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

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

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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

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