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

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

Spatial Frequencies

Zero Spatial frequency Low Spatial frequency High Spatial frequency

Example from ERDAS IMAGINE Field Guide, 5th ed.

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)

Moving Window concept

Kernel scans across row, then down a row and across again, and so on.

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

Example: noise filtering

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

Texture: variance

3x3 texture 7x7 texture

Pixel ConvolutionBV = int [ SUM i->q (SUM j->q fij dij) ]

---------------------------------- F

where

i = row location j = column location

fij = the coefficient of a convolution kernel at position i, j

dij = 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

Example: kernel convolution

8 8 6 6 6

2 8 6 6 6

2 2 8 6 6

2 2 2 8 6

2 2 2 2 8

-1 -1 -1

-1 16 -1

-1 -1 -1

Example from ERDAS IMAGINE Field Guide, 5th ed.

Convolution Kernel

Example: kernel convolution

Kernel: -1 -1 -1 -1 16 -1 -1 -1 -1

Original: 8 6 6 2 8 6 2 2 8

XResult

= 11

J=1 j=2 j=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

11 6 6 6 6

0 11 6 6 6

2 0 11 6 6

2 2 0 11 6

2 2 2 0 11

Example: kernel convolution

8 6 6 6 6

2 8 6 6 6

2 2 8 6 6

2 2 2 8 6

2 2 2 2 8

Input Output

Edge

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

Example: Low Frequency EnhancementKernel: 1 1 1

1 1 11 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

Low pass filter

Orignal IKONOS pan 7x7 low pass

Example: High Frequency EnhancementKernel: -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

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

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

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: BVi,j = BVi,j - BVi,j+1 + KHorizontal: BVi,j = BVi,j - Bvi-1,j + Kconstant K added to make output positive

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)

Example: Linear Edge Detecting Templates

Vertical: -1 0 1 Horizontal: -1 -1 -1-1 0 1 0 0 0 -1 0 1 1 1 1

Diagonal 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 2 2 2 8 8 8 0 18 18 0 0

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

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 -1 Horizontal: -1 -1 -1 -1 2 -1 2 2 2 -1 2 -1 -1 -1 -1

Example: Linear Line Detecting Templates

Vertical: -1 2 -1 Horizontal: -1 -1 -1-1 2 -1 2 2 2 -1 2 -1 -1 -1 -1Original

2 2 2 8 2 2 22 2 2 8 2 2 22 2 2 8 2 2 2

Linear Edge Detection. 0 18 0 18 0 .. 0 18 0 18 0 .. 0 18 0 18 0 .

Linear Line Detection. 0 -6 12 -6 0 .. 0 -6 12 -6 0 .. 0 -6 12 -6 0 .

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

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 11 -2 1

-1 -1 -1

Example: Compass gradient masks

North: 1 1 1 South: -1 -1 -11 -2 1 1 -2 1

-1 -1 -1 1 1 1

Example: North vs. south gradient mask

North SouthOriginal: 8 8 8 Output: . . . Output: . . .

8 8 8 0 0 0 0 0 0 8 8 8 18 18 18 -18 -18 -18 2 2 2 18 18 18 -18 -18 -18 2 2 2 0 0 0 0 0 0 2 2 2 . . . . . .

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

Nonlinear Edge Detection

Sobel edge detector: a nonlinear combination of pixels

Sobel = SQRT(X2 + Y2)

X: -1 0 1 Y: 1 2 1 -2 0 2 0 0 0 -1 0 1 -1 -2 -1

Nondirectional edge filter

Laplacian filter Sobel filter

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

Original IKONOS pan

Edge enhancement

Laplacian

-

Original – edge = edge enhanced

Original IKONOS pan Unsharp masking to enhance detail

7x7 low

-

Original – low pass = edge enhanced

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

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

Fourier Analysis Example

Side scan sonar image of sea bottom

Fourier spectrum

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

Fourier Analysis Example

Low pass filter Back transformed image

Fourier Analysis Example

Wedge filter Back transformed image