MULTIMEDIA SYSTEMS DESIGN –CS576 INSTRUCTOR – PARAG HAVALDAR MID TERM EXAM A
Mon April 11, 2022
Time allotted: 2hr 30 mins (7:00– 9:30) Closed Book, Closed Notes Calculators Needed
Name: _________________________________ Student ID Number: __________________ Check if DEN __
Question 1 2 3 4 5 6 7 Total
Marks Maximum Marks Obtained
15 10 15 15 15 15 15 100
The questions and expectations should be clear. If any question seems ambiguous, please write down your assumptions and proceed. We will decide about the ambiguity, if any, based on all the responses and evaluate accordingly.
IMPORTANT – It is expected that all answers are accompanied by appropriate working and/or reasoning that will allow us to evaluate your answers for full/partial points. Answers with no reasoning or working will get zero.
1) Digital Data – 15 points
• A camera captures frames with 480 lines per frame, 640 pixels per line, and 50 Hz field rate. The color subsampling scheme is 4:2:2, and the original pixel aspect ratio is 1:1, ie square pixels. The camera uses interlaced scanning, and each sample of Y, Cr, Cb is quantized with 8 bits
• What is the bitrate produced by the camera? (3 points)
• We want to store the video signal on a hard disk, and, to save space, we re-quantize
each channel signals with only 6 bits per channel and use 4:2:0 instead of 4:2:2. What is
the minimum size of the hard disk required to store 5 minutes of video? (4 points)
• If the above 6 bit per channel, 4:2:0 formatted 5 min video is streamed in real time at
the rate it is generated (instead of storing it to disk) over a typical household bandwidth of 100 Mbps, how much time per second is available for the sender/receiver processes to do their processing tasks (capturing, 4:2:0 conversion, packetizing, reformatting for display at receiver, rendering etc.)? Ignore network related delays. (4 points)
• For visualizing this video, the receiver needs to reformat/resample the video for a HD video player, where each frame is 1920 pixels horizontally by 1080 pixels vertically. How does each pixel’s aspect ratio change? (4 points)
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2) Color – 10 points
• The chromaticity space is a 2D space obtained by projecting the 3D conical XYZ space onto a plane.
• What is the equation of this plane? (1 points)
• The colors in the chromaticity space are pure hues and variations thereof. Why is there
no brown color seen? (3 points)
• Answer the following about red and cyan colors.
• If you took red torch and a cyan torch and shined it on a white wall together, what color
would you see? Explain your reasoning! (3 points)
• Changing the setup if you wore a cyan colored shirt and walked into a room lit by red
light, what would others perceive the color of your shirt (3 points)
Generic Compression – 15 points
• If a source produces three symbols {X, Y, Z} with probabilities 0.2, 0.5 and 0.3 respectively, using Arithmetic encoding compute the interval bounds for the string YXYZ. Start your initial bounds as X: [0,0.2), Y: [0.2,0.7) and Z: [0.7,1.0) (5 points)
• For the bounds computed above what is the code for the string YXYZ assuming minimum number of bits. (2 points)
• Consider two independent information sources S1 and S2. S1 emits eight numbers {a, b, c, d, e, f, g, h} and does so with uniform probability. S2 on the other hand emits any integer k such that k>0 and has probability = 2−k.
Which source is observed to be more random S1 or S2 and why? (8 points)
Github
4) Image Compression – 15 points
31.0 51.7 1.2 -24.5 -12.0 -25.8 -2.5 6.1 113.5 6.9 -13.9 43.2 -6.09 35.6 3.5 5.5 195.6 10.1 -8.7 -2.9 -28.9 -7.9 6.9 5.6 35.9 -24.3 -15.6 -20.8 11.6 -19.1 8.0 6.2 40.8 -20.6 -13.7 17.1 -14.2 22.4 1.3 7.7
7.2 -13.6 -7.5 -11.9 18.3 3.9 1.3 9.2 -1.5 -13.3 -0.9 1.3 10.4 4.2 1.0 1.1 -6.8 -2.8 4.1 1.1 10.5 5.1 1.3 4.3
16 11 10 16 24 40 51 61 12 12 14 19 26 58 60 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109 103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112100103 99
The left image represents the Quantization Table values provided by the JPEG format for an 8×8 block and the right image represents an example 8×8 channel block after DCT computation.
• Explain why the Quantization table on the left is not evenly distributed with smaller numbers the upper left going towards larger numbers to the lower right (2 points)
• What does the quantized output look like for the DCT block on the right in a JPEG pipeline? (4 points)
• If the entire quantized block (including quantized DC & AC coefficients) is further processed into the intermediary representation, how many terms are generated?
(4 points)
• When using standard imaging software like photoshop, gimp or paint to save images, there is a quality slider to lower image quality (and save bytes). This is a positive integer multiplied to all values in the quantization table prior to quantizing. What should the minimum integer value be so that the intermediary terms would result down to at least 50% of the original. (5 points)
5) Video Compression – 15 points
Motion vector computation is one of the most computationally intensive operations in video compression.
• Let’s take a simple setup with 2×2 block. The right image below gives an example 2×2 block in frame n+1 which you want to predict from frame n. The left image gives example values of pixels in frame n around the corresponding co-located search area (k=2) for the for block. Compute the motion as an integral [dx, dy] value for the block. (5 points)
Given an HDTV 720p (1280×720) frame with three channels (RGB) that needs to be predicted as a P frame in a standard MPEG2 format
• How many motion vectors need to be computed for all channels together for this frame? (2 points)
• Using brute force MAD, and a search parameter = 16, approximately how much time is used up in motion vector computation for this frame. Assume that each MAD difference for a motion vector candidate position for a block takes 0.01 microseconds. (4 points)
• The 720p is a progressive video format has support for NTSC at 29.97 fps and for PAL at 25 fps. Which of these (if any or both) can be streamed in real time assuming all the time is just limited to motion vector computation? (4 points)
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31 35 34 33
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6) Digital Rights Management – 15 points
A famous painting is scanned and watermarked. This watermarked digital painting is then posted on the internet. Pirates make a copy and physically print large prints and sell them. You take steps to embed imperceptible watermarks in the uploaded images
• Are there any kinds or classes of digital images where imperceptible watermarking can be hard? Give reasons (2 points)
To help with the piracy, the original digital image (stored as JPEG) was further encrypted after compression. The compression step quantizes the DC and AC coefficients of the 8×8 DCT block. However, instead of generating 64 coefficients from a zig-zag order as is traditional, we decide to reorder the 64 coefficients according to a random permutation list
• Argue why (or why not) this might be a viable encryption method? (2 points)
• Mentioning giving reasons if this method is completely secure? (2 points)
• If you used this encryption scheme, explain how and why it will affect the size of the
compressed bitstream. (3 points)
• If you want to use this encryption scheme along with the JPEG standard (which you
cannot change), how can you use the standard to your advantage so as to mitigate this compressed bit stream size issue – Explain. (6 points)
7) Graphics – 15 points
2D meshes are described in terms of vertices (2D x y locations) and edges giving the interconnectivity between the vertices. Assume that the mesh is triangulated with each vertex coordinate is represented as a double data type and on an average, there are twice the number of faces as there are vertices.
• Making these assumptions if a mesh has 1024 vertices, how many bytes are needed to represent the mesh? Assume each double data type needs 64 bits. (5 points)
• A simple 2D mesh is represented as shown below, Find the transformation matrix where the left mesh has undergone a transformation to arrive at the right mesh.
A = (3, -4) B = (1, -4) C = (2, -2) D = (4, -2)
A = (-1, 1) B = (-3, 1) C = (-3, 3) D = (-1, 3)
Additional Space 1
Additional Space 2