IMAGE CODING Motivation • Large amount of data in images Color video: 200Mb/sec Landsat TM multispectral satellite image: 200MB • High potential for compression Redundancy (aka correlation) in images – spatial, temporal, spectral storage versus transmission applications source source source coder source coder channel coder image image storage channel retrieved retrieved image source decoder image source decoder channel decoder ECE/OPTI533 Digital Image Processing class notes 288 Dr. Robert A. Schowengerdt 2003 IMAGE CODING • High correlation for close neighbors Joint probability plots (scattergrams) between pixels with given horizontal spacing • As pixel separation increases, correlation decreases ∆ = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ECE/OPTI533 Digital Image Processing class notes 289 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Lossy coding • Some acceptable loss of data, without loss of “information” • Error measures ˆ Mean Square Error MSE() DN = Variance() f – f Root Mean Square Error RMSE() DN = MSE Normalized Mean Square Error NMSE()% = 100()MSE ⁄ Variance()f Signal-to-Noise Ratio SNR() dB = 10log() 100 ⁄ NMSE () []()2 ⁄ Peak-to-peak SNR PSNR dB = 10log fmax – fmin MSE • Problems Error measures don’t emphasize visually important features such as contrast edges • Can improve correlation of any of these error measures with visual quality by restricting to “edge pixels” only How to define and quantify “image quality?” ECE/OPTI533 Digital Image Processing class notes 290 Dr. Robert A. Schowengerdt 2003 IMAGE CODING example with JPEG coding 1/8 RMSE = 2.91 DN NMSE = 0.16% SNR = 27.9dB 1/16 RMSE = 4.63 DN NMSE = 0.42% SNR = 23.8dB 1/32 RMSE = 7.37 DN NMSE = 1.05% SNR = 19.8ddB ECE/OPTI533 Digital Image Processing class notes 291 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Run-Length Coding typical behavior (image dependent) • Simple, image domain, lossy compression ratio compression algorithm • Exploits neighboring pixel correlation, line-by-line 0 T Works best for simple, low-frequency content, near-binary images, e.g. faxes number of runs • DN threshold controls quality loss and compression rate T • Look for “runs” 0 contiguous pixels with similar values (within threshold of starting pixel value) average runlength • Code starting pixel value (Q bits) and length of line (≤ logN/log2 “intrinsic” runlength T bits) 0 ECE/OPTI533 Digital Image Processing class notes 292 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Lossless Coding • No data loss • Minimal compression (typically 2:1) • Example algorithms Run-Length (with zero threshold) Lempel-Ziv-Welsh (LZW) Huffman Coding ECE/OPTI533 Digital Image Processing class notes 293 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Components of source coder • Data transformation waveform coder transform coder image model coder • Quantization bits, transform coefficients, or model parameters • Codeword Assignment unique bit string for each quantized parameter ECE/OPTI533 Digital Image Processing class notes 294 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Waveform Coding • Pulse Code Modulation (PCM) Image intensity quantized by uniform quantizer At low bit rates (typically less than 4 bits/ pixel), quantization noise appears as false contours in areas of low intensity 16 levels slope 8 levels 4 levels ECE/OPTI533 Digital Image Processing class notes 295 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Example 2-bit uniform quantizer ∆ =1 out in codeword out error 11 3∆/2 1.2 11 1.5 -0.3 10 1.5 11 1.5 0 ∆/2 in -2 00 -1.5 -0.5 −∆ 01 +∆ -0.5 01 -0.5 0 −∆/2 0.5 10 0.5 0 bits 00 −3∆/2 0.6 10 0.5 0.1 -0.75 01 -0.5 -0.25 1.2 11 1.5 -0.3 MSE = 0.0628 Alternate representation: bits 00 01 10 11 mid-rise uniform quantizer −3∆/2 −∆ −∆/2 ∆/2+∆ 3∆/2 bits 000 001 010 100 101 mid-tread uniform quantizer −3∆/2−∆ −∆/2 0 ∆/2+∆ 3∆/2 ECE/OPTI533 Digital Image Processing class notes 296 Dr. Robert A. Schowengerdt 2003 IMAGE CODING • PCM with Nonuniform Quantization Assign quantization levels according to image intensity distribution Small improvement for typical images • Depends on nonuniformity of image histogram For example, use CDF as nonlinear transform, i.e. histogram equalization • Assigns more levels where there are more pixels source nonlinear nonlinear coded uniform PCM image transform transform-1 image ECE/OPTI533 Digital Image Processing class notes 297 Dr. Robert A. Schowengerdt 2003 IMAGE CODING PCM with Pseudo-noise • Add random noise to image before PCM • Subtract same random noise after PCM source decoded uniform PCM image image η(m,n) • Removes spatial correlation of quantization noise ECE/OPTI533 Digital Image Processing class notes 298 Dr. Robert A. Schowengerdt 2003 IMAGE CODING example with 3 bits/pixel and uniform random noise add noise PCM (3bits/pixel) uniform PCM (3bits/pixel) minus noise ECE/OPTI533 Digital Image Processing class notes 299 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Delta Modulation example row-by-row image scan pattern • Code difference of neighboring pixels with 1 bit Assume some “scan” pattern in image • Reduces spatial correlation before coding ECE/OPTI533 Digital Image Processing class notes 300 Dr. Robert A. Schowengerdt 2003 IMAGE CODING Example image: in difference codeword out error 6 788 66 11-0.3 5910 8 71 170 81 18-0.5 6 897 80 190 7911 9 10 2 1 0 9-10 0.1 differences: 5-40 -0.25 6 110 61 1 -0.3 82 1 -4 -1 2 0 91 1 12 1 -2 7-20 92 1 -2 -2 2 2 11 2 1 9-20 difference ≥ 0: codeword = 1 7-20 difference < 0: codeword = 0 ECE/OPTI533 Digital Image Processing class notes 301 Dr. Robert A. Schowengerdt 2003.