圖像多重分形測度的速降函數(shù)投影方法與圖像奇異性分析
The Projection Method of Fast Decreasing Functions for Multifractal Measure and Image Singularity Analysis
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摘要: 該文給出了一個基于多重分形理論的圖像奇異性分析框架.該框架通過定義在圖像梯度級上的測度,證明了該測度在速降函數(shù)上的投影與尺度之間滿足冪指數(shù)關(guān)系.給出了將圖像分解為一系列具有不同奇異性指數(shù)和分數(shù)維的分形集合的分解算法.最后理論分析并提出了選擇速降函數(shù)的基本原則,討論了僅根據(jù)分形集合上的導數(shù)信息就可以重建該分形層面圖像分量的重構(gòu)算法.實驗表明,該文給出的多重分形框架在圖像奇異性檢測和分析中具有十分重要的意義.
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關(guān)鍵詞:
- 邊緣重構(gòu)圖像; 邊緣檢測; 奇異性分析; 多重分形; 速降函數(shù)
Abstract: The framework for image singularity analysis based on multifractal theory is presented in this paper. The measure is defined which gives the local distribution of the gradient of the image. The exponential formalism between the projection of fast decreasing functions of the defined measure and scale is proved. According to the exponential formalism, the paper also presented an algorithm, in which the nature image can be decomposed in a serial fractal sets with different singularity exponent and fractal dimension. Finally, some basic theoretical results of the choice for the fast decreasing functions are proposed. Also an investigation of how to reconstruct the different fractal image components with derivative information contained in the different fractal sets is made. Experiments show that the multifractal formalism has significance in image singularity analysis and detection. -
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