灰階影像二值化法為一尋找將輸入灰階影像二值化之最佳門檻值的
偵測方法。過去 Kapur等人發表一植基於平均消息量之二值化演算法
並受到廣泛的使用。本論文首先根據數學理論基礎利用不同策略來計
算平均消息量，並透過多階科西不等式來減少不必要之計算量藉此降
低計算時間且可以得到和 Kapur二值化法相同之結果。經過五張灰階
影像的測試，我們所提出之演算法與 Kapur二值化法比較平均可減少
22%的計算時間。

The purpose of binarization is to determine a threshold to segment the gray image into a binary image. Previously, based on entropy approach, Kapur et al. presented an efficient, classical binarization algorithm. This thesis first transfers the concerned entropy criterion into a new mathematical formula. According to the transferred formula, by adopting the multi–level Cauchy–Schwarz inequality, some unnecessary computations can be discarded in the proposed computational platform, and it leads to a significantly computation–saving effct while preserving the same binarized image. Under five testing gray images, experimental results demonstrate that our proposed faster algorithm has 22% execution–time improvement ratio in average when compared to Kapur et al.’s banarization algorithm.

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