CS4551 Spring 2020 HW #2 1 CS4551 Multimedia Software Systems Homework2 (15%) – Vector Quantization and DCT Coding • Due: Electronic submission via CSNS by Sunday, 04/19/2020. • What to turn in: o Submit source code with necessary files for “compile and run”. o Do NOT submit data files. o You MUST provide a readme.txt file containing all information to help with the grading process. • If your program produces any compile errors, you will receive 0 automatically no matter how close your program is to the solution. • Programming requirements: o You are not allowed to use any Java built-in image class methods, library, or tools to complete this homework. o Do not create one mega-size main class. o Do not change any given methods of MImage class nor create a new class that duplicates MImage class. Treat MImage as a part of imported library. o Test your program with all test data. o If you do not meet any of the requirements above, you will receive a significant reduction. 0. What your program should do Name your main application CS4551_[YourLastName].java (e.g. CS4551_Doe.java) and expand the given template program to perform the following tasks. Receive the input file as command line arguments. On Command Prompt java CS4551_Doe Ducky.ppm Read a 24bit input PPM image and display the following main menu to the user and receive the user’s input. Main Menu———————————– 1. Vector Quantization 2. DCT-based Coding 3. Quit Please enter the task number [1-3]: After performing a selected task, go back to display the menu again. 1. Task 1 – Vector Quantization (50 pts) Compress the 24 bits per pixel input image to 2 bits per pixel using Vector Quantization (VQ). Implement VQ encoding/decoding using the requirements below. CS4551 Spring 2020 HW #2 2 Encoding: • Input vectors are formed by 2×2 blocks of RGB pixels. Each input vector consists of RGB values of FOUR pixels, P1, P2, P3, and P4, and therefore is 12 dimensional. P1 P2 P3 P4 Diagram of a 2×2 pixel block of the input image = {1 , 1 , 1, 2 , 2 , 2, 3 , 3 , 3, 4 , 4 , 4} • Codebook and codebook vectors: The 2-bits per pixel quantization is equivalent to using 8 bits per 4 pixels. Therefore, the VQ should the vector space into 256 (=28) cells and the codebooks should have 256 entries that are centroids of the 256 cells. After the vector quantization, each vector belongs to one cell and each cell number is represented by 1 byte. In order words, after the quantization, each 2×2 block (4×3=12 bytes) is encoded by a 1-byte codebook index. So, the compression ratio is 12. • Codebook generation: Use K-means clustering algorithm to generate codebook vectors (centroids of cells). K-means Clustering Algorithm Inputs: K, number of clusters and the data set (input vectors ) K is 256 in our case. Assume that [] store the K centroids. = 0, 1, ⋯ , 255. Each [] is a 12-dimensional vector. 1. Assign randomly generated initial values for the centroids. 2. For each , For each = 0 to 255 If [] is the closest cell (cluster) to based on the Euclidean distance between and [], assign to [] cluster 3. Update the centroids. 4. Iterate 2 & 3 until the algorithm meets a stopping condition (i.e. no data points change clusters, the sum of the distance is minimized, or the maximum number of iterations is reached.) • Display the codebook. This is equivalent to displaying [], = 0, 1, ⋯ ,255. • Extra credit (10 pts) – Save the quantized image (i.e. indices of all 2×2 blocks) into a PPM file. Given × input image, the quantized image resolution is /2 × /2. The quantized image is a grayscale image because each pixel is an 8-bit index. Decoding: • Given the quantized image and the codebook, for each pixel of the quantized image, recover RGB pixel values of 4 pixels. • Save the decoded image so that you can compare the output with the input. 2. Task 2 – DCT-based Coding (50 pts) Implement a DCT-based transform coding. Notice that this is different from the standard JPEG steps. The encoder/decoder steps are shown below. CS4551 Spring 2020 HW #2 3 Encoding Steps Decoding Steps E1. Read and resize the input image Read the input ppm file containing RGB pixel values for encoding. First, if the image size is not a multiple of 8 in each dimension, make (increase) it become a multiple of 8 and pad with zeros. For example, if your input image size is 21×14, make it become 24×16 and fill the extra pixels with zeros (black pixels). D4. Remove Padding and Display the image Display the decompressed image. Remember that you padded with zeros if the input image size is not multiple of 8 in both dimensions (width and height). Restore the original input image size by removing extra padded rows and columns. E1. Resize Input Image E2. Color Conversion & Subsampling E3. Forward DCT E4. Quantization D4. Restore Original Size D3. Supersampling & Inverse Color Conversion D2. Inverse DCT D1. De-quantization Input RGB Image (PPM) Decompressed RGB Image (PPM) Compressed Image 01001… Entropy Encoding/Decoding CS4551 Spring 2020 HW #2 4 E2. Color space transformation and Subsampling Transform each pixel from RGB to YCbCr using the equation below: ( ) = ( 0.2990 0.5870 0.1140 −0.1687 −0.3313 0.5000 0.5000 −0.4187 −0.0813 ) ( ) Initially, RGB value ranges from 0 and 255. After color transformation, Y should range from 0 to 255, while Cb and Cr should range from -127.5 to 127.5. (Truncate if necessary.) Subtract 128 from Y and 0.5 from Cb and Cr so that they span the same range of values [-128,127] Subsample Cb and Cr using 4:2:0 (MPEG1) chrominance subsampling scheme. If Cb(Cr) is not divisible by 8, pad with zeros. D3. Supersampling and Inverse Color space transformation Supersample Cb and Cr so that each pixel has Cb and Cr. Add 128 to the values of the Y component and 0.5 to the values of the Cb and Cr components. If using a color image, transform from the YCbCr space to the RGB space according to the following equation: ( ) = ( 1.0000 0 1.4020 1.0000 −0.3441 −0.7141 1.0000 1.7720 0 ) ( ) Common mistake: After this step, you have to make sure that the resulting RGB values are in the range between 0 and 255. Truncate if necessary. E3. Forward DCT Perform the forward DCT for Y image using the following steps: • Divide the image into 8×8 blocks. Scan each block in the image in raster order (left to right, top to bottom) • For each 8×8 block, perform the DCT transform to get the values from the values . The elements range from −2 10 to 210 Check max and min and assign −210 or 210 for the values outside of the range so that the values range from −210 to 210. Perform the DCT for Cb and Cr images, too. D2. Inverse DCT Perform the inverse DCT to recover the values from the values and recover Y, Cb, Cr images. CS4551 Spring 2020 HW #2 5 Forward DCT Formula = 1 4 ∑ ∑ cos ( (2 + 1) 16 ) cos ( (2 + 1) 16 ) 7 =0 7 =0 = { 1/√2, = 0 1, otherwise = { 1/√2, = 0 1, otherwise is the -th row and -th column pixel of the 8×8 image block ( and range from 0 to 7); is the DCT coefficient value in the -th row and -th column ( and range from 0 to 7). Inverse DCT Formula ′ = 1 4 ∑ ∑ ′ cos ( (2 + 1) 16 ) cos ( (2 + 1) 16 ) 7 =0 7 =0 E4. Quantization Given in an 8×8 DCT block, quantize using: Quantized() = round ( ) The default intervals corresponding and are specified in Table 1 and Table 2. In this homework, we want to provide a variety of compression quality options (high compression or low compression). User shall specify one parameter ( 0 ≤ ≤ 5 ), which controls the quality of the compression by changing the quantization intervals. The actual quantization is done by Quantized() = round ( ′ ) ′ = × 2 For example, if = 0, ′ is same as ; if = 1, ′ is double of , which will divide with bigger values and result in more compression. D1. De-quantization Assume that the qu
antization tables (basis ones) and the compression quality parameter are available for decoding. Given the quantized value for DCT coefficient , multiply it by the corresponding quantization interval ′ . ′ = Quantized() × ′ Notice that the recovered ′ will be different from the original . CS4551 Spring 2020 HW #2 6 Default Quantization Tables The following table gives the default quantization intervals for each element in the 8×8 DCT block for the luminance (Y) and chrominance (Cb and Cr). Table 1. Luminance Y Quantization Table Table 2. Chrominance Cb and Cr Quantization Table 4 4 4 8 8 16 16 32 8 8 8 16 16 32 32 64 4 4 8 8 16 16 32 32 8 8 16 16 32 32 64 64 4 8 8 16 16 32 32 32 8 16 16 32 32 64 64 64 8 8 16 16 32 32 32 32 16 16 32 32 64 64 64 64 8 16 16 32 32 32 32 48 16 32 32 64 64 64 64 96 16 16 32 32 32 32 48 48 32 32 64 64 64 64 96 96 16 32 32 32 32 48 48 48 32 64 64 64 64 96 96 96 32 32 32 32 48 48 48 48 64 64 64 64 96 96 96 96 • E1/D4 – 10 pts • E2/D3 – 10 pts • E3/D2 – 20 pts • E4/D1 – 10 pts An important requirement – After each encoding step, implement the corresponding decoding step immediately and check if your output is correct or not. You will receive credits for each encoding step if only if you complete to implement the corresponding decoding step. Sample results will be posted on CSNS.
