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

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

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

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

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

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.

Animation of LBG Algorithm ( )

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

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

VQ scheme of Beer’s paper

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

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

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

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

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

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

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