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Efficient Vector Quantization with Fast Searching Algorithm

The paper presents a fast-searching algorithm for vector quantization using projection and triangular inequality. It discusses the method's experimental results and concludes on its performance benefits. The algorithm efficiently reduces computation time by finding the closest code vector and implementing partial search. By utilizing vector properties, it enhances codebook search accuracy and optimizes distortion calculations.

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Efficient Vector Quantization with Fast Searching Algorithm

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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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