# LECTURE I: GRAPHICS & IMAGE DATA REPRESENTATION DR. OUIEM BCHIR

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1 1 LECTURE I: GRAPHICS & IMAGE DATA REPRESENTATION DR. OUIEM BCHIR

2 2 DIGITAL IMAGE REPRESENTATION An image is a spatial representation of an object, a2d or 3D scene, etc. Abstractly, an image is a continuous function defining a rectangular region of a plane An image can be thought of as a function with resulting values of the light intensity at each point over a planar region.

3 DIGITAL IMAGE REPRESENTATION 3 For computer representation, the function (e.g. intensity) must be sampled at discrete intervals. Sampling quantizes the intensity values into discrete intervals. Points at which an image is sampled are called picture elements or pixels. Resolution: specifies the distance between points - accuracy

4 DIGITAL IMAGE REPRESENTATION 4 A digital image is represented by a matrix of numeric values each representing a quantized intensity value. I(r,c) - intensity value at position corresponding to row r and column c of the matrix. Intensity value can be represented by 1-bit: black & white images 8-bits: grayscale images 24-bits: color images (RGB)

5 5 1-BIT IMAGES Each image is stored as a single bit (0 or 1), so also referred to as binary image. Such an image is also called a 1- bit monochrome image since it contains no color. Monochrome 1-bit Lena image

6 8-BIT GRAY-LEVEL IMAGES 6 Each pixel has a gray- value between 0 and 255. Each pixel is represented by a single byte: e.g. dark pixels might have a value of 10, and a bright one might be 230. Bitmap: The two- dimensional array of pixel values that represent the graphics/image data. Image resolution: The number of pixels in a digital image (higher resolution better quality).

7 7 8-BIT GRAY-LEVEL IMAGE Each image is usually stored as a byte (value between 0&255) A 640x480 grayscale image requires a 300 KB of storage (640 x 480 = 307,200 bytes) When an image is printed, the basic strategy of dithering is used, which trades intensity resolution for spatial resolution to provide ability to print multi-level images on 2-level (1-bit) printers.

8 8 DITHERING Dithering is used to calculate patterns of dots such that values from 0 to 255 correspond to patterns that are more and more filled at darker pixel values, for printing on a 1-bit printer. Main strategy: replace a pixel value by a larger pattern, say 2x2 or 4x4, such that the number of printed dots approximates the varying-sized disks of ink used in analog, in halftone printing (e.g. for newspaper photos). Half-tone printing is an analog process that uses smaller or larger filled circles of black ink to represent shading, for newspaper printing.

9 9 DITHERING Example: If we use a 2x2 dither matrix Re-map image values in into the new range 0..4 by (integer) dividing by 256/5. If pixel value = 0 print nothing in a 2x2 area of printer output. If pixel value = 4 print all four dots Rule: If intensity > dither matrix entry print an on dot at that entry location: replace each pixel by a nxn matrix of dots.

10 10 DITHERING Note: Image size may be much larger for a dithered image (replacing each pixel by a 2x2 array of dots, makes an image 4 times as large). Can get around this problem. Ordered dither: turn on the printer output bit for a pixel if the intensity level is greater than the particular matrix element just at that pixel position

11 11 AN ALGORITHM FOR ORDERED DITHER Using n x n dither matrix

12 12 EXAMPLE 4x4 dithering matrix

13 13

14 14 IMAGE DATA TYPES The most common data types for graphics and image file formats: 24-bit color and 8-bit color. Some formats are restricted to particular hardware/operating system platforms, while others are cross-platform formats. Even if some formats are not cross-platform, there are conversion applications that will recognize and translate formats from one system to another. Most image formats incorporate some variation of compression technique due to the large storage size of image files. Compression techniques can be classified into either lossless or lossy.

15 15 24-BIT COLOR IMAGES In a color 24- bit image, each pixel is represented by three bytes, usually representing R, G, B. This format supports 256 x 256 x 256 possible combined colors, or a total of 16,777,216 possible colors. Such flexibility does result in a storage penalty: A 640 x bit color image would require KB of storage without any compression.

16 EXAMPLE 16

17 17 8-BIT COLOR IMAGES Many systems can make use of 8 bits of color information (the so-called 256 colors ) in producing a screen image. Such image files use the concept of a lookup table to store color information. Basically, the image stores not color, but instead just a set of bytes, each of which is actually an index into a table with 3- byte values that specify the color for a pixel with that lookup table index.

18 18 COLOR QUANTIZATION With 8 bits per pixel and color lookup table we can display at most 256 distinct colors at a time. To do that we need to choose an appropriate set of representative colors and map the image into these colors

19 19 COLOR QUANTIZATION

20 20 QUANTIZATION PHASES Sample the original image for color statistics Select color map based on those statistics Map the colors to their representative in the color map Redraw the image, quantizing each pixel

21 COLOR LOOK-UP TABLES (LUTS) 21 The idea used in 8-bit color images is to store only the index, or code value, for each pixel. Then, e.g., if a pixel stores the value 25, the meaning is to go to row 25 in a color look-up table (LUT).

22 HOW TO DEVISE A COLOR LUT? 22 The most straightforward way to make 8-bit look up color out of 24-bit color would be to divide the RGB cube into equal slices in each dimension. The centers of each of the resulting cubes would serve as the entries in the color LUT. Simply scaling the RGB ranges into the appropriate ranges would generate the 8-bit codes. Since humans are more sensitive to R and G than the B, we could Shrink the R range and G range into the 3 bit range Shrink the B range down to 2 bit range To shrink R and G, we could simply divide the R and G value by (256/8)=32 and then truncate. Each pixel in the image gets replaced by its 8-bit index, and the color LUT serves to generate 24-bit color.

23

24

25 25 MEDIAN-CUT ALGORITHM A simple alternative solution that does a better job for the color reduction problem. Sort the R byte values and find their median. Values smaller than the median are labeled with a 0 bit. Values larger than the median are labeled with a 1 bit. This type of scheme will concentrate bits where they most need to differentiate between high populations of close colors. We can easily visualize finding the median by using a histogram showing counts at position

26 MEDIAN-CUT ALGORITHM 26

27 24 BIT 27

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