Vector Quantization for Texture Compression Qiu Wu

1. CS 395 T Real-Time Graphics Architectures, Algorithms, and Programming SystemsSpring’03 Vector Quantization for Texture Compression Qiu Wu Dept. of ECE & TICAM University of Texas at Austin Feb. 4th, 2003

2. Overview • Review of Vector Quantization • VQ for texture compression (paper of Beers etc) discussion of its contributions and weakness • DXT1 Texture Compression

3. Signal Compression • Purpose : reduce the bit rate for transmission/storage • Principles: • Exploit the signal redundancy in spatial domain • Human vision system has different sensitivities for different frequencies, low frequency noise is more noticeable

4. Signal Compression 1. Reconstruction error==0? • Lossy Compression: often eliminate high frequency components • Lossless Compression: exact reconstruction 2. Scalar based or Vector based Quantization? • Scalar Quantization : transform+SQ, state of the art • Vector Quantization

5. Vector Quantization • Block coding: consecutive n pixels as a block(vector) • Map each vector to an index of the code which is closest to this vector • This index is compressed info • In decoding, look up table for a vector by this index

6. Training algorithm: GLA • 1. Begin with an initial codebook C1. • 2. Repeat • (a) Given a codebook (set of clusters defined by their centroids) redistribute each vector x into one of the clusters in by selecting the one whose centroid is closer to x. • (b) Recompute the centroids for each cluster just created, to obtain the new codebook Cm+1. • (c) Compute the average distortion Dm+1 for Cm+1, Until the distortion has only changed by a small enough amount since last iteration.

7. Animation of LBG Algorithm(http://www.data-compression.com/index.html)

8. Pros and Cons of VQ • Pros: Fast decoding ---lookup table • Cons: Long training time, unstable process, low CR,

9. VQ for texture compression • Presented by AndrewC.Beers, ManeeshAgrawala,and NavinChaddha on SIGGRAPH 1996 • VQ for generating compressed texture in memory • VQ for compressed MIPMAP • Performance: CR=20, 2—20% saving on time

10. VQ scheme of Beer’s paper

11. Details of VQ for texture compression • Multiple-codebooks or Single codebook Option 1: Each codebook for each color component Option 2: Components of color as a single value Too simple description and just experimental, more statistical discussion would be necessary and wonderful

12. Details of VQ for texture compression • Large codebook or Small codebook Large codebook---more representative vectors---better reconstruction quality but More bits per index—>low compression ratio • Vice versa for small codebook

13. Details of VQ for texture compression • RGB-YUV • More CPU time for tansforming back and forth though additional compression • Just mention borrowing concept from video coding, no reason given in the paper, then in coding YUV combined together or in separate? • My explanation: more energy in Y component

14. Details of VQ for texture compression(Fig 2 of Beers’ paper) • Mipmaping

15. DXT1 texture compression • compressed textures stored in memory at a ratio of 4:1 • supported by Direct3D • 4 by 4 pixel blocks---compressed block has a size of 64 bits while an original, uncompressed block is 4x4x16 = 256 bits in size

16. DXT1 texture compression:Opaque Case • When compressing an entirely opaque block, two extreme colours are chosen from all the colours present in the original block • All 16 pixels contained in a block are represented with two bits each. These two bits enable four possible combinations to encode a pixel color • While two of these combinations indicate to use either of the stored colours, the other two specify a gradient of the defined colours

17. Reference: • Image coding using vector quantization: A review. IEEE Transactions on Communications, 36(8):957--971, August 1988. • Rendering from Compressed Textures",Beers, Agrawala and Chaddha, SIGGRAPH 1996. • DXT1 Texture Compression", Imagination Technologies