1. 1 Ethics of Computing MONT 113G, Spring 2012 Session 11 Graphics on the Web Limits of Computer Science

2. 2 What is a Graphics file? moon.gif GIF89a¶ˇÃˇˇôˇˇfˇˇ3ˇˇÊøß5뢑Zµ´T¨Yß6;≥YØh7^ „ŸMöù;r- €êπÑ+˜`À≥t€Ω´w!PÅ|≈Bå[8∞cƒw€ée‹±/‚ƒç?Ã6≥C ߬=<∞f™ ú¡z.kyÊ^“°O”uJÿÙ^≥d%äîÕr‰êäC~Àÿvo¥©U moon.gif ?

3. 3 Storage of Graphic Images Graphics are stored as 1's and 0's on the disk. The numbers form a code that the browser interprets to display the graphic on the monitor. Computer displays are composed of many dots, known as picture elements (pixels). The numeric code in an image file specifies the color of each pixel in the image.

4. 4 Resolution The number of pixels on the screen determines the resolution of the image. More pixels per inch implies better resolution and better image quality. Older PC's had resolutions of 800 pixels x 600 pixels. Older Macs had resolutions of 640 pixels x 480 pixels. Newer PC's and Macs have much higher resolutions (e.g. 1152 x 768).

5. 5 Resolution affects Image Size The more pixels there are per inch (ppi) the smaller each pixel is. Image sizes are specified in terms of pixels. So the same image will appear smaller on a monitor with a higher resolution. Increasing resolution decreases the image size.

6. 6 Bit Depth The number of colors each pixel can assume contributes to image quality. The bit depth of an image is the number of bits used to specify color for that image. The bit depth determines how many colors can be shown. Black and white monitors have 2 colors. Only one bit is needed to specify color (bit depth = 1). A bit depth of n allows representation of 2 n colors.

7. 7 Changing Bit Depth Some images don't need a large bit depth: Bit depth 8 Bit depth 4 Bit depth 1 Smaller bit depths help to keep the file size (in kb or mb) small. This makes it faster to download the image file.

8. 8 Bit Depth and Image Quality For more complex images, higher bit depth leads to better resolution: Bit depth = 32 (16.7 million colors)

9. 9 Indexed Color With indexed color, the computer stores a table of colors (256 colors for bit depth of 8). Each pixel is given a value between 0 and 255, which corresponds to one of the colors in the table.

10. 10 RGB (Red, Green, Blue) Color In the RGB color system, each pixel is given a specified amount of red, green and blue (between 0 and 255). The color value is written in Hexadecimal, using 2 digits for each color: #FF0000Red #00FF00Green #0000FFBlue #FFFFFF? #000000? #880066Purple

11. 11 Image File Compression Images on the web are stored as separate files that must be downloaded from the server to the client to be viewed. If the image file size is large, it will take a long time to download. Therefore, it is important to try to keep the file size as small as possible without losing much image quality. Ways to reduce file size: 1. Reduce the size of the image (in pixels) 2. Reduce the resolution of the image. 3. Reduce the bit depth of the image 4. Use image file compression (GIF or JPEG)

12. 12 GIF files The Graphics Interchange Format (GIF) is excellent for compressing images with large areas of uniform color. It is "lossless", meaning that the original image can be regenerated with no loss of information. GIF supports transparency in images. GIF supports animations (animated GIF's) This format is limited to 256 colors.

13. 13 JPEG compression The JPEG (Joint Photographic Experts Group) compression method works well for complex images, such as photographs. JPEG supports millions of colors (up to a bit depth of 24). JPEG is "lossy", meaning that the original image cannot be regenerated exactly from the original. Some information is lost in the conversion to JPEG.

14. 14 Church-Markov-Turing Hypothesis The Church-Markov-Turing Thesis: Any non-trivial computer language is apparently capable of computing no more and no fewer functions than all other non- trivial programming languages. So, all languages are equally powerful. Python is at least as powerful as any other programming language. Therefore we might think that we can solve any problem with a Python program. In practice we cannot, because...

15. 15 Limitations of Computer Science In practice, we cannot solve every problem with a program because... 1)The execution time of a program may be too long. 2)The problem may be non-computable. 3)We may not know how to solve the problem. E.g. Computer Vision Artificial Intelligence Modeling complex systems such as weather etc.

16. 16 Execution Time The execution time of a program can be a limitation in what we can compute. Examples: Taxes: How long would it take to sort taxpayers by Social Security number? Electricity: What is the most efficient routing of power lines through a region or neighborhood? Tractable problems can be solved in a reasonable amount of time. Intractable problems require huge amounts of time to solve.

17. 17 A Tractable Problem Suppose we have a list of patients and an associated list of patient weights. We want to write a program that prints out the names of patients with weight above a given value. The names are stored in a list of strings. The weights are stored in a parallel list of real numbers. AmyTedAnnTom name 1 2 3 4 5... n 115145132224 weight 1 2 3 4 5... n...

18. 18 The solution and its running time The program examines each patient in turn. The running time is proportional to the number of patients in the list (n). n (# patients)time (seconds) 25001.275 50002.550 75003.825 100005.100 time n 5.1 10000 Python solution: for i in range(n): if weight[i] > targetWeight: print name[i]

19. 19 Linear Running time The graph of the running time of the previous problem is a line. t = 5.1 x 10 -4 n We say the the running time is linear. Problems that have linear running times can be solved in a reasonable amount of time. These problems are tractable.

20. 20 Another example Suppose we want to sort the patients by their weight. I.e. we would like to rearrange the list so that the weights go from lowest to highest. Many sorting algorithms run as a function of n 2. For example: t = 3.2 x 10 -3 n 2 Others run as a function of n log 2 n. For example: t = 2.1 x 10 -3 n log 2 n Logarithms: If 2 x = n, then log 2 n = x 2 3 = 8, log 2 8 = 3

21. 21 Graphing the running time for a sorting function # people (n)t (seconds) 250059.261 5000129.021 7500202.745 10000279.042 time n n n2n2 n log n Sorting a list takes more time than searching a list, but it still can be done in a reasonable amount of time.

22. 22 Polynomial and Polylogarithmic running times In general, tractable problems are problems that have running times that are a polynomial function of n (the size of the input) or a polylogarithmic function of n. Examples: t = 4n 3 + 5n 2 -3 t = n 2 (log 2 (n)) 3 t = 17 n 6 - log 2 n + 6n