Chapter 9, DIGITAL VIDEO COMPRESSION TECHNIQUES Video Solutions, Multimedia Signals and Systems

Problem 1

A multimedia presentation contains the following types of data:
i) 10000 characters of text ( 8 bit, high ASCII)
ii) 200 color images $(400 \times 300,24$ bits)
iii) 15 minutes of audio ( $44.1 \mathrm{KHz}, 16 \mathrm{bits} /$ channel, 2 channels)
Calculate the disk space required to store the multimedia presentation. How much space percentage does each data type occupy?

Aaron Goree

Numerade Educator

Problem 2

What is the principle behind color subsampling? Consider the video data in the above problem. Assume that the video is stored in i) $4: 2: 2$, or ii) $4: 2: 0$ format. How much space would be required in cach case to store the video?

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02:13

Problem 3

What is motion compensation in video coding? Why is it so effective?

Jennifer Stoner

Numerade Educator

03:14

Problem 4

Compare and contrast various motion estimation techniques.

Darshan Maheshwari

Numerade Educator

07:07

Problem 5

While performing motion estimation for the football sequence using a full search algorithm, the displaced block difference energy of a $16 \times 16$ block was found to be as given in the following table. The energy shown is normalized for better clarity. The search range is $(-7,7)$ in both horizontal and vertical direction. Calculate the motion vector and the motion predicted error energy if we use i) three-step, ii) 2-D logarithmic, and iii) conjugate direction search. Are these fast-search techniques able to find the global minimum?
$$
\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline 86 & 91 & 94 & 95 & 94 & 89 & 83 & 76 & 69 & 65 & 64 & 68 & 73 & 76 & 75 \\
\hline 75 & 80 & 86 & 90 & 93 & 91 & 84 & 74 & 63 & 52 & 46 & 45 & 50 & 58 & 65 \\
\hline 62 & 65 & 71 & 78 & 82 & 83 & 80 & 71 & 60 & 48 & 36 & 28 & 28 & 35 & 47 \\
\hline 54 & 53 & 56 & 61 & 68 & 73 & 75 & 73 & 64 & 51 & 36 & 21 & 13 & 15 & 28 \\
\hline 57 & 53 & 51 & 54 & 59 & 65 & 70 & 70 & 66 & 56 & 43 & 27 & 13 & 9 & 18 \\
\hline 65 & 60 & 54 & 53 & 57 & 61 & 64 & 66 & 65 & 60 & 53 & 43 & 30 & 21 & 21 \\
\hline 72 & 71 & 64 & 60 & 59 & 60 & 61 & 63 & 63 & 62 & 60 & 58 & 50 & 39 & 32 \\
\hline 75 & 76 & 73 & 68 & 64 & 61 & 61 & 63 & 64 & 64 & 64 & 64 & 60 & 52 & 43 \\
\hline 75 & 79 & 81 & 79 & 74 & 68 & 64 & 63 & 64 & 64 & 65 & 66 & 65 & 61 & 53 \\
\hline 75 & 79 & 82 & 82 & 78 & 72 & 66 & 63 & 62 & 63 & 65 & 67 & 67 & 67 & 63 \\
\hline 74 & 77 & 78 & 77 & 76 & 70 & 63 & 60 & 60 & 63 & 65 & 68 & 69 & 68 & 64 \\
\hline 74 & 77 & 78 & 77 & 76 & 70 & 63 & 60 & 60 & 63 & 65 & 68 & 68 & 67 & 64 \\
\hline 73 & 74 & 72 & 72 & 71 & 67 & 61 & 60 & 62 & 65 & 66 & 68 & 68 & 67 & 64 \\
\hline 73 & 71 & 69 & 67 & 67 & 64 & 60 & 60 & 63 & 66 & 67 & 69 & 71 & 70 & 68 \\
\hline 73 & 70 & 65 & 61 & 59 & 59 & 58 & 58 & 62 & 66 & 68 & 71 & 73 & 72 & 70 \\
\hline
\end{array}
$$

Nicholas Majtenyi

Numerade Educator

01:36

Problem 6

Repeat the above problem for the following table. Do the fast search algorithms find the global minima? If we had use the search range $(-15,15)$ instead of $(-7,7)$, what would be the performance for the three fast search techniques?
$$
\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline 24 & 30 & 36 & 42 & 47 & 51 & 55 & 57 & 58 & 59 & 61 & 62 & 63 & 62 & 61 \\
\hline 25 & 32 & 39 & 46 & 51 & 55 & 59 & 61 & 62 & 64 & 66 & 68 & 68 & 66 & 65 \\
\hline 28 & 34 & 41 & 48 & 53 & 59 & 64 & 66 & 67 & 69 & 72 & 73 & 73 & 71 & 69 \\
\hline 30 & 37 & 43 & 50 & 53 & 58 & 66 & 70 & 70 & 73 & 77 & 78 & 78 & 76 & 74 \\
\hline 31 & 38 & 46 & 53 & 53 & 55 & 64 & 71 & 72 & 76 & 81 & 84 & 83 & 81 & 80 \\
\hline 31 & 38 & 47 & 55 & 56 & 54 & 57 & 64 & 71 & 78 & 83 & 86 & 86 & 84 & 84 \\
\hline 32 & 38 & 46 & 55 & 59 & 57 & 52 & 51 & 62 & 78 & 85 & 86 & 88 & 88 & 88 \\
\hline 34 & 39 & 45 & 54 & 59 & 60 & 53 & 41 & 47 & 70 & 83 & 86 & 88 & 90 & 90 \\
\hline 36 & 41 & 47 & 53 & 58 & 61 & 57 & 45 & 44 & 59 & 76 & 85 & 89 & 91 & 92 \\
\hline 37 & 43 & 49 & 54 & 57 & 60 & 59 & 55 & 54 & 59 & 70 & 83 & 91 & 94 & 95 \\
\hline 39 & 43 & 52 & 56 & 57 & 57 & 59 & 64 & 67 & 68 & 72 & 82 & 92 & 98 & 99 \\
\hline 43 & 44 & 50 & 57 & 56 & 52 & 54 & 64 & 73 & 77 & 77 & 80 & 89 & 96 & 99 \\
\hline 48 & 47 & 47 & 55 & 57 & 50 & 48 & 60 & 72 & 80 & 80 & 79 & 85 & 94 & 97 \\
\hline 51 & 52 & 49 & 51 & 54 & 51 & 48 & 53 & 64 & 77 & 81 & 79 & 82 & 88 & 90 \\
\hline 50 & 53 & 54 & 50 & 46 & 49 & 50 & 49 & 53 & 66 & 75 & 76 & 78 & 77 & 78 \\
\hline
\end{array}
$$

Clarissa Noh

Numerade Educator

Problem 7

Is DCT coding of motion compensated error frame as effective as DCT coding of natural images? Explain.

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Problem 8

Explain the usefulness of the B-frames in MPEG-1 video coding standard.

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Problem 9

The I-frames in the MPEG standard help to provide fast forwarding and random access while watching a digital movie. What GOP length would you choose if the movie is required to display at least one frame every $0.5 \mathrm{sec}$ while fast forwarding? Assume a progressive frame rate of 30 frames/sec. What are some of the possible GOP structures (i.e., number of $\mathrm{P}$ - and $\mathrm{B}$-frames) with this GOP length?

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Problem 10

An MPEG video uses the GOP structure: IBBBPBBB. Determine the order of encoding for the first 20 frames.

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Problem 11

You are designing a digital video database and looking for a good video compression algorithm. One of the main requirements is that you should be able to retrieve a video based on its content. Which video compression standard algorithm will you select? Explain the main principles of this standard algorithm.

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Problem 12

Encode the first 20 frames of the Claire sequence using the image coder in Example 8.7. Plot the bit-rate versus PSNR of each frame.

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Problem 13

Implement a simple inter-frame coder assuming a GOP of 20 frames. Encode the first frame using the image coder in Example 8.7, and the remaining 19 frames as $P$ frames. Use the FSA with search window $(-7,7)$ for the motion estimation. Calculate the DCT of the motion predicted error frame, and quantize the DCT coefficients with different step-sizes. Calculate the entropy of the motion vectors and the quantized DCT coefficients for each frame, and use the entropy as the bit-rate for the frame. Plot the bit-rate versus PSNR of each frame.

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01:56

Problem 14

Compare the performance obtained in the previous two problems, and discuss the advantages of the motion compensation.

Mariana Roldan

Numerade Educator