Remote Sensing I-2011 2

Module 2, Remote Sensing 1 MSc Course PHOTOGRAMMETRY

1st semester AND GEOINFORMATICS

Lecture Notes of Prof. Dr. M. Hahn

Last printed 20 September 2011 Page 1 of 56

Module 2

Photogrammetry and

Remote Sensing

Lecture Notes

Prof. Dr. M. Hahn

WS 2011/2012

Topic: Remote Sensing (Part 1)





Remote Sensing (Part 1)

Table of Contents

1. Basic Principles of Remote Sensing

1.1. Definitions, overall Remote Sensing process 1.2. Electromagnetic radiation 1.3. The electromagnetic spectrum 1.4. Interaction of electromagnetic radiation with the atmosphere 1.5. Interaction of electromagnetic radiation with Earth-surface

material 1.6. Energy sources and sensing 1.7. Satellite images and visualization

2. Preprocessing of remotely-sensed data

2.1. Removal of data errors 2.2. Registration and geometric correction 2.3. Atmospheric correction 2.4. Sensor calibration

3. Classification

3.1. Concept of supervised and unsupervised classification 3.2. Scatterplot and decision making 3.3. Supervised classification 3.4. Unsupervised classification





Chapter 1

Basic principles of Remote Sensing

1.1 Definitions, Overall Remote Sensing process

‘Remote Sensing is the science (and to some extent: art) of acquiring

information about the Earth’s surface without actually being in contract

with it. This is done by sensing and recording reflected or emitted energy

and processing, analysing and applying that information.’

Source: Canada Centre for Remote Sensing, CCRS Tutorial

‘Remote Sensing: the science and art of obtaining useful information

about an object, area, or phenomenon through the analysis of data

acquired by a device that is not in contact with the object, area or

phenomenon under investigation.’

T.M. Lillesand and R.W. Kiefer

Remote Sensing and Image Interpretation, Wiley book

‘Remote Sensing may be broadly defined as the collection of the

information of natural sources and environmental information about an

object without being in physical contact with the object. The term Remote

Sensing is restricted to methods that employ electromagnetic energy as

the means of detecting and measuring target characteristics.’

F.F. Sabins,

Remote Sensing principles and interpretation, Freeman book





‘The science of Remote Sensing consists of the interpretation of

measurements of electromagnetic energy reflected or emitted by a target

from a vantage-point that is distant from the target.’

‘Earth observation (EO) by Remote Sensing is the interpretation and

understanding of measurements …… ’

P.M. Mather

Computer processing of Remotely-sensed images, Wiley book

‘Aircraft and satellites are the common platform from which Remote

Sensing observations are made.’

F.F. Sabins

Remote Sensing principle and interpretation, Freeman book

Elements of an overall Remote Sensing process

Energy Source

The first requirement for remote sensing is to have an energy source

which illuminates or provides electromagnetic energy to the target of

interest.

Radiation and the Atmosphere

As the energy travels from its source to the target, it will interact with the

atmosphere it passes through.





This interaction may take place a second time as the energy travels from

the target to the sensor.

Source: CCRS Tutorial

Interaction with the Target

The energy (electromagnetic radiation) interacts with the target depending

on the properties of both the target and the radiation.

Recording of Energy by the Sensor

After the energy has been scattered by, or emitted from the target, a

sensor is required to collect and record the electromagnetic radiation.





Transmission, Reception, and Processing

The energy recorded by the sensor has to be transmitted, often in

electronic form, to a receiving and processing station where the data are

processed into an image (hardcopy and/or digital).

Interpretation and Analysis

The processed image is interpreted, visually and/or digitally (image

analysis), to extract information about the target which was illuminated.

Application

The extracted information assists to solve a particular problem.

1.2 Electromagnetic radiation

Electromagnetic energy /radiation is the means by which information is

transmitted from an object (target) to a sensor.

1.2.1 Basic terminology

Energy - the capacity to do work, expressed in J

(Joules)

Radiant energy - the energy associated with electromagnetic

radiation (EMR)

Flux of energy - the rate of transfer of energy from one





place to another (Latin word, meaning =

‘flow’)

- is measured in W (Watts)

Radiant flux density - to understand the interaction between

electromagnetic radiation and surfaces

Radiant flux is the rate of transfer of radiant

(=electromagnetic) energy

Density implies variability over the two-dimensional

surface on which the radiant energy falls.

Radiant flux density is the magnitude of the radiant flux

that is incident upon or, conversely, is emitted by a surface of

unit area (measured in W/m2)

== Irradiance (if radiant energy falls upon a surface)

== Radiant emittance ( if the energy flow is away from surface)

Radiance - is the radiant flux density transmitted from a unit

area on the Earth’s surface as viewed through a unit solid (3D) angle.

is measured in steradians

= 3 D equiv. of the radian

Example thermal energy solar energy reflected

emitted by the Earth by the Earth





Assume:

Diffuse reflectance = radiance incident

upon the surface is back scattered in all

upward directions

Then: (based on diffuse reflection)

A proportion of the radiant flux might be measured per unit solid viewing

angle

--- this proportion is the radiance

Radiance is measured in watts per square meter per

steradiant [ W/(m2*sr) ]

surface

flux

solid (3D ) angle

surface

normal

source area





Reflectance --- is the ratio between the irradiance and the

radiant emittance of an object.

Diffuse reflectance ( see above)

Specular reflectance:

= angle of incidence and angle of reflectance

are equal and no scattering occurs at the surface.

Remarks:

1 When remotely-sensed images collected over a time period

(= multi-temporal images) are to be compared it is common

practice to convert the radiance values recorded by the sensor

into reflectance factors in order to eliminate the effects of

variable irradiance over the seasons of the year.

2 All these described quantities refer to particular wavebands

rather than to the whole electromagnetic spectrum.

Precede the terms by the adjective spectral

Spectral reflectance, spectral irradiance,……etc.

angle of

reflection

angle of

incidence





1.2.2 Nature of electromagnetic radiation (or the view of quantum

mechanics)

Controversy in physics over the past 250 years

EMR: wave theory corpuscular theory

considers radiation as considers radiation as

a wave form a stream of particles

(wave-like form of energy) so-called photons

Importance to remote sensing

Today’s view of quantum mechanics: EMR is both a wave and a stream

of particles.

1.2.3 Wave characteristics of electromagnetic radiation

EMR is travelling at a velocity c (=speed of light) equal to 3*108 m/s in a

sinusoidal, harmonic fashion.

EMR consists of an electrical (E) field and a magnetic (M) field

the wave-like characteristics of

EMR allows the distinction with

regard to wavelength e.g.

microwave, infrared radiation

in order to understand the

interactions between EMR

and the Earth’s atmosphere

and surface.





Source: CCRS tutorial

Characterisation of electromagnetic waves

Wavelength ---- length of one wave cycle

λ = distance between successive wave crests

Frequency ---- number of cycles (or crests) of a wave passing a fixed f point per unit of time ( = 1 sec)

Wavelength and frequency are related according to

c= λ * f

c --- speed of light (is essentially constant) = 3*108m/s (in a vacuum)

λ --- unit is [m] or mm, m, m

f --- unit is [Hz=cycle/sec] inverse is period T = 1/f

= time elapsed in seconds per cycle





Examples:

Source: CCRS tutorial

Explanation

i) 2.5 cycles per second f = 2.5Hz

period = 0.4 sec per cycle

ii) 4 Hz

iii) 1.5 Hz

Example 1: Given f = 4 Hz, calculate λ:

with c = λ*f = 3*108 m /sec = 300 000 km/sec

and f = 4 Hz

λ = c/f = (3*108m/sec)*(1/4)sec = 75 000 km





Example 2: Given wavelength in micrometers, λ = 1µm, calculate f:

λ = 1µm (Near infrared)

= 10-6m

f = (3*108m/sec) / (1/10-6m) = 3*1014 Hz

These examples demand for a closer look to the EM spectrum.

1.2.4 Corpuscular characteristics of electromagnetic radiation

In the particle description, electromagnetic energy travels in quanta

(discrete units) of energy.

The energy of a quantum is given as

Q = h * f

Q = energy of a quantum (Joules J)

h = Planck’s constant h=6.26*10-34 J*sec

f = frequency (Hz=1/sec)

Energy Q is delivered to a target.

Note: delivery is on a probabilistic basis - not in such a

way that it is evenly spread over the wave





Relate the wave model to the quantum model

Substituting f = c/λ into Q = h*f

yields Q = h*c/λ h*c = constant

Conclusion:

The shorter the wavelength , the higher the energy content

and vice visa shorter wavelengths are easier to sense.





The Electromagnetic Spectrum

The electromagnetic spectrum represents the continuum of

electromagnetic energy

from extremely short wavelengths (cosmic and gamma rays)

to extremely long wavelengths (radio and television waves)





The names assigned to regions of the spectrum make a discussion of the

spectrum more convenient. In each of the regions adjacent

wavelengths ‘’behave similarly’’ or are generated by similar

mechanisms.

However the division between UV and visible or microwave and

thermal infrared is not hard. The regions blur into each other.

Three regions are of particular importance for RS:

a) The visible spectrum (visible light)

is so called because it is detected by the eyes, whereas other forms of

EMR are invisible to the unaided eye.

The spectrum range of visible light is 0.4-0.7 um

wavebands are perceived as particular colours:

waveband

violet -- blue -- green -- yellow - orange -- red

0.40 0.46 0.50 0.58 0.60 0.62 0.70 µm

Blue, green and red are the primary colours or wavelengths of the

visible spectrum. All other colours can be formed by combining

R-G-B.





b) The infrared spectrum (infrared = beyond the red)

covers the wavelength range from approximately 0.7 µm to 100 µm

Regions: Near IR Mid IR Thermal/Far IR

Note: different definitions/boundaries are found in the literature.

c) The microwave spectrum

ranges from submillimetre to 1 (to 3) metres

further subdivided in bands : K, X, C, S, L, P – band

Some microwave sensors can detect small amounts of radiation at

those wavelengths that are emitted by the Earth. passive sensors

But the important RS microwave sensors are all active systems

Generation, transmission and recording of the reflected radiation

0.7 100 1.3 3.0 µm

Radiation property

reflective emissive, radiative, thermal

reflected energy

≈ visible light

emitted from Earth’s surface in the form of heat





Question: which spectral bands can be used most effectively in RS?

Figure: Wavelengths that can be used most effectively

depends on interaction with the Earth’s atmosphere

(particles and gases in the atmosphere)

obviously absorption (cf. figure above) happens not everywhere and

not to the same degree in the spectrum

high spectral transmission in the visible area and other

“atmospheric windows”

energy level of the sun has its peak in the visible area

all passive RS sensor systems have to take these two aspects

(transmission and energy) into account.

the heat energy emitted by the Earth corresponds to a windows around

10 µm (max energy) in the thermal IR





1.4 Interaction of Electromagnetic Radiation with the

Atmosphere

As the energy travels from a source (the sun) to the target (the Earth’s

surface) it interacts on its travel with the Earth’s atmosphere.

Interaction with particles and gas molecules in the

atmosphere

The total amount of radiation that strikes an object is equal to

reflected off absorbed by transmitted through

the object the object the object

Two mechanisms of interaction:

scattering absorption

reflected

radiation

absorbed

radiation

transmitted

radiation

incident

radiation + + =





1.4.1 Scattering

Particles or large gas molecules present in the atmosphere cause

the EMR to be redirected from its original path.

How much scattering takes place depends on

the wavelength of the radiation

the abundance of the particles or gases

the distance the radiation travels through the atmosphere

Three types of scattering take place:

a) Rayleigh scattering

occurs when particles are very small (0.1 µm and less)

compared to the wavelength of the EMR

particles: small specks of dust or nitrogen and oxygen

molecules

shorter wavelengths of energy are much more scattered than

longer wavelengths

Rayleigh scattering is the dominant scattering

mechanism in the upper atmosphere





Remarks:

Blue sky phenomenon (during the day) ---- stronger scattering of the

blue wavelength of the sunlight

the blue light seems to reach our eyes from all directions

Sunrise and sunset ---- the scattering of the shorter

wavelengths is more complete (longer distance through

atmosphere)

longer wavelengths (orange, red) penetrate

b) Mie scattering

occurs when particles are just above the same size

as the wavelength of the radiation

particles: dust, pollen, smoke (industrial or domestic pollution),

water vapour, salt particles from oceanic evaporation

Mie scattering tends to affect longer wavelengths than those

affected by Rayleigh scattering.





occurs mostly in the lower portions of the atmosphere

where larger particles are more abundant.

dominates when cloud conditions are overcast.

(a) and (b) are selective scattering processes i.e. scattering affects

specific wavelengths of energy.

c) Nonselective scattering

occurs when the particles are much larger than the wavelength

of the radiation (above 10 µm)

particles: water droplets, ice fragments, large dust particles

all wavelengths are scattered about equally

causes fog and clouds to appear white to our eyes.

All wavelengths are scattered (by the water droplets) in

approximately equal quantities. (∑ white light)





1.4.2 Absorption

Molecules present in the atmosphere absorb energy at various

wavelengths.

The three main constituents (gases) which absorb radiation are

ozone

carbon dioxide

water vapour

Ozone absorbs the harmful UV radiation from the sun.

protective layer in the atmosphere avoids skin burn

Carbon dioxide — the “greenhouse gas”

tends to absorb radiation in the far infrared portion of

the spectrum thermal heating

and serves to trap this heat inside the atmosphere.

Water vapour absorbs much of the longwave IR and shortwave

microwave radiation. The presence of water vapour in the lower

atmosphere greatly varies from location to location and at different times

of the year.

(Little water vapour above deserts but high humidity in the tropics)





These gases absorb EM energy in very specific regions of the spectrum

(called absorption bands ). Those areas which are not severely

influenced by absorption are called atmospheric windows. .

(= areas which are useful for RS purposes).

cf. figure in section 1.3 transmission





1.5 Interaction of EMR with Earth surface materials

Electromagnetic energy that is not absorbed or scattered in the

atmosphere can reach and interact with the Earth’s surface.

Three forms of interaction:

Absorption

Transmission

Reflection

The total incident energy will interact with the target in one or more of

these three ways.

The proportions of each will depend on

The wavelength of the EMR

The material and condition of the target

Target dependency: There will be a variation of the interaction from time

to time during the year.

Example: vegetation, from leafing stage to maturity.





A: absorption: radiation is absorbed into the target

T: transmission: radiation passes through a target

R: reflection: radiation “bounces” of the target, is redirected

reflected energy travels upwards through the atmosphere

(interaction with the atmosphere)

that part which enters the field of view of the sensor is

detected and recorded by the sensor

most interest in RS is in measuring radiation reflected from

targets

Amount and distribution of reflected energy are used in RS to infer

the nature of the reflecting surface.

Background: basic assumption made in remote sensing is that specific

targets (soils, rocks, vegetation, water, ) have an

individual and characteristic manner of interacting with

incident radiation.





spectral response

Distinction between two types of reflection that occur at a surface:

specular reflection diffuse reflection

mirror-like

directed away in a

single direction

(no scattering)

αi = αr

reflected almost

uniformly in all

directions (scattered in

all directions)

like a piece of paper

- specular and diffuse reflection represent the two extreme ends of the

way in which energy is reflected

- most Earth surface features are located somewhere between

perfectly diffuse or perfectly specular

αi

incidence

angle

reflection

angle αr





- but: in the visible part of the spectrum

terrestrial targets ≈ diffuse reflectors

calm water ≈ specular reflector

diffuse reflector -- rough surface

specular reflector -- smooth surface

Rough/smooth is defined by surface variations or particle sizes

that make up the surface in comparison to the wavelength of the incoming

radiation

Example: fine-grained sand

would appear fairly smooth to microwaves (long

wavelength) but quite rough to the visible (short wavelength).





Examples: target interactions --- leaves/vegetation and water

--- visible and infrared wavelength

Spectral response curve / pattern

(sometimes also called the spectral signature )

A spectral reflection curve describes the spectral response of a target for

a certain region e.g. 0.4 - 2.5 µm.

Note: A satellite sensor operating in the visible and NIR region does not

observe and detect all reflected energy FOV.

To make use of such measurements, the distribution of radiance

all possible observation and illumination angles, called the

bi-directional reflectance distribution function (or BRDF) must be

taken into consideration

water (1)

water (2)

vegetation 20

10

30

0.5 0.7 0.6 0.4 0.8 λ (µm)

reflectance

%





Spectral response curses for about 2000 materials can be found in the

JPL ASTER library:

e.g. 9 different ones for water/ snow/ ice

1350 minerals

etc.……

Reminder

Example

1. leaves: lower reflection = higher absorption in B, R

higher reflection in G

very higher reflection in IR ---- not plotted

2. water: lower reflection = higher absorption in R, NiR

darker if viewed in R, NiR

higher reflection in B, G

water looks blue, green

violet blue green yellow orange red

0.4 0.46 0.50 0.58 0.60 0.62 0.70





Example

Target interaction with leaves

Summer : chlorophyll content is at its maximum “greenest”

Autumn : less chlorophyll

healthy leaves: internal structure of leaves act as all excellent diffuse

reflector of NiR wavelengths

extremely bright ( but not visible to our eyes )

measure + monitor the near-iR reflectance to determine healthiness

of vegetation

Target interaction with water

longer wavelength radiation R, NiR is absorbed more by water

than shorter wavelength

water looks blue or blue-green due to stronger reflectance

of B,G and darker if viewed in R, NiR

Chlorophyll absorbs radiation

in B, R wavelengths but

reflects G





If sediment is present in the upper layers of the water body.

slight shift to longer wavelengths ( green, yellow ) because of a

better reflectivity brighter appearance of water.

Chlorophyll (algae) absorbs blue, reflects green

water will appear in a more green colour

Topography of the water surface (rough, smooth, floating material,

etc.) can also lead to complications for water-related interpretations

due to problems of specular reflection or other influences on colour or

brightness.

spectral response can be quite variable, even for the same target

type, and can also vary with time and location.

important to know where to “look” spectrally

Water and vegetation is similar in the visible area but

completely different in NiR





1.6 Energy Sources and Sensing

The sun is the most obvious source of the electromagnetic energy

measured in remote sensing. The sun’s energy is either reflected

(visible, reflected iR) or absorbed and re-emitted (thermal iR).

EM energy that is naturally available comes from a passive source.

The RS instruments which detect the naturally available energy are called

passive sensors.

Passive source:

solar energy

Visible

iR (include thermal)

UV, X- and Gamma-ray

Passive sensors: Can only be used to detect energy when natural energy is available. reflected energy: -- requires illumination of the Earth (daytime)

re-emitted energy: -- can be detected day or night, as long as the amount of energy is large enough.





Sensing

Recording with passive sensors: Reflected energy is mainly recorded by

instruments which travel in sun-synchronous orbits (the satellite

travels southwards over the illuminated side of the Earth and crosses the

Equator at the same local Sun time on each orbit). Data are recorded only

on the way from North pole to South pole because the other

half of the orbit is in the Earth shadow.

Active sensors provide their own energy source for illumination.

The sensor emits radiation which is directed toward the target.

The reflected radiation is detected and recorded by the sensor.

Active sensors can be used to examine wavelengths that are not

sufficiently provided by the Sun, such as microwaves.

Microwave imaging radar (synthetic aperture radar, SAR) and laser

scanner (airborne platform) are examples of active sensors.

Man-made energy source

An active system requires the

generation of a fairly large amount

of energy to adequately illuminate

targets.





1.7 Satellite Images and Colour Display

Satellite-borne sensors record digital images in channels or bands

which represent reflected radiation of specific wavebands.

Example:

SPOT 1, 2

(2 HRV-instruments)

SPOT 4

1986, 1990 1998

XS-bands 0.50 – 0.59 um 1.58 –1.75 um

(mid iR

additionally)

0.61 – 0.68 um

0.79 – 0.89 um

M (= pan) band 0.51 – 0.73um

Note: SPOT3, launched in 1993, failed.

Data formats for digital satellite imagery

Unfortunately, no world-wide standard for storage and transfer

of remotely-sensed data has been agreed upon specific

procedures for reading satellite image data requested

CEOS (Committee on Earth Observation Satellites) tries to

standardise.

Display of satellite images

Display of one band: grey scale image

Display of three bands: pseudo colour image





Example: (Honolulu data)

6 bands, wavelength between 0.4 and 12 µm

Note: different waveband width of the individual bands.

Inspection of three images of Honolulu (cf. the corresponding pictures)

Band 2 0.45 – 0.52 um (blue-green 0.46–0.5–0.58 µm)

Band 7 0.76 – 0.90 um (NiR 0.7 – 1.0/1.3 µm)

Band 11 0.5 – 14.0 um (thermal iR 3 – 15 µm)

Observation: For different regions of Honolulu different brightness levels

can be observed in different wavebands

value of obtaining multiple images at different wavelength.

Discussion:

1) Region indicated by (a) in band 2

blue wavelength: one can see through the shallow water

along the coast line.

2) Region (b) in band 2 and band 7

blue: rain forest appears fairly dark

NiR: rain forest (vegetation) appears quite bright.

reflective nature of chlorophyll.





3) Region (c) in band 11

Thermal iR: dark patches are clouds, which in the thermal iR are

cold.

Blue, NiR: at shorter wavelengths the high reflectivity of the water

droplets leads to bright patches.

4) Region (d) in band 11

Bright areas in the thermal band that are dark in the other bands.

Areas (d) include parts of the airport runways which are facing the

sun are warmer than the average scene and so are bright.





Chapter 2

Preprocessing of the Remotely-sensed Data

The raw remotely-sensed image data generally contain flaws or

deficiencies. Removal of flaws and correction of deficiencies are termed

preprocessing. Some corrections are carried out at the ground

receiving station.. Nevertheless there is often a need on the user’s

part for some further preprocessing.

Preprocessing may include:

Corrections for geometric, radiometric and atmospheric deficiencies

Removal of flaws (data errors)

Note: not all operations will be applied in all cases.

2.1 Removal of data error

Defects in the data can be due to errors in the scanning or sampling

equipment or in the transmission or recording of image

data.

a) Partially or entirely missing scan lines

are normally seen as horizontal black (0) and white (255) lines on the

images.





b) Horizontal banding pattern

electro-mechanical scanners (Landsat’s MSS and TM) have several (a

small number of) detectors that are used in the scanning process. The

imbalance in the six (MSS) detectors shows up by strips (banding

pattern) in the image.

Missing scan lines and banding patterns can be considered to be a

cosmetic defect that interferes with the visual appreciation of the patterns

on the image. It might be even more problematic for statistical/pattern

analysis of images.

a) Missing scan lines

There is no means of knowing which values should be present at missing

scan lines.

Solution: Estimate the values by looking at the data values of

the scan lines above and below.

Background:

Spatial autocorrelation = points that are close geographically tend to

have similar values.

Therefore, neighboring pixels of objects will strongly correlate





Processing for replacement of missing scan lines

Option 1: Replace a missing pixel value by the value of the

corresponding pixel on the immediately preceding scan line.

Option 2: Replace the missing value by the average of the

neighbouring pixels on the scan lines above and below of a defective line.

I (i, k) = (I (i, k-1) + I (i, k+1))/2

Note: read as ''pixel i on scan line k''

Option 3: Use the neighboring bands of multi-spectral imagery.

For instance, the Landsat (1 to 3) MSS band 4 (green) and 5 (red) are

normally highly correlated. In general, bands in the same region of the

spectrum are highly correlated and can be used to correct missing scan

lines.

I ( i, k, b) = σb/σr*( I( i, k, r) - ( I(i, k+1, r) + I(i, k-1, r) )/2 )

+ ( I(i, k+1, b)+ I(i, k-1, b) )/2

b, r -- bands

Detection of missing scan lines

is a tedious task if such lines are located interactively (by visual

examination)

k

band b band r





the auto-correlation property can be used for semi-automatic

localization. E.g. by comparison of the average grey values of

neighbouring scan lines. In case of large differences search along

these scan lines for unexpected sequences of values (strings of either

0's or 255's). Mark the suspected sequence and display it for inspection

by a operator.

b) De-striping methods

A horizontal banding pattern is sometimes seen on Landsat’s MSS and

TM data. (electro-mechanical scanners). This pattern is more apparent

when seen against a dark, low-radiance background such as water

areas. The MSS has six detectors for each band (MSS: 4 spectral

bands) why the banding pattern is known as sixth-line banding in Landsat

MSS images. TM has 16 detectors per band and produces seven bands

of imagery.

The underlying idea of de-striping is based upon the assumption that

each detector “sees” a similar distribution of all the land cover

categories that are present in the imaged area. In consequence,

the histograms generated for a given band from the pixel values

produced by all n detectors should be identical. This implies that

the mean and standard deviation of the data from each detector should

be the same. To get rid of the stripping effects the means and standard

deviations are calculated from lines 1, 7, 13, 19, …… (histogram 1),





lines 2, 8, 14, 20, ……(histogram 2) and so on (MSS six detector

situation).

All n histograms are equalized by forcing mean and standard deviation

to be equal to the corresponding average values of mean and standard

deviation of all of the pixels in the image.

2.2 Registration and geometric correction

Registration is the fitting of the coordinate system of one image

to that of a second image (or map) of the same area.

Geometric correction or rectification is a related technique. An image is

transformed so that it has the scale and projection properties of a

map.

The integration of information extracted from remotely-sensed images

with map data into a GIS requires registration. Image

registration, also called rubber-sheeting, is typically defined by a

polynomial transformation of an image to a set of control points.

For presentation of RS images in a map-like form rectification (geometric

correction) has to be carried out. Rectified images can be overlaid with

maps or used to locate features of interest on the map and the image.

Rectification may also be used to bring adjacent images into

registration or to overlay images of the same area acquired by

different sensors. Rectification procedures of photogrammetry range from

simple plane rectification to the more complex process of generating

digital orthophotos.





Sources of geometric errors in digital satellite imagery are

instrument errors

- distortions of the optical system, non-linearity of the scanning

mechanism and non-uniform sampling rates.

panoramic distortion

is a function of the angular field of view and affects instruments with wide

AFOV (such as AVHRR) more than those with a narrow AFOV (Landsat

MSS + TM, SPOT HRV)

Earth rotation

During the movement of a satellite southwards above the earth’s surface

the Earth moves eastwards thus the effect of Earth rotation is to skew the

image.

Skew angle at latitude L:

θ = 900- arccos (sinθEquator / cos L )

Satellite’s

ground track

scan lines at time t1

Potential scan lines at time t2

without Earth rotation

scan lines at time t2 with Earth rotation





platform instabilities

Include variations in altitude and attitude . The information needed

to correct for the variations is not generally available (modern

satellites carry GPS, INS, star sensors, ……) or not precise enough

for correction of the image data. Therefore a correction band on

nominal orbital parameters must be replaced by a transformation using

ground control points.

Instead of the attempt to define the sources of error and their effects an

alternative method is to look at the problem from the opposite end ,

the differences between the positions of points recorded on image and

map can be used to estimate the distortions present in the image.

Processing:

a) Relate the image and map coordinate system by an empirical

transformation.

--- commonly polynomials of second or third order are used for

map-to-image (image-to-map) coordinate transformation.

b) Locate suitable ground control points by using GPS or locate gcp’s

on the map and measure its corresponding image coordinates.

Note: gcp chips (19*19 pixels) of existing image maps may also be used.

c) Estimate the transformation parameter by least squares

and

d) Determine the pixel values of the rectified image by resampling

(gray scale interpolation)





Third-order polynomial for mapping (x, y) map coordinates to (r, c) image

coordinates (and vice versa).

X = a00+a10*c+a01*r+a20*c2+a11*c*r+a02*r

2+a30*c3+a21*c

2*r+a12*c*r2+a03*r3

Y = b00+b10*c+b01*r+b20*c2+b11*c*r+b02*r

2+b30*c3+b21*c

2*r+b12*c*r2+b03*r3

The unknowns are the parameters aij, bij of the transformation.

First order polynomial: 6 unknowns ( 3 or more gcp’s)

Second order polynomial: 12 unknowns ( 6 or more gcp’s)

Third order polynomial: 20 unknowns ( 10 or more gcp’s)

To have reasonable redundancy significantly more gcp’s should be used.

Experience:

Around (<) 10 gcp’s give acceptable result for a first-order fit with a

small image area of up to 10242 pixels.

More gcp’s will be needed in area of moderate relief (where a second-

order polynomial may be required)





2.3 Atmospheric correction

From Chapter 1 it is already known that a value recorded at a given pixel

location is not a recording of the true ground-leaving radiance at

that point. Scattering redirects some of the incoming EM energy and

some of the reflected EM energy within the atmosphere into the field of

view of the sensor.

Relationship for estimating atmospheric effects on multi-spectral images

in the 0.4 – 2.4 µm reflective solar region:

LS = Htotal * ρ * T + LP (2.1)

Htotal is the total downwelling radiance in a specific spectral band

sensor

ground





ρ is the reflectance of the target.

(ratio: “downwelling”/“upwelling” or irradiance/radiant emittance)

T is the transmittance given by the transmission curves as a

function of the wavelength.

LP is the atmospheric path radiance.

The reflectance ρ relates to the interaction of EMR to the target,

the transmittance to the interaction with the atmosphere.

Model (2.1) is a simplified model which does not explicitly take account of

the following aspects:

reflectance of a surface will vary with the view angle as well as with the

solar illumination angle (particularly important for wide FOV and off-

nadir viewing)

the slope of the ground and the disposition of topographic features.

More complex models are developed but operational use of these models

is limited by the need to supply data relating to the condition of

the atmosphere at the time of imaging. The costs of such data-collection

activities is considerable, hence reliance is placed upon the use of

“standard atmospheres” such as “mid-latitude summer”. In this case

only a very small number of parameters, e.g. the horizontal visibility

in kilometres have to be supplied.





Atmospheric correction might be beneficial in three cases:

1) If ratios of the values in two bands of a multi-spectral image are

computed

e.g. the normalised difference vegetation index.

NDVi=(NiR-R)/(NiR+R)

study vegetation patterns

A simple technique for compensation of atmosphere path radiance

might be sufficient.

2) If upwelling radiance from a surface is related to some property of

that surface in terms of a physically based model

=> the atmospheric component must be estimated and removed.

3) If results found at one time are to be compared with results achieved

at a later date

=> the state of the atmosphere will undoubtedly vary from time 1 to

time 2.

R

NiR

Estimate of path radiance





2.4 Sensor calibration

Sensor calibration, combined with atmospheric and view angle correction,

aims at the estimation of target reflectance. A number of

methodologies for the calibration of the Landsat TM optical bands, SPOT

HRV, other optical sensors and Radar are proposed.

The relationship between radiance and pixel value (PV) can be defined

for spectral band as

Ln* = a0 + a1 *PV

Where a0 and a1 are offset and gain coefficients and Ln* is apparent

radiance at the sensor. (Measured in units of mW/(m*sr*µm))

Spot provides gain values ai in the header of the XS image. The

apparent radiance of a given pixel is calculated from

L = PV/ ai

Given the value of radiance L it is usual to convert to apparent reflectance

by

ρ= (π*L*d2)/(ES*cos(θS))

d = relative Earth - Sun distance

Es = exoatmospheric solar irradiance

θs = solar zenith angle (Reference: Floyd F. Sabins, Remote

Sensing: Principles and Interpretation, 3rd edition, W.H.Freeman and company, 1997

Note: ρ is not corrected

for atmospheric effects





Chapter 3 Classification

3.1 Supervised and unsupervised classification

Image classification can be decided into two categories:

Supervised and unsupervised classification.

Supervised classification refers to the process of measuring

characteristic features of the entities (or objects) one wants to classify

by using training sets of known objects or object classes

and use them to determine the class membership of all other pixels in an

image.

Unsupervised classification is a clustering process which aims

at the determination of the number of distinct, naturally occurring

groups and the allocation of pixels to these groups (or classes). In this

respect it can be considered as a segmentation technique which

aims at subdividing an image into meaningful regions.

In both cases the properties (features) of the pixel to be classified are

used to label that pixel. In the simplest case, a pixel is

characterised by a vector whose elements are its grey levels

in each spectral band. This feature vector (also called pattern) represents

the spectral properties of that pixel. Further features such as

texture or context may be included in the feature vector.





Note: If classification does not lead to proper results:

i. try to find a more sophisticated classification scheme not

recommended

ii. try to find better or more features, e.g. from other sensors (Laser,

Radar, in addition to optical sensors) or existing databases (DTMs,...)

3.2 Scatterplot (scattergram) and decision making

A scatterplot is one of the easiest ways to perceive the distribution of

values measured on two features. One feature is plotted against the

other for each pixel and the vector (feature 1, feature 2) determines the

position of that pixel in the two-dimensional Euclidean space.

Example

Pixel Feature 1 / R Feature 2 / NiR

Water body low low

Vigorous vegetation

Low high

Feature 2

NiR, 255

Feature 1

R, 255

0

0





The position of a point in the feature space is directly

related to the values of the two features. Obviously points belonging to

the same class tend to cluster and points belonging to different classes

tend to be separated. This is the underlying assumption

of any classification scheme.

Example 2

R NiR MidiR

Water body low low low

Shadow region low low Any grey value possible

Adding a third feature leads to a three-dimensional scattergram. The

problem of N-dimensional feature spaces is that they can not be

visualised properly.

3D 1+2 3 two-dimensional scatterplots

4D 1+2+3 6 two-dimensional scatterplots

5D 1+2+3+4 10 two-dimensional scatterplots

Decision making:

Given a scatterplot (cf. figure 3.2 ) one can recognise

Two district clusters

The compactness of each cluster

The distance in feature space (example: d12, d23 )

A linear decision boundary (boundary between two clusters/classes)

use several 2D

scatterplots ?





Figure 3.2 Decision making

3.3 Supervised classification

Supervised classification methods require external knowledge of

the area shown in the image. This knowledge may be derived from

fieldwork, analysis of aerial photos, maps or other sources like reports.

Most statistical methods assume that the type of the distribution of

features in each class is known and only parameters derived from sample

data ( training samples ) have to be estimated before using them to

make classification decisions. (Parametric decision making or parametric

classification methods.)

Training samples (learning phase)

Task: Determine statistical characteristics of each class (the number of

classes must be known)

If X is a feature vector: X =

Feature 2

Feature 1

②

③

①

feature value 1 feature value 2 feature value n





Determine:

mean X

extreme values: min, max, for each feature in each class

variances and covariances –> variance–covariance matrix

Supervised classification methods

1) Parallelepiped or box classifier

all points within min-max region (box)

class i

all other points are unclassified

2) K-means or centroid method

calculate mean/centre X of each training class

calculate Euclidean distance from each unknown pixel

to the centre of each class. The pixel is given the label of the

centre to which its distance is smallest. (nearest centre decision)

2X

4X

3X

1X3X





In n-dimensional feature space the decision boundary corresponds to a

hyper plane which is perpendicular to the line connecting the two

centroids 1X and 2X .

3. Maximum likelihood method

If one of two neighbouring clusters is much smaller than the other one, it

makes sense to move the boundary between them closer to the

centroid of the smaller one. Similarly, if the clusters are elongated in a

certain direction, the boundary should be tilted toward the direction of

their elongation.

model of probability distribution (Gaussian normal distribution)

variance

covariance

matrix

Probability that P belongs to 1X is higher than probability that

P belongs to 2X .

2X P

equi-probability

contours

1X





3.4 Unsupervised classification

Occasionally points will form such distinct clusters that automated

means of discovering which points belong together with be successful.

This process is referred to unsupervised learning.

Principles of automatic cluster formation

1. Each point is considered a separate embryonic cluster. In an iterative

process points (clusters) are merged together if they are closer

than any other two points. The iteration stops either when the

expected number of clusters has been found or when the next points

to be added to a clusters is more than some threshold distance away.

K-means clustering

2. Initially the whole collection of points is considered to be one huge

cluster. Iteratively, existing clusters are split along lines of

weakness in two clusters. The splitting is repeated until some limits

(max number of expected clusters) are passed. Splitting can be

combined with merging to improve the results.

ISODATA algorithm

(Iterative Self-Organising Data Analysis Technique)

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