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Fast-searching algorithm for vector quantization using projection and triangular inequality

Fast-searching algorithm for vector quantization using projection and triangular inequality. Source: IEEE Transactions on Image Processing , vol. 13, issue: 12, Dec. 2004, pp. 1554 - 1558. Author: Lai, J.Z.C.; Yi-Ching Liaw Speaker: Chang-Chu Chen Date: 05/26/2005. Outline. Introduction

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Fast-searching algorithm for vector quantization using projection and triangular inequality

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  1. Fast-searching algorithm for vector quantization using projection and triangular inequality Source: IEEE Transactions on Image Processing, vol. 13, issue: 12, Dec. 2004, pp. 1554 - 1558. Author: Lai, J.Z.C.; Yi-Ching Liaw Speaker: Chang-Chu Chen Date: 05/26/2005

  2. Outline • Introduction • Projection and Inequality • Experimental Results • Conclusions

  3. 0 1 2 253 254 255 VQ Codebook search • Find closest code vector • Full search : reduce computation • Partial search Codebook Image vector Index (20,45,…,76) (21,44,…,78) 2

  4. Property 1 : projection (1/4) • If code vector Ci close to image vector Xthen ,r =d(Ck , X) for some Ck X Ci V1 ci1 x1

  5. Property 1 : projection (2/4) • Compute ci1 for all Ci • If X=(21,44,…,78), x1=715, r=50search 665~765 Sort byprojection

  6. Property 1 : projection (3/4) X = (X1 , X2 , X3 ,…, X16) • projection • because = 4 · mean x1 = ¼ (1,1,1,…,1) V1 inner product if = projection x θ x

  7. Property 1 : projection (4/4) • Projection on V2, V3 for X and all Ci • Edge gradient in vertical direction • Edge gradient in horizontal direction V2 =1/4 (1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1) V3 =1/4 (1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1) x2 0 x3 0

  8. X SX X Property 2 : inequality 1 (1/2) • Projection on space spanned by V1 , V2 , V3(16 dimension project to 3 dimension) • and • then

  9. Property 2 : inequality 1 (2/2) • Since • Then inequality 1

  10. 2r r Cj Ci X Property 3 : inequality 2 (1/2)

  11. dn2 dnN dn3 dn1 C2 dni CN C3 C1 Ci Property 3 : inequality 2 • If X inside circle of Ci( d(X,Ci) ≤ dni )then stop search … …

  12. Experimental Results(1/2)

  13. Experimental Results (2/2)

  14. Conclusions • Use features of a vector to eliminate many of the unlikely codeword. • Algorithm has best performance in computing time and number of distortion calculations.

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