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段汕,劉丹,周奇魚.適用于圖像恢復的最優形態濾波設計方法[J].中南民族大學學報自然科學版,2019,(2):298-303
適用于圖像恢復的最優形態濾波設計方法
Design method of optimal morphological filtering for image restoration
  
DOI:10.12130/znmdzk.20190226
中文關鍵詞: 圖像恢復  SV結構映射  SV形態濾波  形態模式譜
英文關鍵詞: image restoration  SV structure mapping  SV morphological filtering  morphological pattern spectrum
基金項目:國家自然科學基金資助項目(61771021)
作者單位
段汕,劉丹,周奇魚 中南民族大學 數學與統計學學院,武漢430074 
摘要點擊次數: 215
全文下載次數: 183
中文摘要:
      針對噪聲圖像的恢復問題,研究了基于SV形態學理論的最優形態濾波設計方法. 通過建立SV形態模式譜解決圖像與相關幾何結構相似性度量問題;通過引入集差距離函數,解決由形態濾波所產生的幾何和拓撲畸變程度的量化問題;通過優化問題的設計,在有效去噪和保持圖像基本結構之間尋求一個平衡策略,使得優化問題得以求解. 最終從理論上證明了一類SV交替濾波和一類SV交替慣序濾波是SV形態學方法下,適用于圖像恢復的最優濾波.
英文摘要:
      Aiming at the problem of noise image restoration, this paper studies the optimal morphological filtering design method based on SV morphology theory.The similarity measurement problem between image and related geometric structure is solved by establishing SV morphological pattern spectrum, and the quantization problem of geometric and topological distortion caused by morphological filtering is solved by introducing the distance function of set difference. Through the design of the optimization problem, a balance strategy is sought between the effective denoising and preserving the basic structure of the image, and the optimization problem can be solved.Finally, it is proved theoretically that a class of SV alternating filtering and a kind of SV alternating sequence filtering are the optimal filtering for image restoration under the SV morphological method.
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