Image and Video Coding I: Fundamentals

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1 Image and Video Coding I: Fundamentals Heiko Schwarz Freie Universität Berlin Fachbereich Mathematik und Informatik

2 H. Schwarz (FU Berlin) Image and Video Coding Organization Vorlesung: Montag 14:15-15:45 Raum SR 006 / T9 Übung: Montag 12:30-14:00 Raum SR 006 / T9 Material: Literatur: Cover, T. M. and Thomas, J. A. (2006), Elements of Information Theory, John Wiley & Sons, New York. Gersho, A. and Gray, R. M. (1992), Vector Quantization and Signal Compression, Kluwer Academic Publishers, Boston, Dordrecht, London. Jayant, N. S. and Noll, P. (1994), Digital Coding of Waveforms, Prentice-Hall, Englewood Cliffs, NJ, USA. Wiegand, T. and Schwarz, H. (2010), Source Coding: Part I of Fundamentals of Source and Video Coding, Foundations and Trends in Signal Processing, vol. 4, no (available on web page)

3 Introduction encoder bitstream decoder

4 Motivation H. Schwarz (FU Berlin) Image and Video Coding: Introduction 2 / 33 Motivation for Source Coding Source Coding / Data Compression Efficient transmission or storage of data Use less throughput for given data Transmit more data for given throughput Source Coding: Enabling Technology Enables new applications Makes applications economically feasible Examples Distribution of digital images Distribution of digital audio (first mobile audio players) Digitial television (DVB-T, DVB-T2, DVB-S, DVB-S2) Internet video streaming (YouTube, Netflix, Amazon,...)

5 Motivation H. Schwarz (FU Berlin) Image and Video Coding: Introduction 3 / 33 Practical Source Coding Examples File Compression Compress large document archives GZIP, WinZIP, WinRar,... Audio Compression Compress audio for storage on mobile device FLAC, MP3, AAC,... Image Compression Compress images for storage and distribution Raw camera formats, JPEG, JPEG-2000, JPEG-XR,... Video Compression Compress video for streaming, broadcast, or storage MPEG-2, H.264 AVC, VP9, H.265 HEVC,...

6 Motivation H. Schwarz (FU Berlin) Image and Video Coding: Introduction 4 / 33 Types of Compression Lossless Compression Invertible / reversible form of data compression Original input data can be completely recovered Required for document compression Examples: Lempel-Ziv coding (GZIP), FLAC, JPEG-LS Lossy Compression Not invertible Only approximation of original input data can be recovered Achieves much higher compression ratios Dominant form of compression for media data (audio, images, video) Examples: MP3, AAC for audio JPEG, JPEG-2000 for images MPEG-2, H.264 AVC, H.265 HEVC for video

7 Source Data Sampling and Quantization H. Schwarz (FU Berlin) Image and Video Coding: Introduction 5 / 33 Source Data Analog Signals Continuous-time/space and continuous-amplitude signals Typically resulting from physical measurements Most signals in reality (audio and visual signals) Digital Signals Discrete-time/space and discrete-amplitude signals Often generated from analog signal Sometimes directly measured Input Data for Source Coding Require digital signals Need to be stored and processed with a computer Compression methods are computer programs

8 Source Data Sampling and Quantization H. Schwarz (FU Berlin) Image and Video Coding: Introduction 6 / 33 Analog-to-Digital Conversion Sampling Maps continuous-time/space signal into discrete-time/space signal Quantization Maps continuous-amplitude signal into discrete-amplitude signal Simplest case: Rounding

9 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 7 / 33 Source Data Sampling and Quantization Impact of Sampling (Spatial Resolution) samples samples samples samples

10 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 8 / 33 Source Data Sampling and Quantization Impact of Quantization (Bit Depth) 8 bits per component 4 bits per component 3 bits per component 2 bits per component

11 Source Data Sampling and Quantization H. Schwarz (FU Berlin) Image and Video Coding: Introduction 9 / 33 Raw Images and Videos Single-Component Image Matrix of integer samples x s[x, y] Characterized by Number of samples in horizontal and vertical direction W H Sample bit depth B y Color Images Three color components (typically RGB or YCbCr) Additionally characterized by color sampling format Videos Sequence of images Additionally characterized by frame rate

12 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 10 / 33 Source Data Sampling and Quantization Color Sampling Formats RGB YCbCr 4:4:4 YCbCr 4:2:2 YCbCr 4:2:0 most common format

13 Source Data Sampling and Quantization H. Schwarz (FU Berlin) Image and Video Coding: Introduction 11 / 33 Raw Data Rate Raw Data Rate Bit rate R of raw data format R = (samples per time unit) (bit depth per sample) (1) Example: Full High Definition (HD) Video luma samples, 50 frames per second (Europe) 4:2:0 chroma format (chroma components with 1/4 luma resolution) 8 bits per sample raw data rate = 50 Hz (1 + 2/4) 8 bits 1.24 Gbit/s Example: Ultra High Defintion (UHD) Video luma samples, 60 frames per second (USA, Japan) 4:2:0 chroma format, 10 bits per sample raw data rate = 60 Hz (1 + 2/4) 10 bits 7.5 Gbit/s

14 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 12 / 33 The Source Coding Problem Typical Video Communication Scenario capture raw input video samples preprocessing encoded bitstream video encoder transmission channel (can be replaced by storage) bitstream channel no transmission errors demodulator channel decoder modulator channel encoder video decoder received bitstream postprocessing raw output video samples display and perception

15 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 12 / 33 The Source Coding Problem Typical Video Communication Scenario capture raw input video samples preprocessing encoded bitstream video encoder transmission channel (can be replaced by storage) bitstream channel no transmission errors demodulator channel decoder modulator channel encoder video decoder received bitstream postprocessing raw output video samples display and perception

16 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 12 / 33 The Source Coding Problem Typical Video Communication Scenario capture raw input video samples preprocessing encoded bitstream video encoder transmission channel (can be replaced by storage) bitstream channel no transmission errors demodulator channel decoder modulator channel encoder video decoder received bitstream postprocessing raw output video samples display and perception

17 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 13 / 33 The Source Coding Problem Application Examples HD movie on Blu-ray Disc UHD broadcast over DVS-S2 raw video format luma samples luma samples 4:2:0 chroma format 4:2:0 chroma format 8 bits per sample 10 bits per sample 24 frames per second 60 frames per second raw data rate ca. 600 Mbit/s ca. 7.5 Gbit/s channel bit rate 36 Mbit/s (read speed) 58 Mbit/s (8PSK 2/3) video bit rate ca. 20 Mbit/s ca. 25 Mbit/s required compression ca. 30:1 ca. 300:1

18 The Source Coding Problem H. Schwarz (FU Berlin) Image and Video Coding: Introduction 14 / 33 The Basic Communication / Source Coding Problem Basic Source Coding Problem Two equivalent formulations: and Representing source data with highest fidelity possible within an available bit rate Representing source data using lowest bit rate possible while maintaining a specified reproduction quality Source Codec Source codec: System of encoder and decoder encoder bitstream decoder

19 The Source Coding Problem H. Schwarz (FU Berlin) Image and Video Coding: Introduction 15 / 33 Practical Communication / Source Coding Problem Characteristics of Source Codecs / Overall Communication Bit rate: Throughput of the communication channel Quality: Fidelity of the reconstructed signal Delay: Start-up latency, end-to-end delay Complexity: Computation, memory, memory access Practical Source Coding Problem Given a maximum allowed complexity and a maximum delay, achieve an optimal trade-off between bit rate and reconstruction quality for the transmission problem in the targeted application In this course: Will concentrate on source codec Ignore aspects of transmission channel (e.g., transmission errors)

20 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

21 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

22 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

23 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

24 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

25 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

26 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

27 Coding Efficiency Image Compression Example Original Lossless Lossy Compressed: Compressed: Image ( JPEG GZIP PNG image (Quality points, 95)945 KB) ) 50) 25) 1) % % 100 % H. Schwarz (FU Berlin) Image and Video Coding: Introduction 16 / 33

28 Coding Efficiency H. Schwarz (FU Berlin) Image and Video Coding: Introduction 17 / 33 Trade-Off between Quality and Compression Ratio Coding Efficiency Ability to trade-off bit rate and reconstruction quality Want best reconstruction quality for a given bitrate (or vice versa) quality better codec B codec A bit rate

29 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 18 / 33 Coding Efficiency Coding Efficiency Example 1:100 Compression: JPEG H.265 HEVC

30 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 18 / 33 Coding Efficiency Coding Efficiency Example 1:100 Compression: JPEG H.265 HEVC

31 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 19 / 33 Coding Efficiency Measuring Coding Efficiency Average Bit Rate R = number of bits in bitstream for a video sequence nominal duration of the video sequence (2) Quality / Distortion Typically: Mean square error (MSE) and peak-signal-to-noise ratio (PSNR) For a W H array s[x, y] of original samples, the array s [x, y] of reconstructed samples, and a sample bit depth B MSE = 1 W H (x,y) ( s[x, y] s [x, y] ) 2 ( (2 B 1) 2 ) PSNR = 10 log 10 MSE For videos: Average PSNR over entire video sequence (3) (4)

32 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 20 / 33 Basic Design of Image and Video Codecs Image Compression Example: JPEG Partition color components into 8 8 blocks Transform coding of 8 8 blocks of samples block of samples 2D transform scalar quantization entropy coding sequence of bits reconstructed block 2D inverse transform decoder mapping entropy decoding

33 Basic Design of Image and Video Codecs JPEG: Transform of Sample Blocks Linear Transform: Matrix multiplication of the form c = A s Orthogonal Transform: Rotation and reflection in signal space Separable Transform: Reduced complexity In practice: Discrete Cosine Transform (DCT) or approximation thereof horizontal DCT vertical DCT original block after 2d DCT Effect of transform Compaction of signal energy Quantization is more efficient in transform domain H. Schwarz (FU Berlin) Image and Video Coding: Introduction 21 / 33

34 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 22 / 33 Basic Design of Image and Video Codecs JPEG: Quantization s' -4 s' -3 s' -2 s' -1 s' 0 s' 1 s' 2 s' 3 s' 4 u -3 u -2 u -1 u 0 u 1 u 2 u 3 u 4 z 3 z 2 z 1 z 0 z 0 z 1 z 2 z 3-4 Δ -3 Δ -2 Δ -Δ 0 Δ 2 Δ 3 Δ 4 Δ s Uniform reconstruction quantizers Equally spaced reconstruction levels (indicated by step size ) Simple decoder mapping t = q Encoder has freedom to adapt decision thresholds to source Simplest encoder: Rounding q = round(t/ ) Quantization step size determines tradeoff between quality and bit rate

35 Basic Design of Image and Video Codecs H. Schwarz (FU Berlin) Image and Video Coding: Introduction 23 / 33 JPEG: Entropy Coding Scanning: Traverse quantization indexes from low to high frequency positions probabilities P(q k 0) zig-zag scan (JPEG) Map list of numbers into bitstream Simplest approach: Codeword table Optimization problem: Minimize average codeword length l = k p k l k number codeword

36 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 24 / 33 Basic Design of Image and Video Codecs Similarities between Successive Pictures in a Video Sequence t

37 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 25 / 33 Basic Design of Image and Video Codecs Video Codecs: Motion-Compensated Prediction already coded reference picture FRESH FOOD moving object best-matching block in reference picture current picture displacement vector for current block FRESH FOOD FRESH FOOD m = m x m y current block x displaced object y Predict current block using a displaced block in an already coded picture ŝ[x, y] = s ref[x + m x, y + m y ] Displacement is characterized by displacement vector or motion vector m = ( m x, m y ) T Estimate suitable motion vector in encoder = Motion estimation Transmit motion vector to decoder as part of the bitstream

38 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 26 / 33 Basic Design of Image and Video Codecs Example for Motion-Compensated Prediction

39 Basic Design of Image and Video Codecs H. Schwarz (FU Berlin) Image and Video Coding: Introduction 27 / 33 Hybrid Video Encoder s k [x, y] u k [x, y] encoder control transform & quantization transform coefficient levels and quantization parameters entropy coding bitstream input video pictures (in coding order and partitioned into blocks) s k[x, y] scaling & inv. transform u k [x, y] coding modes, intra pred. modes, motion data s k [x, y] coding mode decision f( s k x, y ) s r [x +m x, y +m y ] intra mode decision intra-picture prediction motion-comp. prediction in-loop filtering s k [x, y] s k [x, y] buffer for current picture motion estimation decoded picture buffer reconstructed video (for monitoring)

40 H. Schwarz (FU Berlin) Image and Video Coding: Introduction 28 / 33 Basic Design of Image and Video Codecs Hybrid Video Decoder bitstream entropy decoding transform coefficient levels and quantization parameters scaling & inv. transform s k[x, y] u k [x, y] intra prediction modes coding modes intra-picture prediction f( s k x, y ) s r [x +m x, y +m y ] in-loop filtering s k [x, y] s k [x, y] s k [x, y] buffer for current picture motion data motion-comp. prediction decoded picture buffer decoded video

41 Outline H. Schwarz (FU Berlin) Image and Video Coding: Introduction 29 / 33 Outline of Course Image and Video Coding I: Fundamentals Lossless Coding Rate-Distortion Theory Quantization Predictive Coding Transform Coding Image and Video Coding II: Algorithms and Applications Acquisition, Representation, Display, and Perception of Images Video Coding Overview Video Encoder Control Intra-Picture Coding Inter-Picture Coding Video Coding Standards

42 Exercises H. Schwarz (FU Berlin) Image and Video Coding: Introduction 30 / 33 Exercise 1: Typical Compression Factors for Media Files Determine typical compression factors for media files you use every day. Choose one or more examples for the following categories: Images: Pictures (JPEG) taken with your smartphone Audio: Songs (MP3 or AAC) you listen Video: Videos (AVC or...) you captured or downloaded Determine the compression factors by Measuring the file size Calculating the raw data rate, based on for images: image size, color format, and bits per sample for audio: duration, sampling rate, and bit depth for video: duration, frame rate, picture size, color format, bits per sample

43 Exercises Exercise 2: Compare Lossy and Lossless Image Compression 1 Choose one or more of the raw image files (PPM format) provided at the course web site: 2 Try to compress the file(s) with a general lossless compression tool (such as zip, rar,...) and measure the compression factor 3 Convert the file(s) into the PNG format (lossles image compression format) and measure the compression factor 4 Convert the file(s) into the JPEG format (lossy image compression format) and measure the compression factor 5 Can you see a difference between lossy and lossless compression? The conversion into PNG and JPEG can be done with any suitable software. One example is ImageMagick (available for Window, Linux, MacOS): Available at Conversion from PPM to PNG: convert test.ppm test.png Conversion from PPM to JPEG: convert test.ppm test.jpg H. Schwarz (FU Berlin) Image and Video Coding: Introduction 31 / 33

44 Exercises H. Schwarz (FU Berlin) Image and Video Coding: Introduction 32 / 33 Exercise 3: Analysis of JPEG Compression Choose one or more of the raw image files (PPM format) provided at the course web site: Compress the image using JPEG with varying quality parameter (Q = ) # with image magick, you can use the following command line convert -quality (Q) test.ppm test.jpg What effect has the quality parameter on compression factor / file size reconstruction quality Up to which compression factor you cannot distinguish the compressed and the original image does the compressed image looks acceptable What kind of compression artefacts do you observe in highly compressed JPEG images?

45 Exercises H. Schwarz (FU Berlin) Image and Video Coding: Introduction 33 / 33 Exercise 4: Lossless Compression of Media Files Choose one or more files for the following categories: Compressed picture (JPEG) Compressed audio file (MP3 or AAC) Compressed video file (AVC or...) Try to further compress the media files using universal lossless compression tools, such as zip, rar, etc. Which additional compression factors can you achieve? What can you conclude?

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