International Journal of Data Envelopment Analysis and *Operations Research*. 2014, 1(2), 34-39
DOI: 10.12691/ijdeaor-1-2-4
Open AccessArticle
Tanvir Prince1, , William Ashong-Katai2, Ildefonso Salva3, and Karina M. Shah4
1Assistant Professor of Mathematics Department of Mathematics Hostos Community College The City University of New York USA
2Undergraduate Student Hostos Community College The City University of New York USA
3High School Teacher Department of Mathematics Mott Haven Village Preparatory High School Bronx, New York USA
4High School Student The Dalton School New York, USA
Pub. Date: September 02, 2014
Cite this paper:
Tanvir Prince, William Ashong-Katai, Ildefonso Salva and Karina M. Shah. Mathematics Behind Image Compression: An Experiment of Mean Compression of Various Sizes and Their Relative Compression Ratio of NASA Images. International Journal of Data Envelopment Analysis and *Operations Research*. 2014; 1(2):34-39. doi: 10.12691/ijdeaor-1-2-4
Abstract
A study of the fundamentals of image compression was conducted in correspondence with NASA (National Aeronautics and Space Administration). NASA uses images to reveal information, data, and evidence concerning astronomical research. For this reason each NASA image must have the best quality and adequate dimensions. The purpose of this project was to compare the compression ratios resulting from compression by three variations of pixel matrices, and to understand the difference between arithmetic mean and geometric mean compression methods. For this task, a total of 50 planetary images were selected from the NASA website. With the aid of the Mathematica software, the team created a program to compress the images. The team then recorded the findings from the experiment in the form of graphs; visual representation helped to understand the produced trends. The source code for the program is attached in the appendix. This code can be used by anyone who wish to perform and/or repeat the research for a classroom activity or a short project. .Keywords:
image compression wolfram mathematica NASA Arithmetic mean Geometric mean
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References:
[1] | P. V, “Through the History and Mystery of Data Compression,” CSI Communications. Mumbai, India: Suchit Gogwekar for Computer Society of India, 2012. |
|
[2] | Z. Rattner. (2012). Here’s how it works [online]. Available: http://xstitch.zachrattner.com/HowItWorks.html |
|
[3] | D. S. Taubman and M. W. Marcellin, JPEG2000 Image Compression Fundamentals, Standards and Practice. Norwell, MS: Kluwer Academic Publishers, 2002. |
|
[4] | Microsoft Real-Time Communications: Protocols and Technologies (2014) [online]. Available: http://technet.microsoft.com/en-us/library/bb457036.aspx |
|
[5] | A. P. Godse, “Multimedia Systems,”Computer Graphics, first ed. Pune, India: Technical Publications Pune, 2009. |
|
[6] | JPG vs. GIF vs. PNG (2014) [online]. Available: http://www.webopedia.com/DidYouKnow/Internet/JPG_GIF_PNG.asp |
|
[7] | R. Seaman, W. Pence, R. White, M. Dickinson, F Valdes, N. Zarate, “Astronomical Tiled Image Compression: How & Why,” Astronomical Data Analysis Software and Systems XVI, vol. 30, 2006. |
|
[8] | J. N. Maki, et al., “Mars Exploration Rover Engineering Cameras,” J. of Geophyical Research, vol. 108, no. E12, 8071, 2003. |
|
[9] | W. A. Whyte and K. Saywood, Data Compression for Full Motion Video Transmission. Cleveland, OH: cosponsored AIAA, NASA, and OAI, 1991. |
|
[10] | Wolfram Mathematica: The world's definitive system for modern technical computing (2014) [online]. Available: http://www.wolfram.com/mathematica/ |
|