An improved fullsearchequivalent vector quantization method using the

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An improved full-searchequivalent vector quantization method using the law of cosines Source: IEEE Signal

An improved full-searchequivalent 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 n n n Vector Quantization FS-equivalent Improved Search Method Experimental Result Conclusions 2

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

Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20, 45, …, 76)

Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20, 45, …, 76) 51 2 46 6 84 41 52 74 3 … … … Original image 253 254 255 … … Index table Vector Quantization Encoder 3

Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20, 45, …, 76)

Vector Quantization (VQ) Image compression technique Codebook 0 1 2 (20, 45, …, 76) 51 2 46 6 84 41 52 74 3 … … … Original image 253 254 255 … … Index table Vector Quantization Decoder 4

Codebook search n Find closest code vector Codebook Image vector 0 1 2 (20,

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

Euclidean Distance n n n The dimensionality of vector = k An input vector

Euclidean Distance n n n The dimensionality of vector = k An input vector v = (v 1, v 2, …, vk) A codeword u = (u 1, u 2, …, uk) The Euclidean distance between v and u Full Search (FS) To find closest uw , where codebook C of size Nc 6

FS-equivalent (2002 Mielikainen) u n law of cosines u-v θ v where n a

FS-equivalent (2002 Mielikainen) u n law of cosines u-v θ v where n a fixed vector x since so x u θ 1 θ θ 2 v 7

FS-equivalent (cont. 1) n Estimation then n If then code vector u cannot be

FS-equivalent (cont. 1) n Estimation then n If then code vector u cannot be closest code vector 8

FS-equivalent (cont. 2) 1 1 2 2 where n 4 3 3 < >

FS-equivalent (cont. 2) 1 1 2 2 where n 4 3 3 < > : inner product Computation analysis n n Offline : Online : (just once) Multiplication * 4 , Addition * 3 9

Improved Search Method n New estimation by let then 10

Improved Search Method n New estimation by let then 10

Search flowchart n Step 1 n Step 2 Compute yes of all code vector

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

Improved Search Method (cont. ) by u n ux, θ 1 Compute u x

Improved Search Method (cont. ) by u n ux, θ 1 Compute u x , , x , more efficiently with less memory and let x as mth standard basis vector 12

Experimental Result n n n Image : 512 x 512, gray level Block size

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

Conclusions n n Proposed a new estimation with light computation in full search of

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

Example 1 n Euclidean distance 15

Example 1 n Euclidean distance 15

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

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

An improved fullsearchequivalent vector quantization method using theAn improved fullsearchequivalent vector quantization method using the
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