Image Compression JPEG Video Compression MPEG Audio compression

Image Compression - JPEG

Video Compression • MPEG – Audio compression • Lossy / perceptually lossless / lossless • 3 layers • Models based on speech generation (throat), or ear characterisitics – Image compression • JPEG based – Images take much more memory than voice • An image is worth a thousand words • Which thousand words? – Video – next week, can we extrapolate?

Image Compression Basics • Model driven • Reduce data redundancy – Neighboring values on a line scan in an image – DPCM, predictive coding • Human perception properties – Human visual system {eye/brain} is more sensitive to some information as compared to others {low frequencies vs high frequencies}: be careful. . edges are often critical – Enhancement approaches

Entropy • Entropy – measurement of the uncertainty of the input. Higher the uncertainty the higher the entropy. – Which has higher entropy noise or a 300 Hx sine wave? – Computation is histogram based – p(i) = probability of occurrence of a gray level in the image – E = - Si p(i) lg {p(i)} – Identifies the minimum number of bits required to represent the image

Compression Issues • Progressive display – Display partially decompressed images – User begins to see parts of the image, does not have to wait for complete decompression • Hierarchical encoding – Encode images at multiple resolution levels. – Display images at lower resolution level and then incrementally improve the quality • Asymmetry – Time for encoding – Time for decoding

Types of compression • Lossless – Huffman, LZW, Run length, DPCM? – Typical compression: 3: 1 • Lossy – Predictive – Frequency based: transform, subbands – Spatial based: filtering, non-linear quantization, vector quantization • Hybrid

JPEG is based on • Huffman coding – Optimal entropy encoding • Run length encoding – Used in G 3, fax • Discrete Cosine Transform – Frequency based – Apply perception rules in the frequency domain • The fidelity and level of compression can be controlled – 15: 1 or even better

Huffman encoding • Assign fewer bits to symbols {pixel values} that occur more frequently • Number of bits per symbol is non-uniform • The code book has to be made available to the decoder, i. e. this file leads to increase in the file size. • Results in optimal encoding – Number of bits required is close to the entropy

Run length Encoding • Run length, size, amplitude – RL: 4 bits – Size: 4 bits – Amplitude: 10 bits • Maximum compression if the run lengths are long • G 3 used for fax • Usually use Huffman to encode the parameters

Discrete Cosine Transform • Real cousin of Fourier transform • Complexity – N*N – Fast DCT – similar to FFT – To reduce cost • Divide image into 8 x 8 blocks • Compute DCT of blocks • Reduce the size of the object to be compressed

Quantization • The eye is more sensitive to the lower frequencies. • Divide each frequency component by a constant • Divide higher frequency components with a larger value • Truncate, and this will reduce the non-zero values • Four quantization matrices are available in JPEG

Color • RGB planes • Transform RGB into YUV – Y – luminance – U, V – chrominance – UV have lower spatial resolutions • Down sampled to take advantage of lower resolution

Overview of JPEG • RGB YUV • Down sample UV • Original data is 8 bits per pixel, all positive [0, 255]. Shift to [-128, 127]. • Divide image into 8 x 8 blocks • DCT on each block • Use quantization table to quantize values in each block {Reducing high freq content} • Use zig-zag scanning to order values in each block • Organize data into bands {DC, low f, mid f, high f} • Run length encoding • Huffman encoding

Reference • G. K. Wallace, “The JPEG Still Picture Compression Standard”, Communications of the ACM, April 1991, vol 34, No. 4, pp 30 - 44