e178-L14.ppt

# E178-L14 - Image Compression-II 1 Block Transform Coding Section 8.2.8 Image Compression-II 2 Transform coding Construct n X n subimages Forward

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Image Compression-II 1 Block Transform Coding Section 8.2.8 Image Compression-II 2 Transform coding Construct n X n subimages Forward transform Quantizer Symbol encoder N X N images Compressed image Compressed image Symbol decoder Inverse transform Merge n X n subimages Uncompressed image Blocking artifact: boundaries between subimages become visible Image Compression-II 3 Transform Selection DFT Discrete Cosine Transform (DCT) Wavelet transform Karhunen-Loeve Transform (KLT) …. T ( u , v ) = g ( x , y ) r ( x , y , u , v ) y = n − 1 ∑ x = n − 1 ∑ − − − − (8.2.10) g ( x , y ) = T ( u , v ) s ( x , y , u , v ) − − − − 8.2.11 v = N − 1 ∑ u = N − 1 ∑ Image Compression-II 4 Transform Kernels Separable if E.g. DFT: E.g. Walsh-Hadamard transform (see page 568, text) E.g. DCT r ( x , y , u , v ) = r 1 ( x , u ) r 2 ( y , v ) − − − − (8.2.12) r ( x , y , u , v ) = exp( − j 2 π ( ux + vy ) / n ) Image Compression-II 5 Approxima tions using DFT, Hadamard and DCT, and the scaled error images Image Compression-II 6 Discrete Cosine Transform Ahmed, Natarajan, and Rao, IEEE T-Computers, pp. 90-93, 1974. Image Compression-II 7 1-D Case: Extended 2N Point Sequence Consider 1- D first; Let x(n) be a N point sequence 0 n N -1. x(n) 2 - N point y(n) point Y(u) point C(u) ≤ ≤ ↔ − ↔ − = + − − = ≤ ≤ − − − ≤ ≤ − ↔ DFT N N y n x n x N n x n n N x N n N n N 2 2 1 1 2 1 2 1 ( ) ( ) ( ) ( ), ( ), 0 1 2 3 4 x(n) 0 1 2 3 4 5 6 7 8 y(n) Image Compression-II 8 DCT & DFT Y ( u ) = y ( n )exp − j 2 π 2 N un n = 2 N − 1 ∑ = x ( n )exp − j 2 π 2 N un n = N − 1 ∑ + x (2 N − 1 − n )exp − j 2 π 2 N un n = N 2 N − 1 ∑ = x ( n )exp − j 2 π 2 N un n = N − 1 ∑ + x ( m )exp − j 2 π 2 N u (2 N − 1 − m ) m = N − 1 ∑ = exp j π 2 N u x ( n )exp − j π 2 N u − j 2 π 2 N un n = N − 1 ∑ + exp j π 2 N u x ( n )exp j π 2 N u + j 2 π 2 N un n = N − 1 ∑ = exp j π 2 N u 2 x ( n )cos π 2 N u (2 n + 1) n = N − 1 ∑ . Image Compression-II 9 DCT The N-point DCTof x(n), C(u), is given by C ( u ) = exp − j π 2 N u Y ( u ), ≤ u ≤ N-1 0 otherwise. The unitary DCT transformations are: F ( u ) = α ( u ) f ( n )cos π 2 N (2 n + 1) u , n = N − 1 ∑ ≤ u ≤ N − 1, where α (0) = 1 N , α ( u ) = 2 N for 1 ≤ k ≤ N − 1....
View Full Document

## This note was uploaded on 12/28/2011 for the course ECE 178 taught by Professor Manjunath during the Fall '08 term at UCSB.

### Page1 / 20

E178-L14 - Image Compression-II 1 Block Transform Coding Section 8.2.8 Image Compression-II 2 Transform coding Construct n X n subimages Forward

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online