Fuzzy Color Histogram and Its Use in Color Image retrieval Author: Ju Han and Kai-Kuang Ma Source: IEEE Trans. Image Processing, Vol. 11, No. 8, pp. 944-952, 2002 Date: 2004/4/21 Adviser: Dr. Chin-Chen Chang Speaker: Hao-Yu Lo 2004/4/21

Outline Conclusions The conventional color histogram (CCH) The proposed method fuzzy color histogram(FCH) Experimental results (CCH)和(FCH)的目的都是做image retrieval。 Color histogram在這篇paper被視為顏色分佈的機率。 2004/4/21

Conclusions A new color histogram representation called fuzzy color histogram (FCH)was proposed. FCH is less sensitive than CCH on dealing with lighting intensity changes and region of interest image retrieval. 2004/4/21

conventional color histogram(CCH) H(I)=[h1, h2, …, hn], where hi=Ni /N (R,G,B) image I b r w y o g 用CCH表示一張圖，H(I)=[h1, h2, …, hn]。 N: total pixels in image I。n: color bins in color space。hi=Ni /N 2004/4/21

fuzzy color histogram(FCH) F(I)=[f1, f2, …, fc], where input pixels fuzzy c-mean(FCM) cluster algorithm fi pixels x1 x2 x3 x4………….. xN ij membership 0.2 0.9 0.6 0 ………….. 0.5 value of f1 Pj指的就是，從image I裡選出來的第j個pixel，(據理解，每個pixel被選到的機率都是1/16)。 ij指的是，第j個pixel在第i個bin的隸屬度。 membership 0.3 0.1 0.1 0.2 ………… 0.4 value of f2 . . . . . . 2004/4/21  1 1 1 1 1

Example of fuzzy c-mean(FCM) cluster algorithm(1/3) Initialize two cluster’s center v1=(166,169,189) v2=(120,123,124) t=1 X1=(186, 185, 197) X2=(162, 142, 165) X3=(206, 208, 209) X4=(142, 131, 160) f1 11=0.4 12 =0.7 1 3 =0.2 14 =0.6 f2 21 =0.6 22 =0.3 23 =0.8 24 =0.4 ij i j (1/||xj-vi||2)1/(m-1) , i=1,2; j=1,2,3,4 ( ) 1 1/2-1 11= ( ) ( ) 1 1/2-1 1 1/2-1 f1(1)=(0.4+0.7+0.2+0.6)/4, f2(1)=(0.6+0.3+0.8+0.4)/4 F(1)=(1.9/4, 2.1/4) 2004/4/21

Example of fuzzy c-mean(FCM) cluster algorithm(2/3) Compute new two cluster’s center v1(1)=(163,165,168) v2 (1) =(118,121,125) N ij j j N ij j t=2 X1=(186, 185, 197) X2=(162, 142, 165) X3=(206, 208, 209) X4=(142, 131, 160) f1 11=0.5 12 =0.67 1 3 =0.26 14 =0.55 f2 21 =0.5 22 =0.33 23 =0.74 24 =0.45 f1(2)=(0.5+0.67+0.26+0.55)/4, f2(2)=(0.5+0.33+0.74+0.45)/4 F(2)=(1.98/4, 2.02/4) 2004/4/21

Example of fuzzy c-mean(FCM) cluster algorithm(3/3) Iteration until ||F(t)-F(t-1)||<,stop. else, t=t+1 f1(5)=(0.5+0.67+0.26+0.56)/4=1.99/4, f2(5)=(0.5+0.33+0.74+0.44)/4=2.01/4 F(5)=(1.99/4, 2.01/4) f1(6)=(0.51+0.67+0.26+0.56)/4=2/4, f2(6)=(0.49+0.33+0.74+0.44)/4=2/4 F(6)=(2/4, 2/4) stop. v1(6)=(140,162,171), v2 (6)=(185,193,204) 2004/4/21

fuzzy c-mean(FCM) weighting exponent m, and error tolerance . Step1) Input the number of clusters c, the weighting exponent m, and error tolerance . Step2) Initialize the cluster centers V={vi}, for 1  i  c. Step3) Input data X={x1, x2, …,xN}. Step4) Calculate the c cluster centers V={vi (t)}. Step5) Update new F={f1, f2,…, fc,} Step6) If ||F(t)-F(t-1)||<,stop. else, t=t+1,return to step 4 有效計算 FCH的方法，是一個架構在fuzzy c-mean(FCM)的clustering演算法。介紹fuzzy c-mean在幹嘛。 2004/4/21

Experimental results(1/2) vary lighting intensity from –25, -20, ……,+20, +25 解釋rank的定義。 2004/4/21

Experimental results(2/2) retrieved images by using CCH retrieved images by using FCH 解釋為什麼要做regional retrieval。 2004/4/21 retrieved images by using CCH retrieved images by using FCH