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

An improved full-search-equivalent vector quantization method using the law of cosines. Source: IEEE 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. Outline. Vector Quantization

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

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  1. An improved full-search-equivalent vector quantization method using the law of cosines Source: IEEE 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 closest 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 • a fixed vector x sinceso where

  8. FS-equivalent (cont.1) • Estimationthen • Ifthencode vector u cannot be closest code vector

  9. FS-equivalent (cont.2) 1 4 2 3 • Computation analysis • Offline : • Online : 1 2 3 < > : inner product 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. Improved Search Method (cont.) • Compute more efficiently with less memory by , u ux, , θ1 , x ux and let x as mth standard basis vector

  13. Experimental Result • Image : 512 x 512, gray level • Block size : 4 x 4 • Codebook size : 1024

  14. Conclusions • Proposed a new estimation with light computation in full search of codebook. • Compute efficiently

  15. Example 1 • Euclidean distance

  16. Example 2 Y u(3,4,5) X Z

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