Multi-Histogram Equalization Methods for Contrast Enhancement and Brightness Preserving

1. Multi-Histogram Equalization Methodsfor Contrast Enhancement and Brightness Preserving 指導教授：萬書言 報告學生：賴薏如 作者：David Menotti, Laurent Najman, Jacques Facon, and Arnaldo de A. Araújo IEEE Transactions on Consumer Electronics, Vol. 53, No. 3, AUGUST 2007

2. Histogram equalization(直方圖均勻化) • 利用影像對比統計圖用來決定灰度分佈資訊，讓我們了解灰度分佈，再進行影像處理。 • 是ㄧ種簡單而有效的影像對比修改技術

3. Histogram equalization(2) • Change the mean brightness of the image to the middle level of the gray_level range • 強化對比的方式是將長條圖裡每個強度分佈的數量，依照整個畫面的比例，分配一個對照的新值，強調的是所謂的均勻分佈概念。

4. Multi-Histogram equalization • Consists of decomposing the input image into several sub-images,and then applying the Histogram equalization to each one

5. ¥： natural numbers，¢： integer numbers is a sub set of 0 ≤x < m , 0 ≤ y < n , Image I: to ¢L={0,..., L−1} L is typically 256 ,a point(x,y)∈, l=I(x,y) is called the level of the point (x, y) in I . 0 ≤ ls ≤ lf <L, I[ls,lf ]⊆ I, is a sub set of , I(x,y) = l :absolute frequency of the level l in the imageI 0 ≤ l ≤ L−1,

6. 0 ≤ls≤l≤lf <L , ：relative frequency (or the probability) of level l in the (sub-)image I[ls,lf ] ,0≤ls≤l≤lf ≤L−1 , 0≤ls≤l≤lf ≤L−1 Mean: Standard deviation:

7. Shannon's Entropy (熵 )

8. Minimum Within-Class Variance MHE (MWCVMHE)

9. Minimum Middle Level Squared Error MHE (MMLSEMHE). • (ls+lf)/2, O[ls,lf ] • middle value of the image

10. Classical HE method : uniform histogram of the output image ,ls ≤ l ≤ lf

11. Other Method • Brightness Bi-HE Method (BBHE) • Dualistic Sub-Image HE Method (DSIHE) • Minimum Mean Brightness Error Bi-HE Method(MMBEBHE) • Recursive Mean-Separate HE Method (RMSHE)

12. TEST RESULTS

15. TEST RESULTS