1. Image Display & Enhancement Lecture 2 Prepared by R. Lathrop 10/99 updated 1/03 Readings: ERDAS Field Guide 5th ed Chap 4; Ch 5:137-153; App A Math Topics: 459-469

2. Digital Images Digital Number (DN) or Brightness Value (BV) - the tonal gray scale expressed as a number, typically 8-bit number (0-255) Dimensionality - determined by the number of data layers (bands) Measurement Vector of a pixel - is the set of data file values for one pixel in all n bands

3. Digital Image 0 255 8 bit DN Multiple spatially co-registered bands, can be displayed singly in B&W or in color composite Band 1 Band 2 Band 3

4. Image Notation i = row (or line) in the image j = column k, l = bands of imagery Bv ijk = BV in row i, column j of band k n = total # of pixels in an array Rows = i = 4 Columns = j = 5

5. Calculating disk space [ ( (x * y * b) * n) ] x 1.4 = output file size where: y = rows x = columns b = number of bytes per pixel n = number of bands 1.4 adds 30% for pyramid layers and 10% for other info

6. Digital Image Storage Formats Band sequential (BSQ) - each band contained in a separate file Band interleaved by line (BIL) - each record in the file contains a scan line (row) of data for one band, with successive bands recorded as successive lines Band Interleaved by Pixel (BIP)

7. Image Display Computer Display Monitor has 3 color planes: R, G, B that can display DN’s or BV’s with values between 0-255 3 layers of data can be viewed simultaneously: 1 layer in Red plane 1 layer in Green plane 1 layer in Blue plane

8. Image Display: RGB color compositing Red band DN Blue band DN Red band DN = 0 Blue band DN = 200 Green band DN Green band DN = 90 Blue-green pixel (0, 90, 200 RGB)

9. Landsat MSS bands 4 and 5 GREEN RED

10. Landsat MSS bands 6 and 7 INFRARED 2INFRARED 1 Note: water absorbs IR energy-no return=black

11. combining bands creates a false color composite red=vegetation light blue=urban black=water pink=agriculture Rutgers Manhattan Philadelphia Pine barrens Chesapeake Bay Delaware River MSS color composite

12. Primary Colors Red Green Blue

13. Subtractive Primary Colors Yellow (R+G) absence of blue Cyan (G+B) absence of red Magenta (R+B) absence of green

14. Color Additive Process: the way a computer display works R G B M Y C W Black background

15. YC M R G B B Color Subtractive Process: the way paint pigment works White background

16. Additive Color Process colorRGB white255255255 black000 grey100100100 red25500 yellow2552550 cyan0255255 magenta2550255 orange2551000 dark blue00100

17. Summarizing data distributions Frequency distributions - method of describing or summarizing large volumes of data by grouping them into a limited number of classes or categories Histograms - graphical representation of a frequency distribution in the form of a bar chart

18. Summarizing Data Distributions: Histograms 0255 Digital Number # of pixels

19. Measures of Central Location Mean - simple arithmetic average, the sum of all observations divided by the number of observations Median - the middle number in a data set, midway in the frequency distribution Mode - the value that occurs with the greatest frequency, the peak in a histogram

20. Measures of Central Location 0255 Digital Number # of pixels Mode Mean Median

21. Measures of Dispersion Range - the difference between the largest and smallest value Variance - the average of the squared deviations between the data values and the mean Standard Deviation - the square root of the variance, in the units of data measurement

22. Measures of Dispersion: Range 0 255 Digital Number # of pixels Min = 60 Max = 200 Example: Range = (max - min) = 200 - 60 = 140

23. Image Restoration and Enhancement

24. Image spectral enhancement 0 255 Digital Number # of pixels Min = 0Max = 255 Image display devices typically operate over a range of 256 gray levels. Ideally the image data ranges over this full extent.

25. Image spectral enhancement However, sensor data in a single band rarely extend over this entire range, resulting in a loss of contrast. The objective of spectral enhancement is to determine a transformation function to improve the brightness, contrast and color balance and thereby enhance image interpretability. No data 0 255 Digital Number # of pixels Min = 50 Max = 200

26. Image spectral enhancement: lookup tables Image file values are read into the image processor display memory. These values are then manipulated for display by specifying the contents of the 256 element color look-up- table (LUT). By changing the LUT, the user can easily change the output display without changing the original file DN values. Data File Green band DN = 100 LUT Green band DN = 190 Enhanced Green pixel Display DN = 190 Input LUT Output

27. Image spectral enhancement: Lookup tables Since the same transformation function is used for all the pixels in the image, it is calculated for all possible DN before processing the image. The resulting values of DN are stored in a lookup table (LUT). All possible values are computed only once - computationally efficient. Each pixel’s DN is then used to index the LUT to find the appropriate DN’ in the output image

28. LUT Input-Output relationship: ideal 0 0 255 Output DN Input DN Input = 127 Output = 127 From ERDAS Imagine Field Guide 5th Ed. 1-to-1 transformation function

29. Transformation function 0 0 255 Output DN Input DN The steeper the transformation line -> the greater the contrast stretch

30. Image spectral enhancement: NO contrast stretch 0255 60108158

31. Image spectral enhancement: Min-max linear contrast stretch 0255 60108158 125

32. Linear transformation function The steeper the transformation line -> the greater the contrast stretch 0 0 255 Output DN Input DN Input min = 60 Output min = 0 Input max = 158 Output max = 255

33. Image spectral enhancement: Min-max linear contrast stretching Linear stretch: uniform expansion, with all values, including rarely occurring values, weighted equally DN’ = [(DN - MIN)/(MAX - MIN)] x 255 Example: DN = 108 DN’ = [(108 - 60) / (158 - 60)] x 255 = [48 / 98] x 255 =.49 x 255 = 125 Example from Lillesand & Kiefer, 2nd ed

34. Image spectral enhancement: Std. Dev. linear contrast stretching If data histogram near normal, then 95% of the data is within +- 2 std dev from the mean, 2.5% in each tail 0255

35. Image spectral enhancement: Histogram stretching Histogram stretch: image values are assigned to the display LUT on the basis of their frequency of occurrence greatest contrast near mode least contrast in histogram tails 0 255 108 158 38 60 Example from Lillesand & Kiefer, 2nd ed

36. Histogram stretching 0 0 255 Output DN Input DN Input min = 60 Output min = 0 Input max = 158 Output max = 255 Nonlinear function in tails of distribution

37. Image spectral enhancement: Contrast stretching Special stretch: display range can be assigned to any particular user-defined range of image values Example from Lillesand & Kiefer, 2nd ed 0 255 158 6092

38. Special piecewise stretching 0 0 255 Output DN Input DN Different sections of the input data stretched to different extents; I.e. different pieces of the transformation function line with different slopes

39. Simple Image Segmentation Simplifying the image into 2 classes based on thresholding a single image band, so that additional processing can be applied to each class independently < DN threshold = Class 1 >= DN threshold = Class 2 Example: gray level thresholding of NIR band used to segment image into land vs. water binary mask +