Optimal Linear Interpolation Coding for Server-based Computing

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1 Optimal Linear Interpolation Coding for Server-based Computing Fei Li and Jason Nieh Network Computing Laboratory Columbia University April 30, 2002 ICC

2 Content 1. Server-based computing 2. Coding requirements 3. Interpolation algorithms 1. Optimal linear interpolation 2. 2DLI 2D linear interpolation 4. Experimental results 5. Conclusion April 30, 2002 ICC

3 Server-based computing April 30, 2002 ICC

4 Server-based computing Lightweight client sends user input to server April 30, 2002 ICC

5 Server-based computing Server executes application logic and encodes display updates April 30, 2002 ICC

6 Server-based computing Server sends encoded display updates back to client April 30, 2002 ICC

7 Server-based computing Server-based computing advantages: reduced administrative costs better resource utilization mechanism: screen updates are encoded at the server side and delivered to clients problem: existing screen update approaches do not support multimedia applications effectively April 30, 2002 ICC

8 Coding requirements Coding requirements for pixel-based coding approach (different from traditional image/video coding) complexity for video with window size of 352 * 240: at least 2Mpixels/sec. independent on applications same coding method on video, console, web page, screen dump, etc. April 30, 2002 ICC

9 Coding requirements Take advantages of inter-frame redundancy not much similarity existing between two adjacent frames (even less than 30% for lecture video) much less for adjacent update regions intra-frame redundancy neighboring pixel values are the same or vary at a constant rate April 30, 2002 ICC

10 Coding requirements April 30, 2002 ICC

11 Interpolation algorithms Interpolation linear decoding time how about encoding complexity? how about compression ratio (depends on intra-frame redundancy)? can it be lossy? April 30, 2002 ICC

12 Optimal linear interpolation (OLI) Formula a segment function to describe the curve: f(x) = sigma(tao_i(a_i * x + b_i)) tao_i = 0, if x_i <= x < x_i+1 tao_i = 1, else S = union(s_i, delta(s_i)) Criteria recovering more exact pixel values is preferred recursively selecting pixel values lossy and lossless April 30, 2002 ICC

13 Optimal linear interpolation (OLI) Encoding complexity intrinsic exponential computational complexity: knapsack problem Reason computing for selecting re-sampled pixels under threshold takes exponential complexity April 30, 2002 ICC

14 Lossless linear interpolation (2DLI) Formula x i = x 0 + i * delta x Procedure find independent pixels index dependent pixels: horizontally interpolated or vertically interpolated record independent pixels and index further compression using gzip Properties linear encoding time lossless greedy April 30, 2002 ICC

15 Lossless linear interpolation (2DLI) index matrix x-axis and y-axis interpolation to find dependent pixel values independent pixels April 30, 2002 ICC

16 Lossless linear interpolation (2DLI) Sample independent pixels with delta Gzip encoding index matrix Note: red: independent black: interpolated index: 2: independent 1: vertical interpolated 0: horizontal interpolated April 30, 2002 ICC

17 Experimental results Test-bed CPU: AMD 1000MHz RAM: 256MB Images categories smoothed-toned image desktop (screen-dump) web-page lecture video (to test network collaboration) Comparison on JPEG, gzip (gunzip), hexitle (VNC), 2DLI April 30, 2002 ICC

18 Experimental results (average compression ratio) smooth-toned image compression ratio JPEG Gzip Hextile 2DLI smooth-toned image April 30, 2002 ICC

19 Experimental results (average compression ratio) web page compression ratio web page 0 JPEG Gzip Hextile 2DLI April 30, 2002 ICC

20 Experimental results (average compression ratio) screen dump compression ratio screen dump 0 JPEG Gzip Hextile 2DLI April 30, 2002 ICC

21 Experimental results (average compression ratio) lecture video compression ratio lecture video 0 JPEG Gzip Hextile 2DLI April 30, 2002 ICC

22 Experimental results (en/decoding complexity Mpixels/sec) smooth-toned image coding complexity coding complexity JPEG JPEG gzip gunzip Hextile Hextile 2DLI 2DLI Series1 April 30, 2002 ICC

23 Experimental results (en/decoding complexity Mpixels/sec) web page coding complexity coding complexity web page JPEG JPEG gzip gunzip Hextile Hextile 2DLI 2DLI April 30, 2002 ICC

24 Experimental results (en/decoding complexity Mpixels/sec) screen dump coding complexity coding complexity screen dump JPEG JPEG gzip gunzip Hextile Hextile 2DLI 2DLI April 30, 2002 ICC

25 Experimental results (en/decoding complexity Mpixels/sec) lecture video coding complexity coding complexity lecture video JPEG JPEG gzip gunzip Hextile Hextile 2DLI 2DLI April 30, 2002 ICC

26 Conclusion 2DLI achieves a good combination of high compression ratio with low coding time Much better compression ratio than JPEG, gzip or VNC on web pages, screen dumps, and lecture video Compression ratio is second only to JPEG on smooth-toned images, but with much lower coding time Further research: higher compression ratio with system approaches, like process migration with X window, to reduce coding complexity at the server side April 30, 2002 ICC

Optimal Linear Interpolation Coding for Server-based Computing

Optimal Linear Interpolation Coding for Server-based Computing Optimal Linear Interpolation Coding for Server-based Computing Fei Li and Jason Nieh Department of Computer Science Columbia University New York, NY, 10027, U.S.A. {fl200, nieh}@cs.columbia.edu Abstract

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