20-10-2012, 11:11 AM
DCT and Transform Coding
ImageCoding_DCT.pdf (Size: 543.9 KB / Downloads: 208)
Motivation for “Transformation”
• Motivation for transformation:
– To yield a more efficient representation of the original samples.
– The transformed parameters should require fewer bits to code.
• Types of transformation used:
– For speech coding: prediction
• Code predictor and prediction error samples
– For audio coding: subband decomposition
• Code subband samples
– For image coding: DCT and wavelet transforms
• Code DCT/wavelet coefficients
Transform Basis Design
• Optimality Criteria:
– Energy compaction: a few basis images are sufficient to
represent a typical image.
– Decorrelation: coefficients for separate basis images are
uncorrelated.
• Karhunen Loeve Transform (KLT) is the Optimal transform for a
given covariance matrix of the underlying signal.
• Discrete Cosine Transform (DCT) is close to KLT for images that
can be modeled by a first order Markov process (i.e., a pixel only
depends on its previous pixel).
Quantization of DCT Coefficients
• Use uniform quantizer on each coefficient
• Different coefficient is quantized with different step-size (Q):
– Human eye is more sensitive to low frequency components
– Low frequency coefficients with a smaller Q
– High frequency coefficients with a larger Q
– Specified in a normalization matrix
– Normalization matrix can then be scaled by a scale factor (QP)