Radiometric Corrections 3

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1Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Radiometric Distortions in RS Images and Their CorrectionRadiometric Distortions in RS Radiometric Distortions in RS Images and Their CorrectionImages and Their Correction

EREG RS Core ModuleDr. Tsehaie Woldai

(With data from C. Pohl and E. Schetselaar)

EREG RS Core ModuleEREG RS Core ModuleDr. Tsehaie Woldai

(With data from C. Pohl and E. Schetselaar)

2Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

ContentContent

IntroductionRadiometric Distortions

Optical CaseRadar Case

Atmospheric EffectsCorrection Methods

3Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Image DistortionsImage Distortions

Distortions (errors) in RS imagesradiometricgeometric

Radiometry influenced byseasonatmospheresensor

Geometry influenced bysatellite configurationsensor viewing geometryobserved terrain

Topic of this lecture!Topic of this lecture!

4Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Image DistortionsImage Distortions

Distortions (errors) in RS images (optical systems)

RadiometricSystem errors minimized by cosmetic

corrections

Atmospheric distortions minimized by atmosphericcorrections

Geometric minimized by geometriccorrections

5Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Radiometric DistortionRadiometric Distortion

What is a radiometric distortion?It’s an error that influences the radiance or radiometric value of a scene element (pixel).

Why?Signal travelling through atmosphere; atmosphere affects the signalSun illumination influences radiometric valuesSeasonal changes affect radiometric valuesSensor failures or system noise affects valuesTerrain influences radiance

Multi-temporal or multi-sensor analysis requires corrected images

6Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Radiometric Distortion Radiometric Distortion ~ ~ Optical CaseOptical Case ~~

Sensor noise or failures

Seasonal variations

Effect often neglectable due to larger influence of atmospheric effects

7Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Sensor noise and failures (1)Sensor noise and failures (1)((Eg., a whiskbroom LandsatLandsat--TM Scanning PatternTM Scanning Pattern))

16 detectors scan the scene alternating from left to right and back by use of an oscillating mirror

At any time 100 detectors are operating simultaneously (6x16 VNIR plus 1x4 TIR).

8Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Sensor noise and failures (2) Sensor noise and failures (2)

Types of sensor noise and failuresTypes of sensor noise and failures

1. Line Striping

2. Periodic line drop outs

3. Random or spike noise

9Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

1. Line Striping1. Line Striping

Cause:non-identical response of one or more detectors resulting from drift in response after calibration of the detectors

Correction method (one of them):

1. Compute the histogram of one detector as standard

2. Match the histograms of the other detectors to the histogram of the standard detector

10Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line StripingLine Striping

DeDe--stripedstripedStripingStriping

11Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line StripingLine StripingLandsat TM ExampleLandsat TM Example

DeDe--stripedstripedStripingStriping

12Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line StripingLine StripingSPOT XS ExampleSPOT XS Example

DeDe--stripedstripedStripingStriping

13Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line Striping The amplitude of every sixth line is multiplied by a factor of 0.5 to produce the correct digital value from which the restored image is plotted.

Line Striping

14Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

2. (Periodic) line drop outs2. (Periodic) line drop outs

Cause:erroneous radiance values for pixels, lines or areasdefective scanner, transmission, receiving or media system

Correction method:Correction by repetition of neighbouring values or averaging or,The amplitude of every sixth line is multiplied by a factor of 0.5 to produce the correct digital value from which the restored image is plotted.

15Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line drop outsLine drop outs

Original

Line drop-out

Corrected

16Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line DropLine Drop--outs (Landsat ETM data)outs (Landsat ETM data)

17Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line DropLine Drop--outsouts

18Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Line drop outsLine drop outsDropped Signal Dropped Signal -- ExampleExample

(CCRS Remote Sensing Tutorial)

19Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

3. Random noise or spikes3. Random noise or spikes

Cause: Transmission errors or temporary disturbances

Correction method:

1. Detect spike by comparing DN with DN of its surrounding pixels (neighbours)

2. Replace DN with DN value interpolated from the surrounding pixels

20Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Random noise or spikesRandom noise or spikes

Example of Spikes in Landsat MSS

21Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Random noise or spikesRandom noise or spikes

Example of correcting for ‘spikes’

56

Image with spike

De-spiked image

22Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Microwave BackscatterMicrowave Backscatter

23Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Radiometric Effects Radiometric Effects ––SAR CaseSAR Case

Speckle‘Salt and pepper effect’Effect of surface roughness and system factors in image productionAccounts for interference contribution of individual scatterersIt is a random and multiplicative effect

Correction methodsMulti-look processingAveragingFiltering

24Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Correction Methods Correction Methods ––

Multi-look processingMovement of sensor - receive backscattered signal from one target several timesCreate several images (=looks)Average images to produce ‘multi-look’ image

Spatial averagingUse full resolution single look imageApply low-pass filter

Speckle filterSmooth homogenous areas, preserve edges

25Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

SAR SpeckleSAR Speckle

ERS-1 SAR original ERS-1 SAR filtered(Pohl, 1996)

26Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

SAR Speckle SAR Speckle

Original Image Filtered image

Speckle reduction

(G. Huurneman, ITC)

27Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric Effects Atmospheric Effects Radiation PrinciplesRadiation Principles

Sun

R.S. Instrument

In ci d e n t e n e r g y

Scattered radiation

Cloud

Atmosphericemission

Emission processesReflection processesEARTH

Atmosperic absortion

Direct radiation

Reflected radiation

Thermal emission

Scattered radiation

Thermal emission

Atmospheric emission

R.S. Instrument

Sun

Cloud

Scattered radiation

Direct radiation

Scattered radiation

Atmospheric absorption

Incident energy

Earth Reflection processes Emission processes

(T. Woldai, ITC)

28Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

29Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Interactions with AtmosphereInteractions with Atmosphere

Measurement of Radiance by Optical Sensors

Sun is source of radiationEMR is reflected by the Earth (amount depends on reflectivity or albedo of Earth surface)Radiation has to pass atmosphere 2x

Interaction with Atmosphere:ScatteringAbsorption

30Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Interaction with Atmosphere Interaction with Atmosphere -- 22

Regions relatively free from effects= Atmospheric WindowsDepending on wavelengthAdds haze to the image= image looses contrast*

Scattering & Absorption= Attenuation or Extinction

* Contrast = Ratio between brightest and darkest areas

31Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric EffectsAtmospheric Effects

AbsorptionAbsorption ScatteringScattering

(CCRS Remote Sensing Tutorial)

32Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

AbsorptionAbsorption

Gases absorb radiationWater vapourCarbon dioxideOzone

Remote Sensing in absorption bands is impossible.

33Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

ScatteringScattering

SelectiveAffects specific wavelengthsExamples

– Rayleigh Scattering– Mie Scattering

Non-SelectiveWavelength independent

34Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric EffectsAtmospheric EffectsSelective ScatteringSelective Scattering

Blue light

Red light

θ1

θ2

Particle smaller than blueλ

Rayleigh principle (the shorter the wavelength, the greater the scattering)

(T. Woldai, ITC)

35Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric EffectsAtmospheric EffectsRayleigh Scattering causes blue skies during daytime and red skies at sunset

Blue sky

Day timeEarth

Atmosphere

BG

R

Earth

Sunset

Blue

Red

Sun

Sun

RayleighRayleigh ScatteringScattering

(T. Woldai, ITC)

36Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

MieMie--scatteringscattering

Mie scattering occurs when the wavelength of the incoming radiation is similar in size to the atmospheric particles (e.g., aerosols: a mixture of gases, water vapor and dust).

Mie scattering is restricted to the lower atmosphere where larger particles are more abundant.

It influences the entire spectral region from the near ultra-violet up to and including the NIR.

37Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Selective Scattering in WaterSelective Scattering in Water

2

hi e igh

Blue light

HO

= colloidal particles less than 1 micron

Wt l

tBG

R

(T. Woldai, ITC)

38Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric EffectsAtmospheric Effects

(CCRS Remote Sensing Tutorial)

NonNon--Selective ScatteringSelective Scattering NonNon--selective scattering is selective scattering is independent of wavelength, with independent of wavelength, with all wavelengths scattered about all wavelengths scattered about

equally. The most prominent equally. The most prominent example includes the effect of example includes the effect of

clouds (consisting of water clouds (consisting of water droplets). Since all wavelengths droplets). Since all wavelengths are scattered equally, a cloud are scattered equally, a cloud

appears white.appears white.

39Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Deleterious Factors of Cloud Deleterious Factors of Cloud CoverCover

CloudCloud

Cloud radiance contribution

Zone of no penetration

Shad

ow z

one

n radiance

Earth Shadow

(T. Woldai, ITC)

Susensor

40Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric effectsAtmospheric effects

SkylightSun radiance is scattered in the direction of the Earth surface by small particles and molecules in the atmosphereCan cause increase in radiance received at the sensorMultiplicative effect

CorrectionMultiplication with factor of stable feature in timeEqualization of images for multiple dates

41Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Atmospheric effectsAtmospheric effects

HazeSun radiance is scattered in the direction of the sensor by small particles and molecules in the atmosphereCan cause increase in radiance received at the sensor

Correction (approximation)Select object that absorbs all radiance (e.g. water body); ideal DN = 0Due to haze DN ≠ 0; subtract radiance value from all pixels

42Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Haze Haze –– Example (Indonesia)Example (Indonesia)

Haze Effect Corrected Image

43Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Haze CorrectionHaze Correction

Dark object subtraction method

Assumption: infrared bands are not affected by Haze

• Identify black bodies: clear water and shadow zones with zero reflectance in the infrared bands

• Identify DN values at shorter wavelength bands of the same pixel positions. These DN are entirely due to haze

• Subtract the minimum of the DN values related to black bodies of a particular band from all the pixel values of that band

44Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Effects of Sun IlluminationEffects of Sun Illumination

Position of sunSun elevation (sun-angle)Sun - earth distance

Correction elevationDivision of each pixel value by the sine of solar elevation angle for particular time and location per spectral band

Correction distanceSun irradiance decreases with square of distance

45Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Effects of Sun Illumination Effects of Sun Illumination

Corrections are needed to compensate for sun illumination variations resulting from different scene acquisition dates

Applications

Change detection studies

Mosaics

46Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Correction for seasonal Correction for seasonal variations in Sun illuminationvariations in Sun illumination

Sun angle correction

Earth-Sun distance correction

)('

αSINDNDN =

2

365)5.93(2sin00167.01'

+=dDNDN π

Where d is the day number in a year

47Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Skylight CorrectionSkylight Correction

Dateref

Datea

FrefFa

BandNIR

Ban

d VIS

a

ref

FFi =θ

iii DD ×=θ'

48Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Summary Radiometric Summary Radiometric CorrectionCorrection

We need to correct for atmospheric effects, variations in sun illumination and system defects

Atmospheric correction is the most complex correction

In many cases only haze correction is applied (dark object subtraction)

If we want to relate RS data with field spectrometric measurements we need to apply full atmospheric corrections, taking into account wavelength dependent factors, such as diffuse sky irradiance, transmission coefficients, path radiance and sensor calibration coefficients

49Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

ReferencesReferences

Bakx, W. (1995): “An introduction to digital image processing”, ITC Lecture Note RSD 65.Schreier, G. (1993): “SAR Geocoding: Data and Systems”, Karlsruhe: Wichmann, ISBN 3-87907-247-7, 435 pages.Wageningen UR, 1999,http://www.gis.wau.nl/cgirs/projects/rsbasics/overview.htm

CCRS Remote Sensing Tutorial: http://www.ccrs.nrcan.gc.ca/ccrs/eduref/tutorial/tutore.html

50Dr. Dr. Dr. TsehaieTsehaieTsehaie WoldaiWoldaiWoldai EREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric CorrectionEREG Module 2,3,4 Radiometric Correction

Further ReadingFurther Reading

Richards, J.A., Remote sensing digital image analysis: an introduction, 2nd revised and enlarged edition, Berlin etc. - Springer Verlag, 1993, ISBN 3-540-54840-8.Lillesand, T.M. and Kiefer, R.W., Remote Sensing and Image Interpretation, 3rd Ed., 1993, J. Wiley & Sons, 720 pp.Jensen, J.R. & Schill, S.R. (1999): The Remote Sensing Core Curiculum, Vol. 3, Digital Image Processing, http://www.cla.sc.edu/geog/rslab/rsccnew/rscc-frames.htmlMather, P.M., Computer Processing of Remotely-Sensed Images: an Introduction, Wiley: New York 1999, ISBN 0-471-98550-3