdf