Image compression

Image Compression Why? A two way event - compression and decompression Reducing transportation times Reducing file size A two way event - compression and decompression

Compression categories Compression = Image coding Still-image compression Compression of moving image

INTERFRAME and INTRAFRAME PROCESSING Point to Point Interframe Processing Predictive Encoding Line to Line Intraframe Processing

Image compression meters Compress ratio = Original image size Compressed image size The larger the compression ratio, the smaller the result image

Image compression Compression method is not same as the image file-interchange format. Example TIFF -file format supports several compression methods

Why Can We Compress? Spatial redundancy Temporal redundancy Neighboring pixels are not independent but correlated Temporal redundancy

DATA = INFORMATION + REDUNDANT DATA Information vs Data REDUNDANTDATA INFORMATION DATA = INFORMATION + REDUNDANT DATA

Image compression fundamentals Same compression method is not to be used more than once. But you can use different methods at the same time, especially different lossless methods like LZW and PKZIP

Image compression: symmetry

Color image compression RGB - apply the same compression scheme to the three color component images Convert the image from the RGB color space to a less redundant space, because RGB components carries a lot of same information. RGB --> HSB, when Hue and Saturation components are well compressed

Color image compression RED GREEN BLUE Color image compression HUE BRIGHTNESS SATURATION

Lossless image compression Image can be decompressed back to original Used when image’s future purpose of use is not known, example space exploration imagery is often studied for years following its origination

Run-Length Coding 76 76 76 76 76 78 79 79 80 80 80 98 98 y 76| 5 78| 1 79| 2 80| 3 98| 2 Run-Length Codes (Brightness | Run-length) x

Run-length coding Codes the nearby pixels which has same brightness values in two values - Run-Length, RLE and brightness value Error sensitive Data explosion Data errors

Huffman or Entropy Coding Converting the pixel brightness values in the original image to new variable-length codes, based on their frequency of occurrence in the image Arrange values in descending frequency of occurrence Assign Huffman variable-length codes Brightness Histogram Huffman Code Image Data Raw Image Data Substitute Huffman codes Append code list 0,10,0,1100 1111,11011 98,100,103, 87,86,95... The flow of the Huffman coding operation.

Lossless or Lossy Compression Lossless compression There is no information loss, and the image can be reconstructed exactly the same as the original Applications: Medical imagery, Archiving Lossy compression Information loss is tolerable Many-to-1 mapping in compression eg. quantization Applications: commercial distribution (DVD) and rate constrained environment where lossless methods can not provide enough compression ratio

Predictive Coding Based on the assumption that pixel’s brightness can be predicted based on the brightness of the preceding pixel Codes only the brightness value of the pixel next to each other DPCM (Differential Pulse Code Modulation)

DPCM (Differential Pulse Code Modulation)

Block Coding Searching for repeated patterns (mostly in rows) Pixel patterns are put in Codebook Original image’s pixel pattern is replaced by codebook index in compressed image

Block Coding LZW- compression (Lempel-Ziv-Welch) Compression ratio 2:1 - 3:1 Starting with a 256 single-pixel long codebook -> adding until it reaches its maximum length LZW+Huffmann, where most common pixel patterns get shortest codes

TRANSFORM CODING • Transform Coding - transform image - code the coefficients of the transform - transmit them - reconstruct by inverse transform • Benefits - transform coeff. relatively uncorrelated - energy is highly compacted - reasonable robust relative to channel errors

Transform Coding A form of lossy block coding, but it does not use codebook Frequency domain Frequency transformation finds the essential data in the image and coding is accurate 8*8 pixel blocks Discrete Cosine Transform (DCT) - Fourier -muunnetussa kuvassa kasautumia erityisesti matalissa taajuuksissa. - Näitä yleisimpiä taajuuksia kuvataan sitten tarkoilla arvoilla ja harvinaisia taajuuksia epätarkemmin - Siten kuvasta ei menetetä oleellista tietoa - yleisimpien komponenttien resoluutiota voidaan myös pudottaa - DCT on kuten FFT, mutta soveltuu paremmin pienille kuville ja 8*8 lohkoissa se on iso etu -JPEG SPatial > frequency domain (DCT), otetaan sitten sioimmat komponentit

Why Do We Need International Standards? International standardization is conducted to achieve inter-operability . Only syntax and decoder are specified. Encoder is not standardized and its optimization is left to the manufacturer. Standards provide state-of-the-art technology that is developed by a group of experts in the field. Not only solve current problems, but also anticipate the future application requirements.

Compression standards: JPEG Joint Photographic Experts Group (JPEG) One of the most important image data compression standards Developed for highly detailed gray-scale and color images / photographs Most commonly used as a lossy image compression method, but lossless modes exist as well JPEG uses several cascaded compression modes Adjustable compression scheme à number of retained frequency components can be changed to achieve different compression ratios DCT > Remove rare frequency components > DPCM/RLE > Huffman - Häviöttömässä JPEG:ssä ei tehdä lainkaan harvinaisten komponenttien poistoa

JPEG (Intraframe coding) First generation JPEG uses DCT+Run length Huffman entropy coding. Second generation JPEG (JPEG2000) uses wavelet transform + bit plane coding + Arithmetic entropy coding.

Why DCT Not DFT? DCT is similar to DFT, but can provide a better approximation with fewer coefficients The coefficients of DCT are real valued instead of complex valued in DFT.

The 64 (8 X 8) DCT Basis Functions Each 8x8 block can be looked at as a weighted sum of these basis functions. The process of 2D DCT is also the process of finding those weights. This is another explanation of 2D DCT.

Zig-zag Scan DCT Blocks Why? -- To group low frequency coefficients in top of vector. Maps 8 x 8 to a 1 x 64 vector.

Original

JPEG 27:1

JPEG2000 27:1

Motion compression standards Moving Picture Experts Group (MPEG) Intended for the mass distribution of motion video sequences Compression-asymmetric = compression techniques require more processing time and computing power than the decompression ones In addition to coding techniques used with JPEG, MPEG utilizes interframe coding methods MPEG-1 use CD-ROM and Internet MPEG-2 use DVD and Digi-TV MPEG-4 most advanced technology