1. Spatial-based Enhancements Lecture 3 prepared by R. Lathrop 10/99 updated 10/03 ERDAS Field Guide 6th Ed. Ch 5:144-152; 171-184

2. Spatial frequency Spatial frequency is the number of changes in brightness value per unit distance in any part of an image low frequency - tonally smooth, gradual changes high frequency - tonally rough, abrupt changes

3. Spatial Frequencies Zero Spatial frequencyLow Spatial frequencyHigh Spatial frequency Example from ERDAS IMAGINE Field Guide, 5th ed.

4. Spatial vs. Spectral Enhancement Spatial-based Enhancement modifies a pixel’s values based on the values of the surrounding pixels (local operator) Spectral-based Enhancement modifies a pixel’s values based solely on the pixel’s values (point operator)

5. Moving Window concept Kernel scans across row, then down a row and across again, and so on.

6. Focal Analysis Mathematical calculation of pixel DN values within moving window Mean, Median, Std Dev., Majority Focal value written to center pixel in moving window

7. Example: noise filtering

8. Texture Texture: variation in BV’s in a local region, gives estimate of local variability. Can be used as another layer of data in classification/ interpretation process. 1st order statistics: range, variance, std dev Window size will affect results

9. Texture: variance 3x3 texture7x7 texture

10. Pixel Convolution BV = int [ SUM i->q (SUM j->q f ij d ij ) ] ---------------------------------- F where i = row locationj = column location f ij = the coefficient of a convolution kernel at position i, j d ij = the BV of the original data at position i, j q = the dimension of the kernel, assuming a square kernel F = either the sum of the coefficients of the kernel or 1 if the sum of coefficients is zero BV = output pixel value

11. Example: kernel convolution 88666286662286622286222288866628666228662228622228 -1 -1 -1 -1 16 -1 -1 -1 -1 Example from ERDAS IMAGINE Field Guide, 5th ed. Convolution Kernel

12. Example: kernel convolution Kernel: -1 -1 -1 -1 16 -1 -1 -1 -1 Original: 8 6 6 2 8 6 2 2 8 X Result = 11 J=1j=2j=3 I=1 (-1)(8) +(-1)(6)+(-1)(6)= -8 -6 -6 = -20 I=2 (-1)(2) +(16)(8)+(-1)(6)= -2 +128 -6 = 120 I=3 (-1)(2) +(-1)(2)+(-1)(8)= -2 -2 -8 = -12 F = 16 - 8 = 8 Sum = 88 output BV = 88 / 8 = 11

13. 116666 011666 201166 220116 2220 11 Example: kernel convolution 86666286662286622286222288666628666228662228622228 InputOutput Edge

14. Low vs. high spatial frequency enhancements Low frequency enhancers (low pass filters): Emphasize general trends, smooth image High frequency enhancers (high pass filters): Emphasize local detail, highlight edges

15. Example: Low Frequency Enhancement Kernel: 1 1 1 1 1 1 Original: 204 200 197 201 100 209 198 200 210 Output: 204 200 197 201 191 209 198 200 210 Original: 64 50 57 61 125 69 58 60 70 Output: 64 50 57 61 65 69 58 60 70 Low value surrounded by higher values High value surrounded by lower values From ERDAS Field Guide p.111

16. Low pass filter Orignal IKONOS pan 7x7 low pass

17. Example: High Frequency Enhancement Kernel: -1 -1 -1 -1 16 -1 -1 -1 -1 Original: 204 200 197 201 120 209 198 200 199 Output: 204 200 197 201 39 209 198 200 210 Original: 64 50 57 61 125 69 58 60 70 Output: 64 50 57 61 187 69 58 60 70 Low value surrounded by higher values High value surrounded by lower values From ERDAS Field Guide p.111

18. High Pass filter 3x3 high pass 3x3 edge enhance -1 -1 -1 -1 17 -1 -1 -1 -1 -1 -1 -1 -1 9 -1 -1 -1 -1

19. Edge detection Edge detection process: Smooth out areas of low spatial frequency and highlight edges (local changes) only 1) calculating spatial derivatives (differencing) 2) edge detecting template (Zero-sum kernels): - directional (compass templates) - non-directional (Laplacian) 3) subtracting a smoothed image from the original

20. Linear Edge Detection techniques Directional gradient filters produce output images whose BVs are proportional to the difference between neighboring pixel BVs in a given directional, i.e. they calculate the directional gradient Spatial differencing: Vertical: BV i,j = BV i,j - BV i,j+1 + K Horizontal: BV i,j = BV i,j - Bv i-1,j + K constant K added to make output positive

21. Zero sum kernels Zero sum kernels: the sum of all coefficients in the kernel equals zero. In this case, F is set = 1 since division by zero is impossible zero in areas where all input values are equal low in areas of low spatial frequency extreme in areas of high spatial frequency (high values become higher, low values lower)

22. Example: Linear Edge Detecting Templates Vertical:-1 0 1Horizontal: -1 -1 -1 -1 0 1 0 0 0 -1 0 1 1 1 1 Diagonal (NW-SE): 0 1 1(NE-SW): 1 1 0 -1 0 1 1 0 -1 -1 -1 0 0 -1 -1 Example: vertical template convolution Original: 2 2 2 8 8 8 Output: 0 18 18 0 0 2 2 2 8 8 8 0 18 18 0 0

23. Linear Edge Detection Horizontal Edge Vertical Edge -1 -2 -1 0 0 0 1 2 1 -1 0 1 -2 0 2 -1 0 1

24. Linear Line Detecting Templates Line features (i.e. rivers and roads) can be detected as pairs of edges if they are more than one pixel wide (using linear edge detection templates). If they are a single pixel wide, they can be detected using these templates: Vertical:-1 2 -1Horizontal: -1 -1-1 -1 2-1 2 2 2 -1 2-1-1 -1 -1

25. Example: Linear Line Detecting Templates Vertical:-1 2 -1Horizontal: -1 -1 -1 -1 2 -1 2 2 2 -1 2 -1-1 -1 -1

26. Linear Line Detection Horizontal Edge Vertical Edge -1 -1 -1 2 2 2 -1 -1 -1 -1 2 -1 -1 2 -1 -1 2 -1

27. Compass gradient masks Produce a maximum output for vertical (or horizontal) brightness value changes from the specified direction. For example a North compass gradient mask enhances changes that increase in a northerly direction, i.e. from south to north: North:1 1 1 1 -2 1 -1 -1 -1

28. Example: Compass gradient masks North:1 1 1South: -1 -1 -1 1 -2 1 -1 -1 -1 1 1 1 Example: North vs. south gradient mask NorthSouth Original: 8 8 8 Output:...Output:... 8 8 8 0 0 0 0 0 0 8 8 818 18 18-18 -18 -18 2 2 218 18 18-18 -18 -18 2 2 2 0 0 0 0 0 0 2 2 2......

29. Non-directional Edge Enhancement Laplacian is a second derivative and is insensitive to direction. Laplacian highlights points, lines and edges in the image and suppresses uniform, smoothly varying regions 0 -1 0 1 -2 1 -1 4 -1 -2 4 -2 0 -1 0 1 -2 1

30. Nonlinear Edge Detection Sobel edge detector: a nonlinear combination of pixels Sobel = SQRT(X 2 + Y 2) X:-1 0 1Y: 1 2 1 -2 0 2 0 0 0 -1 0 1-1 -2 -1

31. Nondirectional edge filter Laplacian filterSobel filter

32. Edge enhancement Edge enhancement process: First detect the edges Add or subtract the edges back into the original image to increase contrast in the vicinity of the edge

33. Original IKONOS pan Edge enhancement Laplacian - Original – edge = edge enhanced

34. Original IKONOS pan Unsharp masking to enhance detail 7x7 low - Original – low pass = edge enhanced

35. Edge Mapping BV thresholding of the edge detector output to create a binary map of edges vs. non- edges Threshold too low: too many isolated pixels classified as edges and edge boundaries too thick Threshold too high: boundaries will consist of thin, broken segments

36. Fourier Transform Fourier analysis is a mathematical technique for separating an image into its various spatial frequency components. Can display the frequency domain to view magnitude and directional of different frequency components, can then filter out unwanted components and back-transform to image space. Global rather than local operator Useful for noise removal

37. Fourier Analysis Example Side scan sonar image of sea bottom Fourier spectrum

38. Fourier Analysis Example Fourier spectrum Low frequencies towards center High frequencies towards edges Image noise often shows as thin line, oriented perpendicular to original image

39. Fourier Analysis Example Low pass filter Back transformed image

40. Fourier Analysis Example Wedge filterBack transformed image