Go over: Geometric correction

Go over: Geometric correction

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Registration or Rectification

Selection of GCPS;Coor transform;DN Resampling.

How to remove noise from an image? How to highlight edges within the image?

Spatial-based Enhancements

Lecture 5

prepared by R. Lathrop 10/99

updated 2/05

ERDAS Field Guide 5th Ed. Ch 5:154-162

Main points of the lecture

• Concept of spatial frequency • Texture • Low vs. Hi frequency enhancement: kernel

convolution.• Edge Enhancement/Sharpening• Edge Detection/Extraction• Global vs. local operator: Fourier vs. kernel

convolution

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

Noise Removal• Noise: extraneous unwanted signal response

• SNR measures the radiometric accuracy of the data. Want high Signal-to-noise-ratio (SNR)

• Over low reflectance targets (i.e. dark pixels such as clear water) the noise may swamp the actual signal

True Signal NoiseObserved

Signal

+

Noise Removal• Noise removal techniques to restore image to

as close an approximation of the original scene as possible

• Bit errors: random pixel to pixel variations, average neighborhood (e.g., 3x3) using a moving window (convolution kernel)

• Destriping: correct defective sensor

• Line drop: average lines above and below

Example: mean or median focal analysis for noise filtering

Example: Line drop

105 156 178 154 167 200 202 205

----- ----- ---- ----- ----- ----- ----- -----

107 152 166 165 173 204 204 207

Interpolated: above and below to fill line

105 156 178 154 167 200 202 205

106 154 172 160 170 202 203 206

107 152 166 165 173 204 204 207

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: mean Euclidean distance• 2nd order: range, variance, std dev• 3rd order: skewness• 4th order: kurtosis• Window size will affect results. Often need larger

moving window sizes for proper enhancement.

Example Image: Ikonos pan

Orignal IKONOS pan

Texture: variance

3x3 texture 7x7 texture

Statistical or Sigma Filters: often used for radar imagery enhancement

• Center pixel is replaced by the average of all pixel values within the moving window that fall within the designated range of sigma: µ+σ

• Sigma may represent the coefficient of variation. The default sigma value (set to 0.15 in ERDAS IMAGINE) can be modified using multipliers to increase or decrease the range of values within the moving window used to calculate the average.

• Use the filter sequentially with increasing multipliers to preserve fine detail while smoothing the image.

Spatial-based Enhancement

• Low vs. Hi frequency enhancement

• Edge Enhancement/Sharpening

• Edge Detection/Extraction

• Many spatial-based enhancement (filtering) techniques use kernel convolution, a type of local operation

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

Pixel Convolution

)

)(

int(F

df

BV

q

i

q

jijij

Where i = row location, j = column locationfij = the coefficient of a convolution kernel at position i, jdij = the BV of the original data at position i, jq = the dimension of the kernel, assuming a square kernel , i.e., either the sum of the coefficients of the

kernel or 1 if the sum of coefficients is zeroBV = output pixel value

q

i

q

jijfF )(


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


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 60 57 61 125 69 58 60 70

Output: 64 60 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

Gaussian filter

• Gaussian smoothing filter is similar to a low pass mean filter but uses a kernel that represents the shape of a Gaussian (“bell-shaped”) curve.

• Example

Graphic taken from http://homepages.inf.ed.ac.uk/rbf/HIPR2/gsmooth.htm

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 (i.e., local changes between bright vs. dark features)

• Zero-sum kernels:

- linear edge/line detecting templates

- directional (compass templates)

- non-directional (Laplacian)

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

• Narrow (single pixel wide) line features (i.e. rivers and roads) are output as pairs of edges using linear edge detection templates. To create a single line edge feature, a linear line detecting template can be used

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 . . . . . .

Directional gradient filters• Directional gradient filters produce output images whose BVs

are proportional to the difference between neighboring pixel BVs in a given direction, i.e. they calculate the directional gradient

• Spatial differencing: calculating spatial derivatives (differencing a pixel from its neighbor or some other lag distance); doesn’t use kernel convolution approach

• Vertical: BVi,j = BVi,j - BVi,j+1 + K

• Horizontal: BVi,j = BVi,j - BVi-1,j + K constant K added to make output positive (usually K=127)

Directional gradient filters

Example: horizontal spatial difference BVi,j = BVi,j - BVi-1,j + K

Original: 2 2 2 8 8 8 Output: 0 0 6 0 0 2 2 2 8 8 8 0 0 6 0 0 8 8 8 2 2 2 0 0 -6 0 0

8 8 8 2 2 2 0 0 -6 0 0

Positive values signify increase left to rightNegative values signify decrease left to right

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/map 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

High Pass Filter (HPF) method for Image Fusion

• Capture high frequency information from the high spatial resolution panchromatic image using some form of high pass filter

• This high frequency information then added into the low spatial resolution multi-spectral imagery

• Often produces less distortion to the original spectral characteristics of the imagery but also less visually attractive

Edge Mapping/Extraction

• 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

Edge Mapping/Extraction:example using Sobel filter

Edge image represents a continuous range of values. Can you determine a threshold?

+

Edge Mapping/Extraction:example using Sobel filter

Edge-extracted image DN = 15 Edge-extracted image DN = 20

Adaptive Filtering

• The selection of a single threshold to differentiate an edge that is applicable across the entire image may be difficult

• An adaptive filtering approach that looks at the relative difference on a more local scale (i.e., within a moving window) may achieve better results.

Band by Band vs. PCA

• Most spatial convolution filtering works waveband by waveband. Some edges may be more pronounced in some spectral wavebands vs. others.

• Alternatively, PCA can be used to composite the multispectral wavebands and run the convolution filtering/edge detection on the PCA Brightness component

Fourier Transform• Fourier analysis is a mathematical technique for

separating an image into its various spatial frequency and directional components.

• Fourier or spectral analysis models the data as a weighted sum of cosine and sine waveforms of varying direction and spatial frequency.

• Think of waves with a high vs. low spatial frequency

Fourier Transform

• 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.

• FT is global rather than local operator• Useful for noise removal or enhancing

particular spatial frequency components

Fourier Analysis Example

Side scan sonar image of sea bottom

Fourier spectrum


Fourier spectrum

Low frequencies towards center

High frequencies towards edges

Image noise often shows as thin line, oriented perpendicular to original image


Low pass filter Back transformed image


Wedge filter Back transformed image

Discrete Wavelet Transform • Wavelet transform is similar to the FFT• DWT: uses short discrete “wavelets” parameterized as

a finite sized moving window rather than a continuous global sine wave (as in FT)

• Form of multi-resolution analysis• Starts at the scale of the entire image and then

successively breaks down into smaller windows (2x the frequency, 3x, 4x, etc. ) using high and low pass filters for the decomposition of low-pass, vertical, horizontal and diagonal components

Graphic from http://www.jinr.ru/programs/jinrlib/wasp/docs/html/img145.png

Discrete Wavelet Transform

Graphic from http://norum.homeunix.net/~carl/wavelet/

This site has a DWT tutorial


http://norum.homeunix.net/~carl/wavelet/

Discrete Wavelet Transform


5 pass Graphic from http://norum.homeunix.net/~carl/wavelet/

5 pass

DWT




Wavelet Transform for image fusion

• Use the wavelet transform on the high spatial panchromatic imagery. Decompose till you have the same spatial resolution as the low spatial resolution multi-spectral data

• The multi-spectral and HI-res imagery should have relative pixel sizes differing by a factor of 2.

• The multi-spectral image is substituted for the low-pass image derived from the HI-res imagery.

• Reverse the wavelet decomposition to produce high spatial imagery with the multi-spectral information


High spectral res image

High spatial res image

Resample Histogram Match

DWT

Fused image

h

v d

h

v d

Adapted from ERDAS IMAGINE Field Guide

s


• Must either compress the multi-spectral info into a single band (i.e. through PCA) or process single bands sequentially.

• The two images should be spectrally identical, i.e., only include the multi-spectral bands that fall within the range of the HI-res panchromatic band

• Often produces less distortion to the original spectral characteristics of the imagery

• DWT also used for image compression with only the low-pass information used

Spatial-based enhancement

• Concept of spatial frequency

• Texture

• Low vs. Hi frequency enhancement

• Edge Enhancement/Sharpening

• Edge Detection/Extraction

• Global vs. local operator: Fourier vs. kernel convolution

Homework

1 Homework: Spatial Filtering;

2 Reading Ch. 8:276-329;

3 Reading ERDAS Ch. 6:157-160, 189-201

4 Article review due to Wednesday (Feb. 14, 2007)

Go over: Geometric correction

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