An improved full-search-equivalent vector quantization method using the law of cosines

1. An improved full-search-equivalent vector quantization method using the law of cosines Source: Signal Processing Letters, Vol. 11, Issue: 2, Feb. 2004, pp. 247-250. Author: Pan, Z.; Kotani, K.; Ohmi, T. Speaker: Chang-Chu Chen Date: 03/24/2005

2. Outline • Vector Quantization • FS-equivalent • Improved Search Method • Experimental Result • Conclusions

3. Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20,45,…,76) 253 254 Original Image Index table 255 Vector Quantization Encoder

4. Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20,45,…,76) 253 254 Original Image Index table 255 Vector Quantization Decoder

5. 0 1 2 253 254 255 Codebook search • Find closest code vector • Euclidean distance • Full search • PCA (Principal component analysis) Codebook Image vector Index (20,45,…,76) (21,44,…,78) 2

6. Euclidean Distance • The dimensionality of vector = kAn input vector v = (v1, v2, …, vk)A codeword u = (u1, u2, …, uk) • The Euclidean distance between v and u • Full Search (FS)To find winner uw , where codebook C of size Nc

7. u u-v θ v x u θ1 θ2 θ v FS-equivalent (2002 Mielikainen) • law of cosines • sinceso where

8. FS-equivalent (cont.1) • Estimationthen • If code vector u cannot be a winner

9. < > : inner product FS-equivalent (cont.2) • Computation analysis • Offline : • Online : where (just once) Multiplication *4, Addition *3

10. Improved Search Method • New estimation by let then

11. Step 1 Step 2 Compute Update index and Search flowchart Compute of all code vector u yes no yes no yes no

12. Experimental Result

13. Conclusions • Proposed a new estimation with light computation in full search of codebook.