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RESEARCH POSTER PRESENTATION DESIGN © 2012 www.PosterPresentations.com QUICK DESIGN GUIDE (--THIS SECTION DOES NOT PRINT--) This PowerPoint 2007 template produces a 42”x60” professional poster. It will save you valuable time placing titles, subtitles, text, and graphics. Use it to create your presentation. Then send it to PosterPresentations.com for premium quality, same day affordable printing. We provide a series of online tutorials that will guide you through the poster design process and answer your poster production questions. View our online tutorials at: http://bit.ly/Poster_creation_help (copy and paste the link into your web browser). For assistance and to order your printed poster call PosterPresentations.com at 1.866.649.3004 Object Placeholders Use the placeholders provided below to add new elements to your poster: Drag a placeholder onto the poster area, size it, and click it to edit. Section Header placeholder Use section headers to separate topics or concepts within your presentation. Text placeholder Move this preformatted text placeholder to the poster to add a new body of text. Picture placeholder Move this graphic placeholder onto your poster, size it first, and then click it to add a picture to the poster. QUICK TIPS (--THIS SECTION DOES NOT PRINT--) This PowerPoint template requires basic PowerPoint (version 2007 or newer) skills. Below is a list of commonly asked questions specific to this template. If you are using an older version of PowerPoint some template features may not work properly. Using the template Verifying the quality of your graphics Go to the VIEW menu and click on ZOOM to set your preferred magnification. This template is at 50% the size of the final poster. All text and graphics will be printed at 200% their size. To see what your poster will look like when printed, set the zoom to 200% and evaluate the quality of all your graphics before you submit your poster for printing. Using the placeholders To add text to this template click inside a placeholder and type in or paste your text. To move a placeholder, click on it once (to select it), place your cursor on its frame and your cursor will change to this symbol: Then, click once and drag it to its new location where you can resize it as needed. Additional placeholders can be found on the left side of this template. Modifying the layout This template has four different column layouts. Right-click your mouse on the background and click on “Layout” to see the layout options. The columns in the provided layouts are fixed and cannot be moved but advanced users can modify any layout by going to VIEW and then SLIDE MASTER. Importing text and graphics from external sources TEXT: Paste or type your text into a pre-existing placeholder or drag in a new placeholder from the left side of the template. Move it anywhere as needed. PHOTOS: Drag in a picture placeholder, size it first, click in it and insert a photo from the menu. TABLES: You can copy and paste a table from an external document onto this poster template. To make the text fit better in the cells of an imported table, right-click on the table, click FORMAT SHAPE then click on TEXT BOX and change the INTERNAL MARGIN values to 0.25 Modifying the color scheme To change the color scheme of this template go to the “Design” menu and click on “Colors”. You can choose from the provide color combinations or you can create your own. © 2012 PosterPresentations.com 2117 Fourth Street, Unit C Berkeley CA 94710 posterpresenter@gmail.com Student discounts are available on our Facebook page. Go to PosterPresentations.com and click on the FB icon. Field Experiment 1: Taking pictures at different times of one object from the same angle with fixed focus, aperture, etc. How does the time of day affect file size for JPEG compression? Field Experiment 2: Fix the time of day but take pictures in various locations, again with focus, aperture, etc. fixed. How do these conditions affect JPEG file sizes? Original Image Discrete cosine transformation of the upper-left 8x8 block. Same processes are applied to other 8x8 blocks. The graph shows a decreasing exponential trend in compression ratio as the number of coefficients increases. Compression ratio approaches 1, since including all singular values creates the original image. Lowest file size – 1 MB. Little variation.Largest file size – 4.4 MB. Varied light and lots of detail. Applying the principles of linear algebra to examine the mathematical algorithm in analyzing SVD and JPEG compression. Using hands on experience on Mathematica software to reinforce the mathematical algorithm of SVD and JPEG image compression. Conducting field experiments using digital camera to study the relationship of image size, time and compression ratio. This project focused on three parts: first, a hands-on mathematical analysis of singular value decomposition (SVD) compression; second, two field experiments that explore the effect of light conditions, shot composition and content, as well as the time of day and other variables on the file sizes of images generated in a digital camera that implements JPEG compression; and third, an in-depth study of the JPEG algorithm. In the SVD compression experiment, the team concluded based on Mathematica’s timing data that there was no trend in compression time versus the number of SVD coefficients taken. The team speculated that this could be due to the fact that Mathematica calculates every singular value and then selects the required values, as well as due to random fluctuations in computer activity. The team also found that the fewer singular values that were used, the smaller the resulting file size was. Moreover, incrementing the number of coefficients caused a greater increase in file size when the number of coefficients was small versus when it was large. As the number of coefficients increased, the compression ratio approached 1. The JPEG field experiments showed that JPEG is much better at compressing scenes that have little variation in light and tone. The image that was best compressed was an image of a uniformly blue sky, whereas JPEG had great difficulty compressing an image with dappled shadows and lots of colors. The experiment also showed that exposing an image with too much light, leading to a ‘washed out’ quality, can lead to smaller file sizes since some detail is eliminated. The theoretical JPEG hands on experiment showed the problems with basic JPEG (not updated JPEG 2000) compression: lots of noise around the borders of the 8 x 8 blocks that the algorithm splits the image into, and obvious compression artifacts around edges, particularly in images of text or line drawings. For future work we might consider studying other compression programs and their algorithm used by NASA such as wavelet-based image compression like JPEG2000 and ICER. SVD is based on a theorem from linear algebra that says that a rectangular matrix A can be decomposed into the product of three matrices. In symbols: Where: A m,n is a given matrix that represents an image U m,m is an orthogonal matrix wherein the columns of matrix U are the orthonormal eigenvectors of AA T V n,n T is the transpose of an orthogonal matrix V wherein the columns of matrix V are the orthonormal eigenvectors of A T A. D m,n is a diagonal matrix wherein the diagonal elements are singular value, σ i, equal to the square root of the eigenvalue associated with the eigenvectors u i and v i in descending order. σ 1 ≥ σ 2 ≥.… ≥ σ n ≥ 0 The five mathematicians who contributed to and were responsible for establishing the theory and existence of Singular Value Decomposition (SVD) are: Eugenio Beltrami (1835—1899); Camille Jordan (1838—1921; James Joseph Sylvester (1814—1897); Erhard Schmidt (1876—1959); Hermann Weyl (1885— 1955). Beltrame, Jordan, and Sylvester focused on linear algebra (matrices) while Schmidt and Weyl focused on integral calculus equations. Mathematics Behind Image Compression Sponsors: National Aeronautics and Space Administration (NASA) NASA Goddard Space Flight Center (GSFC) NASA Goddard Institute for Space Studies (GISS) CUNY Hostos CC & City College USDE NSF Contributors: Mr. Ildefonso Salva (High School Teacher) Stefany Franco (Undergraduate) Charlie Windolf (High School Student) Prof. Tanvir Prince (Faculty Mentor) Special Thanks to Prof. Angulo Nieves 10 SVD Coefficients gives a 63 KB file size. 100 SVD Coefficients gives a 115 KB file size. Two SVD-compressed images of Hyperion, a moon of Saturn. Image compression is fundamental to NASA and the world’s daily operations. Images are transmitted to NASA from satellites and even Mars, making it very important to send data as efficiently as possible through the low-bandwidth links to these locations. This project focuses its studies in three areas: first, a hands-on mathematical analysis of the singular value decomposition (SVD) compression; second, two field experiments that explore the effect of light conditions, shot composition and content, as well as the time of day and other variables on the file sizes of images generated in a digital camera that implements JPEG compression; and third, an in-depth study of the JPEG algorithm. In the SVD study, the team analyzed mathematically how matrices are manipulated to compress an image. The theory about SVD is reinforced by using the software Wolfram Mathematica to compress images from NASA satellites and Mars rovers. Mathematica analyzed the file size and timing data for the compression process. In the field experiment, a camera with fixed focus, aperture, and other shooting parameters was used to take pictures at various times of day of the same scene to see how the amount and quality of daylight influenced JPEG’s ability to compress images. The same camera with the parameters still fixed was used to shoot various locations, indoors and outdoors, at the same time of day to see how the content of the photo influenced JPEG file sizes. Finally, the team looked at JPEG’s compression algorithm in Wolfram Mathematica to better understand its efficiency and power, since NASA’s radiation-hardened computer processors are generally not powerful enough to compress images with JPEG. Loosely, the team found that JPEG is best able to compress images with little variation pixel to pixel in color or brightness, and that it provides better looking images at the same file size than SVD compression. Singular Value Decomposition (SVD) is a matrix operation that takes a given matrix and represents it as a series of coefficients (singular values) which are multiplied by the other matrices that make up the SVD basis. The singular values are arranged in decreasing order, so each contains more information about the original matrix than the next. SVD is not often used for image compression due to its lack of efficiency, but it can be. In SVD compression, the image is converted to a matrix with the same dimensions as the image. Each value in the matrix ranges from 0 to 255, where 0 is black and 255 is white. This image undergoes singular value decomposition. In order to compress the image, only the first few singular values are used. The more singular values that are used, the better the resulting image approximates the original image. Singular value decomposition can compress images to very small file sizes, but with very few singular values the resulting image looks nothing like the original image. Smarter compression algorithms like JPEG are used instead. Image/video data compression is a very critical technology for many operations in NASA. In NASA, image compression is used for three main reasons. First, compression saves space. NASA receives millions of bits of data each day that require a huge storage facility. By using compression, NASA saves an enormous amount of hard drive space. Second, image/video compression saves transmission time. For example, the NASA Mars Rovers send back pictures and data which can take up to years to send if uncompressed due to the massive distance between Mars and Earth. Lastly, compression saves money by saving hard drive space and time. NASA lunar and Mars missions require many uses of video and image transmission. These can be categorized into several types: high rate video, edited high rate video, low rate video, science imaging data, and telerobotics video. Some types of the image and video data mentioned before can benefit greatly from compression because it would take up less space and therefore can be transmitted faster. Other types of image and video data, such as scientific data and telerobotics video, are very valuable and irreplaceable, so NASA is reluctant to consider any type of compression on these. The data doesn’t give any quantitative analysis, but the extremes in the data show qualitatively that pictures with less detail yield smaller JPEG file sizes. The inverse process: the above steps are run in reverse to approximate the original matrix. Matrix representation of the original image Partition the matrix into 8x8 blocks, and subtract 127 from each entry. Divide each entry by a prescribed quantity (8x8 fixed quantization matrix) and round off to the nearest integer. The computer applies Huffman coding and stores the data. The approximation of the original image. The artificial picture below is created using Mathematica and all the steps of JPEG are applied to see the process in detail. Since this is an artificial image, the JPEG compression creates a lot of noise. In an actual image, typically the noise is invisible

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RESEARCH POSTER PRESENTATION DESIGN © 2011 www.PosterPresentations.co m QUICK TIPS (--THIS SECTION DOES NOT PRINT-- ) This PowerPoint template requires.

RESEARCH POSTER PRESENTATION DESIGN © 2011 www.PosterPresentations.co m QUICK TIPS (--THIS SECTION DOES NOT PRINT-- ) This PowerPoint template requires.

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