IMAGE DATA COMPRESSION IN WAVELET TRANSFORM DOMAIN USING MODIFIED LBG ALGORITHM Source: ACM International Conference Proceding of the 1st International Symposium on Information and Communication Tech:pp.88-93, 2003. Author: Othman Omran Khalifa Reporter: Jain Yaun Chang Date：2005/5/3

Outline The Discrete Wavelet Transform Modified LBG Algorithm Using Partial Search Partial Distortion Simulation Results Conclusions

The Discrete Wavelet Transform 第一次水平分割示意圖

The Discrete Wavelet Transform (cont.) 第一次垂直分割示意圖

The Discrete Wavelet Transform (cont.) 三階 Haar 離散小波轉換

The Discrete Wavelet Transform (cont.)

Modified LBG Algorithm Using Partial Search Partial Distortion Step (1). Initialization. n =Number of training vectors N =Codebook size k =Vector dimension C0 =Initial codebook D-1 =Initial average distortion

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) Step (2). => m1=191.5 σ2=22.25 h=0.11 => m2=43.5 σ2=36.25 h=0.83 => m3=191.7 σ2=14.19 h=0.07 => m4=77.2 σ2=57.19 h=0.74 => m5=81.2 σ2=225.6 h=2.77 => m6=21.7 σ2=23.69 h=1.09 => m7=211.2 σ2=181.6 h=0.86 => m8=161 σ2=82 h=0.5

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) cw1’ (191, 198, 190, 188) cw2’ (184, 192, 193, 197) cw3’ (151, 153, 169, 171) cw4’ (77, 83, 84, 65) cw5’ (34, 50, 43, 47) cw6’ (210, 213, 192, 230) cw7’ (23, 29, 16, 19) cw8’ (63, 70, 94, 98)

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) Step (3). Calculate the minimum distortion partition. (a). Compute h for the input vector x v = (150,145,121,130) =>m=136.5 σ2=134.25 h=0.98

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) (b). Find the best match of h from the sorted codebook cw7’ (23, 29, 16, 19)

Modified LBG Algorithm Using Partial Search Partial Distortion (c). Define the partial codebook, window size + - T from the best match vector. Ex: T=1 cw6’ (210, 213, 192, 230) cw7’ (23, 29, 16, 19) cw8’ (63, 70, 94, 98)

Modified LBG Algorithm Using Partial Search Partial Distortion (d). calculating the distortion of each codevector by select the minimum distortion. d(v, cw6’) = 152.5 d(v, cw7’) = 235. d(v, cw8’) = 122.3 So, we choose cw8’ to replace the input vector v

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) Step (4).

Modified LBG Algorithm Using Partial Search Partial Distortion (cont.) Step (5). If (Diteration-1 – Diteration) / Diteration <=δ stop with codebook

Simulation Results

Simulation Results (cont.)

Simulation Results (cont.)

Conclusions the proposed wavelet code performed well when compared with the industrial standard JPEG algorithm and much better than vector quantisation technique. These results show that the algorithm provides a highly competitive solution to the problem of image data compression.