Retinex影像增強法是一種基於人類視覺的演算法，它能增強非均勻影像的對比並能平衡影像的明暗。原始非均勻影像在亮處有良好的表現，而Retinex增強影像在暗處有傑出的表現，因此Kim提出了一個結合兩者優點的演算法。此演算法將原圖以K-means分群演算法分為三區塊，並且對每一區塊採取不同的策略去混合原始與Retinex增強影像。然而此法在分群及混合的過程中仍存在一些問題，例如對比和邊緣資訊的降低、分群的邊界不平滑等。更甚者，K-means分群演算法過於耗時以致於不適合實際應用。

為了解決以上的問題，我們提出了一影像增強演算法，它在分群及混合過程之前先執行小波轉換，小波轉換將影像分解為近似及細節兩成分。分群僅執行在近似成分，而其結果被用作為如何混和原始非均勻影像及Retinex增強影像之依據。由於小波較delta函數更能忠實表示訊號，所提方法非在原來的空間域而是在轉換域執行分群與混合，因此可以獲得更佳的增強效果。在此法中，FGFCM分群演算法取代了K-means分群演算法。相較於K-means，FGFCM不僅能抑制雜訊、保存細節，更降低了計算時間。

在實驗方面，我們首先使用動態範圍獨立影像品質評估量距(DRIM)主觀評估並比較所提演算法與三種現存演算法。結果顯示在暗處所提方法改善之影像有顯著的對比增強，而在其他地方只有輕微的對比喪失和對比反轉。然後我們比較了所提方法搭配不同小波分解階層的效果，實驗結果顯示搭配小波分解的方法顯著保留了原圖的細節部分。接著我們使用峰值訊噪比(PSNR)，信息熵和光線次序誤差(LOE)客觀比較各演算法。實驗結果顯示，所提出演算法具有第二高PSNR，最高信息熵與第二低LOE，因此整體表現為最佳。最後我們比較了所提方法搭配不同分群演算法以及不同小波分解階層之執行時間，並且觀察到使用FGFCM相較使用FCM省了約30%的執行時間，而若再搭配小波分解，則省去了將近60%的執行時間。

Based on the human visual system, the Retinex image enhancement algorithm offers a forcefully improvement for nonuniformly illuminated images and keeps a good balance between darkness and brightness. By observing that the original nonuniformly illuminated image has good performance in the bright area and the Retinex improved image has outstanding performance in the dark area, Kim proposed an algorithm aiming to integrate the merits from both images. The proposed algorithm segments the histogram of an image into three areas by using the K-means clustering algorithm and adopts an appropriate strategy for each area to mix the original image and its Retinex improved images. However, there are still some shortcomings in the process of segmentation and mixing. For example, some contrast and some edge information may be lost and segmentation boundary may not be smooth. Furthermore, the K-means clustering algorithm is time consuming which is unpractical for applications.
To solve the above problems, we proposed an algorithm which performs the wavelet transform (WT) before segmentation and mixing. The wavelet transform decomposes an image into the coarse component and the detail components. The segmentation is performed on the course component and the result is used to fuse the course and detail components from both sources (the original image and the Retinex improved image). By performing the segmentation and mixing in the transformed domain instead of the original spatial domain a gain is obtained since wavelets represent signals more faithfully than the delta function. Instead of K-means, the fast generalized FCM (FGFCM) clustering algorithm is employed in the proposed algorithm. FGFCM guarantees noise-immunity and detail-preserving and reduces computation time significantly as compared to K-means.

The proposed algorithm is first subjectively assessed by using the dynamic range independent image quality assessment metric (DRIM) and compared with three existing algorithms. Experimental results show that the improved images using our proposed algorithm reveal significant amplification of contrast in the dark areas and mild loss and reversal of contrast in other areas. We compared the performance of the proposed algorithm with different DWT levels. Experimental results show that the detail component of the original image is well preserved by applying the multi-level DWT. The proposed algorithm is objectively assessed by using peak signal-to-noise ratio (PSNR), information entropy and lightness order error (LOE). Experimental results show that among the four methods compared the PSNR of our proposed algorithm is the second highest, the information entropy is the highest and the LOE is the second lowest, all together, this indicates that our algorithm is the best among the four algorithms. Finally the execution time of the proposed algorithm with FGFCM and/or DWT is compared. It’s observed that using FGFCM saves about 30% execution time in average as compared with using FCM. When using FGFCM in combination with DWT, the time saved reaches about 60% as compared with using FCM and without DWT.

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