neighborhood and multiband operations

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1

GNR630 Introduction to Geospatial

TechnologiesInstructors: Prof. (Mrs.) P. Venkatachalam

Prof. B. Krishna MohanProf. S.S. Gedam

CSRE, IIT Bombaypvenk/bkmohan/[email protected]

Slot 6

Lecture 5-6 Neighborhood Operations and Multiband Operations

January 20/25, 2012 11.05AM – 12.30PM

Contents of the Lecture

• Concept of Neighborhood

• Image Smoothing

• Edge Enhancement

• Color Transforms

• Band Arithmetic

IIT Bombay Slide 1

GNR630 Lecture 5-6 B. Krishna Mohan

January 20/25, 2012 Lecture 5-6

Neighborhood Operations and Multiband Operations

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Neighborhood Operations

Pixel and Neighborhood

A B C

D X E

F G H

• Pixel under consideration X

• Neighbors of X are A, C, F,H, B,D,E,G

• Size of neighborhood = 3x3

• Neighborhoods of size mxn m and n are odd; Unique pixel at the centre of the neighborhood


IIT Bombay Slide 02

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4-neighborhoods

A B C

D X E

F G H

• B,D,E and G are the 4-neighborhood of X

• 4-neighbors are physically closest to X, at

one-unit distance


IIT Bombay Slide 03

8-neighborhood

A B C

D X E

F G H

• A,C,F and H are ALSO included with B,D,E,G as neighbors; 8-pixel set is the 8-neighborhoodof X

• A,C,F and H are the diagonal neighbors, sqrt(2)

times farther from X


IIT Bombay Slide 04

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Larger Neighborhoodso o o o o

o o o o o

o o X o o 5 x 5 neighborhood

o o o o o

o o o o o

• Larger neighborhoods used based on need; computational load varies exponentially with size of neighborhood

• 3x3 � 9 neighbors; 5x5 � 25 neighbors …


IIT Bombay Slide 05

Point Operations v/s Neighborhood Operations

• Point operations do not alter the sharpness or resolution of the image

• Gray level associated with a pixel is manipulated independent of the gray levels associated with neighbors

• Pixel operations cannot deal with noise in the image, nor highlight local features like object boundaries


IIT Bombay Slide 06

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Neighborhood Effect

• 15 17 16 16 17 19

• 18 17 15 18 70 15

• 17 14 16 16 20 17

• Natural Noise?

• Abnormalities can be located by

comparing a pixel with neighboring pixels


IIT Bombay Slide 07

Neighborhood Effect

• 15 17 16 16 17 50

• 18 17 15 18 50 49

• 17 14 16 49 50 48

Normal region Boundary

• Sharp transitions from one region to

another are marked by large difference in

pixel values at neighboring positions


IIT Bombay Slide 08

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• Results of operations performed on the neighborhood are posted at the location of the central pixel

• The values in the input image are not overwritten, instead the results are stored in an output array or file

• Cannot be computed in real time since the configurations of gray levels in the neighborhood are very large


IIT Bombay Slide 09


• Simple averaging

A B C

D X E

F G H

• g(X) = (1/9)[f(A) + f(B) + f(C) + f(D) + f(X) +

f(E) + f(F) + f(G) + f(H)]

• The output gray level is the average of the gray levels of all the pixels in the 3x3 neighborhood


IIT Bombay Slide 10

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Example15 17 16 15 17 1618 17 15 18 57 1517 14 16 17 14 16Case 1 Case 2

• In case 1, after averaging, the central element 17 is replaced by the local average 16 –negligible change

• In case 2, after averaging, the central element 57 is replaced by 21 – significant change

• Averaging is a powerful tool to deal with random noise


IIT Bombay Slide 11

Neighborhood Operations -Procedure

• The procedure involves applying the computational step at every pixel, considering its value and the values at the neighboring pixels

• Then the neighborhood is shifted by one pixel to the right and the centre pixel of the new neighborhood is in focus

• This process continues from left to right, top to bottom


IIT Bombay Slide 12

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Image

Processing step


IIT Bombay Slide 13

Mathematical form for averaging

• In general, we can write

g(X) =

where K is the number of neighbors Ai. A5 refers to X, the central pixel for a 3x3 neighborhood.

• It is obvious that all neighbors are given equal weightage during the averaging process

1

( )

| ( ) |

K

i

i

f A

N X

=

∑


IIT Bombay Slide 14

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General form for averaging• In case different weights are preferred for different

neighbors, then we can write

• g(X) =

• For simple averaging over a 3x3 neighborhood, wi = (1/9), i=1,2,…,9

• We can alter, for example, the weights for 4-neighbors and 8-neighbors. In such a case, wi is not a constant for all values of i.

1

1

( )K

i i

i

K

i

i

w f A

w

=

=

∑

∑


IIT Bombay Slide 15

Averaging as Space Invariant Linear Filtering

• In signal processing terminology, the weighted averaging

can be represented by convolution:

k,l= -w, …, 0, …, w

For a 3x3 window, w=1; For 5x5 window, w=2, …

, , ,

,

1

(2 1)(2 1)

l j wk i w

i j k l i k j l

k i w l j w

k l

g h f

hw w

= += +

− −

= − = −

=

=+ +

∑ ∑

2-d discrete convolution of h with f: g = f*h


IIT Bombay Slide 16

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Concept of Convolution

• Convolution is a weighted summation of inputs to produce an output; weights do not change anytime during the processing of the entire data

• If the input shifts in position, the output also shifts in position; character of the processing operation will not change

• The weights with which the pixels in the image are modified are represented by the term filter


IIT Bombay Slide 17

Filter Mask

• The filter can be compactly represented using the weights or multiplying coefficients:

• e.g., 3x3 averaging filter

• 0.111 0.111 0.111 1 1 1

• 0.111 0.111 0.111 or (1/9) 1 1 1

• 0.111 0.111 0.111 1 1 1

• This implies that the pixels in the image are multiplied with corresponding filter coefficients and the products are added


IIT Bombay Slide 18

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Reduced neighborhood influence

0.05 0.15 0.05

0.15 0.20 0.15

0.05 0.15 0.05

• Central pixel is given 20% weight, 4-neighbors 15% weight. Diagonal neighbors given 5% weight.

• Note that the weights are all positive, and sum to unity


IIT Bombay Slide 19

Image

Filter

Mask

IIT Bombay Slide 20


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Border Effect

• The computation of the filtering operation

is applicable at those positions of the

image where the filter completely fits

inside.

• At the boundary positions, only part of the

filter fits inside the image. At such

positions, the computation is arbitrarily

defined

IIT Bombay Slide 21


Original

Image

IIT Bombay Slide 22


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3x3

ave

rag

ing

IIT Bombay Slide 23


Gaussian smoothing

• Gaussian filter: linear smoothing

• weight matrix

for all where

W: one or two σ from center

)(2

12

22

),( σ

cr

kecrw

+−

=

,),( Wcr ∈

∑∈

+−

=

Wcr

cr

e

k

),(

)(2

12

22

1

σ

IIT Bombay Slide 24


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Median Filter

• Median filter is the most commonly used

non-linear filter for image smoothing

• When the image is corrupted by random

salt-and-pepper noise, median operation is

very effective in removing the noise,

without degrading the input image

• gij = median {fi-k,j-l | k,l=-w, …, o, …, w}

IIT Bombay Slide 25


Mean v/s Median filter• Consider an example:

• 15 17 16 15 17 17

• 18 17 15 157 18 15

• 17 14 16 17 14 16

• Case 1 Case 2• Mean=16 Mean=32

• Median=16 Median=17

• In arithmetic averaging, noise is distributed over the neighbours

• In median filtering, the extreme values are pushed to one end of the sequence after sorting, hence ignored when filtered

IIT Bombay Slide 26


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Algorithm• Consider the size of the window around the pixel

• Collect all the pixels in the window and sort them in ascending / descending order

• Select the gray level after sorting, according to the rank criterion

• It can easily be verified that median and mode filters are nonlinear, according to the definition of linearity

IIT Bombay Slide 27


Example

Median

filtering

Example here

is over 7x7

neighborhood

IIT Bombay Slide 28


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Some Comments• Neighborhood operations can suppress

unwanted noise as well as minor detail in an image, also called smoothing

• Simple averaging with equal weightage to all neighbors is a well known smoothing method

• Gaussian smoothing is another popular smoothing operation

• Median filter is a popular nonlinear smoothing operation

IIT Bombay Slide 29


Edge Enhancement Methods

IIT Bombay Slide 30


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Edge• Edge: boundary where brightness

values significantly differ

among neighbors

edge: brightness value appears to abruptly

jump up (or down)

IIT Bombay Slide 31


IIT Bombay Slide 33


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What Is An Edge?

• An edge is a set of connected pixels that lie

on the boundary between two regions

• The pixels on an edge are called edge points

• Gray level / color / texture discontinuity

across an edge causes edge perception

• Position & orientation of edge are key

properties

IIT Bombay Slide 34


Different Edges

A

Different colors

Different brightness

IIT Bombay Slide 35


Different Intensities

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Locating an Edge

• Locating an edge is important, since the

shape of an object, its area, perimeter and

other such measurements are possible

only when the boundary is accurately

determined

• Edge is a local feature, marked by sharp

discontinuity in the image property on

either side of it

IIT Bombay Slide 36


Principle of Gradient Operator

The interpretation of this operator is that the

intensity gradient is computed in two

perpendicular directions, followed by the

resultant whose magnitude and orientation

are computed by treating the values from

the two masks as two projections of the

edge vector

IIT Bombay Slide 37


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Gradient Edge Detection• Given an image f(x,y), compute

• �f =

• Squared gradient magnitude

|�f|2 =

Gradient direction =

,f f

x y

∂ ∂

∂ ∂

22f f

x y

∂ ∂ +

∂ ∂ arctan

f f

y x

∂ ∂

∂ ∂

IIT Bombay Slide 38


Gradient Directions

Vertical gradient Horizontal gradient

Diagonal gradient

IIT Bombay Slide 39


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Gradient Edge Detectors

• As seen, two mutually perpendicular gradient detectors are required to detect edges in an image, since edges may occur in any orientation.

• Using two mutually perpendicular orientations, an edge in any direction can be resolved in terms of these two orthogonal components

IIT Bombay Slide 40


Roberts Operator• Roberts operator: two 2X2 masks to

calculate gradient; Operates on 2x size neighborhood

gradient magnitude:

r1 = f(A) – f(D); r2 = f(B) – f(C)

r1, r2 gradient outputs from the masks;

direction = arctan(r2/r1)

2

2

2

1 rr +

1 0 0 1

0 -1 -1 0

A B

C D

IIT Bombay Slide 41


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Gradient Edge Detectors• Prewitt Operator

• gradient magnitude:

• gradient direction: clockwise w.r.t. column axis

• p1, p2 are gradient outputs from the masks

2

2

2

1 ppg +=

)arctan( 21 pp=θ

1 1 1 -1 0 1

0 0 0 -1 0 1

-1 -1 -1 -1 0 1

Prewitt 1 Prewitt 2

IIT Bombay Slide 42



• Prewitt Edge Detector (one part of it)

)()1()(' xfxfxf −+=

)1()()1(' −−=− xfxfxf+

x-1 x x+1

-1 0 1

-1 0 1

-1 0 1 = f (x+1) – f (x -1)

More stable than Roberts, robust to noise in the image, and produces better edges. More time consuming,

IIT Bombay Slide 43


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Input image

IIT Bombay Slide 44


Prewitt Operator Output

IIT Bombay Slide 45


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Sobel edge detector

)arctan( 21 ss=θ

2

2

2

1 ssg +=

gradient magnitude:

gradient direction:

1 2 1 -1 0 1

0 0 0 -2 0 2

-1 -2 -1 -1 0 1

Sobel 1 Sobel 2

Compare with Prewitt!

IIT Bombay Slide 46


Laplacian Operator

• The Laplacian operator is based on the Laplace equation given by

• Laplacian operator is discretized version of the above equation and is based on second derivatives along x and y directions

2 2

2 20

f f

x y

∂ ∂+ =

∂ ∂

IIT Bombay Slide 47


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Laplacian Operator

• Filter coefficients

• The discrete version of the second derivative operator:

• [1 -2 1] and [1 -2 1]T in the horizontal and vertical directions

• Superimposing the two,

we get the discrete Laplace

operator

0 -1 0-1 4 -10 -1 0

IIT Bombay Slide 48


Properties of Laplace Operator

• Isotropic operator – cannot give orientation information

• Any noise in image gets amplified

• Faster since only one filter mask involved

• Smoothing the image first prior to Laplace operator is often needed for reliable edges

IIT Bombay Slide 49


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Image Sharpening

• Achieved by two ways:

• Sharp(x,y) = Image(x,y)+ |Image(x,y) –Smooth(x,y)|

• Alternately,

• Sharp(x,y)=Image(x,y) + GradMag(x,y)

IIT Bombay Slide 50


COLOR TRANSFORMS

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Motivation for Color Transforms• In the multiband (>3) datasets that are

provided by remote sensors, we can

choose any three bands to generate color

composites

• By applying suitable transformations, we

can enhance these images based on

principles of color perception

IIT Bombay Slide 51


Visible Range of EMSpectrum

IIT Bombay Slide 52


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Color• Color is determined by the wavelength bands of

the electromagnetic spectrum

• Color is described (perceived) in terms of

– HUE: dominant wavelength in color

– SATURATION: purity of color

• (depends on the amount of white light mixed with the color)

– INTENSITY: actual amount or strength of light

• All of them contribute to our perception of color

IIT Bombay Slide 53


Our Visual System• Our eyes have 2 types of sensors:

– CONES• Sensitive to colored light, but not very effective in

perceiving color in dim light conditions

– RODS• Strongly sensitive to white (panchromatic) light.

Can sense differences in light even in dim conditions. (Our eyes can adjust to lighting conditions and see outlines of objects even in darkness)

IIT Bombay Slide 54


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Cones

• The cones in our eyes consist of three types of elements sensitive to:

• 440 nm (BLUE)

• 545 nm (GREEN)

• 580 nm (RED)

IIT Bombay Slide 55


Color ModelsThey provide a standard way of specifying a

particular color using a 3D coordinate system.

• Hardware oriented:– RGB (display monitors)

– CMYB (printers)

• Image processing oriented:– HSI

IIT Bombay Slide 56


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R-G-B Model• It is an

additive color model.

• An image consists of 3 components, one for each primary color, Red, Green and Blue.

• Appropriate for image displays.

IIT Bombay Slide 57


Relation between RGB-HSI Models

IIT Bombay Slide 58


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IIT Bombay Slide 59


HSI ModelOriginal artwork from the book Digital Image Processing by R.C. Gonzalez and R.E. Woods © R.C. Gonzalez and R.E. Woods, reproduced with permission granted to instructors by authors on the website www.imageprocessingplace.com

RGB-HSI Conversion(See Gonzalez and Woods)

IIT Bombay Slide 60


1

2

1

2

( ) / 3

min( , , )1

1/ 2[( ) ( )]cos if

( ) ( )( )

1/ 2[( ) ( )]360 cos if

( ) ( )( )

I R G B

R G BS

I

R G R BH B G

R G R B G B

R G R BH B G

R G R B G B

−

−

= + +

= −

− + −

= < − + − −

− + −

= − > − + − −

Look for full discussion in downloadable article on the website www.imageprocessingplace.com

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HSI to RGB Conversion• This conversion depends on whether the

color is in the Red-Green zone or Green-

Blue zone or Blue-Red zone.

• In each case the hue varies from 0 to 120,

121 to 240, 241 to 360 degrees

respectively.

IIT Bombay Slide 61


RG Sector

Hue in the range 0o – 120o

B = I(1-S)

R = I [ 1 + S.cosH/{cos(60o-H)}]

G = 1-(R+B)

IIT Bombay Slide 62


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GB SectorHue in the range 120o – 240o

H = H – 120o

R = I(1-S)

G = I [ 1 + S.cosH/{cos(60o-H)}]

B = 1-(R+G)

IIT Bombay Slide 63


CMY Model

• Cyan-Magenta-Yellow is a subtractive modelwhich is good to model absorption of colors.

• Appropriate for paper printing.

IIT Bombay Slide 64


−

=

B

G

R

Y

M

C

1

1

1

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Title

IIT Bombay Slide 65


RGB Additive CMY Subtractive

BR SectorHue in the range 240o – 360o

H = H – 240o

G = I(1-S)

B = I [ 1 + S.cosH/{cos(60o-H)}]

R = 1-(G+B)

IIT Bombay Slide 66


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Application of HSI System• Direct access to color of an object

• Manipulation of color easier

• While processing documents, color based

separation into different files can simplify

processing / recognition

• Data of different sensors can be fused

using the RGB-to-HSI-RGB transformation

IIT Bombay Slide 67


Example

IIT Bombay Slide 68


Original Image After increased saturation

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Image Arithmetic

Multiband Arithmetic• Operations performed on combinations of

multispectral bands

• Ratio, difference, combination of ratio and

difference etc. are widely employed to

emphasize objects with sharply different

response in a pair of bands

IIT Bombay Slide 69


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Motivation

IIT Bombay Slide 70


Multiband Arithmetic

IIT Bombay Slide 71


• In a given pair of bands the response of two objects is generally different.

• Pixel by pixel comparison between images can highlight pixels that have very high difference in reflectance in those bands

• Operations like band difference and band ratio or combinations of them are popularly used for this purpose

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Band Ratio• Very common operation

Ratioi,j(m,n) = Bandi (m,n) / Bandj(m,n)

If Bandj(m,n) = 0, suitable adjustment has to be made (e.g., add +1 to the denom.)

Minimum ratio will be 0; Maximum ratio will be 255

IIT Bombay Slide 72


Inp

ut Im

ag

e

IIT Bombay Slide 73


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Inp

ut Im

ag

e F

CC

IIT Bombay Slide 74


IR/R

IIT Bombay Slide 75


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Band Ratio• For fast computing, approximations can be

made such as:

0 ≤ ≤ ≤ ≤ Ratioi,j(m,n) ≤1, ≤1, ≤1, ≤1, Ratioi,j(m,n)scaled =

Round [Ratioi,j(m,n)x127]

1 < Ratioi,j(m,n) ≤ 255, ≤ 255, ≤ 255, ≤ 255, Ratioi,j(m,n)scaled =

Round [127 + Ratioi,j(m,n)/2]

• Advantage – in one pass image is generated in range 0-255

IIT Bombay Slide 76


Band Difference• Similar to band ratio, band difference can

also be used to account for difference in reflectance by objects in two wavelengths

• Band ratio - more popular in practical applications such as geological mapping

• Topographic effects on the images are reduced by ratioing.

IIT Bombay Slide 77


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Band Multiplication• Pixel by pixel multiplication of two images

• Not used to multiply gray levels in one band with corresponding gray levels in another band

• Used in practice to mask some part of the image and retain the rest of it by preparing a mask image and performing image to image multiplication of pixels

IIT Bombay Slide 78


Band Addition• Similar to Band Multiplication, band addition has

no direct practical application in adding gray levels of two bands of an image

• This method too can be used to mask a portion of the image and retain the remaining part.

IIT Bombay Slide 79


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Specialized Indices• Combination of band differences, ratios

and additions can result in useful outputs that can highlight features like green vegetation

• One such feature is Normalized Difference Vegetation Index (NDVI)

• NDVI(m,n) =

IIT Bombay Slide 80


( , ) ( , )

( , ) ( , )

IR R

IR R

Band m n Band m n

Band m n Band m n

−

+

NDVI• NDVI results in high values where IR dominates

red wavelength. This happens where vegetation is present

• Range of NDVI is [-1 +1]• NDVI has been widely used in a wide ranging of

agricultural, forestry and biomass estimation applications

• It is also used to measure the length of crop growth and dry-down periods by comparing NDVI computed from multidate images

IIT Bombay Slide 81


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Inp

ut Im

ag

e

IIT Bombay Slide 82


NIR

IIT Bombay Slide 83


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RED

IIT Bombay Slide 84


NDVI

IIT Bombay Slide 85


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Other Vegetation Indices

• Simple Ratio = Red/NIR• NDVI6 = (Band 6 – Band 5)/(Band 6 + Band 5)

• NDVI7 = (Band 7 – Band 5)/(Band 7 + Band 5)

• Standard NDVITM = (TM4 – TM3)/(TM4 + TM3)

These are applicable when seven band data like Landsat

Thematic Mapper data are available

For IRS LISS3 imagery, NDVIIRS =

IIT Bombay Slide 86


4 3

4 3

( , ) ( , )

( , ) ( , )

Band m n Band m n

Band m n Band m n

−

+

IRS L4-NDVI

IIT Bombay Slide 87


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Fast Computation of NDVI• Range of NDVI [-1, +1]

• Scale suitably to generate an NDVI image

• For example, NDVIscaled =127(1+NDVI)

• This ensures that the resultant NDVI has a

range of [0 254]

IIT Bombay Slide 88


Selected Reflectance Curves

IIT Bombay Slide 89


From J.R.

Jensen’s

lecture notes

at Univ. South

Carolina

Used with permission

1/19/2012

47

Time Series of 1984 and 1988 NDVI Measurements Derived from AVHRR Global Area Coverage (GAC) Data Region around El Obeid, Sudan, in Sub-Saharan Africa

IIT Bombay Slide 90


From J.R.

Jensen’s

lecture notes

at Univ. South

Carolina


Simple Ratio v/s NDVI

IIT Bombay Slide 91


From J.R.

Jensen’s

lecture notes

at Univ. South

Carolina


1/19/2012

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Data Fusion

Data Fusion• Combine datasets to prepare a superior

dataset

• Stack up all the datasets to create a large higher dimensional dataset – e.g., multitemporal data from same sensor

• Fuse the datasets to create a higher resolution dataset

• Fuse the datasets to create a new dataset that has attributes of individual ones

IIT Bombay Slide 92


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Data Fusion

• Most commonly employed by endusers of

remotely sensed data

• Supported by most software packages

IIT Bombay Slide 93


Introduction• Merging multi-sensor data can help exploit

strengths of various data sets

– Radiometric resolution advantage

– Spatial resolution advantage

– Spectral resolution advantage

– Temporal resolution advantage

IIT Bombay Slide 94


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Spatial Resolution Enhancement

• This is the most common application of

data fusion

– Low resolution images have fewer pixels per unit area due to larger pixel size

– Improve spatial resolution

– High resolution images provide more pixels per unit area by smaller sampling interval (pixel size)

IIT Bombay Slide 95


Zooming is NOT resolution enhancement

• How is spatial resolution enhanced?

• Low resolution � absence of high spatial

frequency content

• High frequency information is to be

transferred from another data source (of

higher resolution)

IIT Bombay Slide 96


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Resolution Sharpening

• Most often, data from the lower spatial

resolution multispectral sensors and the

higher spatial resolution panchromatic

sensors are merged

• Results in multispectral data at higher

spatial resolution

IIT Bombay Slide 97


Multi-sensor Data Merging

Most common operation

• PAN images to sharpen multispectral data

e.g., IRS pan + IRS ms

• Sharpening low resolution multispectral

images with high resolution multispectral

images

For instance, SPOT ms + TM ms

(20 metres) (30 metres)

IIT Bombay Slide 98


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Input Image Preparation• Contrast Adjustment

– Zoom low resolution image to the same physical size of the high resolution image

– Match histogram of the MS image with that of PAN image using histogram based techniques

• Image Registration– Register the zoomed low resolution image to

the high resolution image. This should be accurate to a fraction of a pixel

IIT Bombay Slide 99


Image Sharpening

• MShr = f(MSlr, PANhr) , where

• MS = multispectral Image

• PAN = Panchromatic Image

• lr = low resolution

• hr = high resolution

IIT Bombay Slide 100


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Sharpening Techniques

• Principal Component Analysis method

• Intensity-Hue-Saturation method

• Ratio-based (Brovey Transform)

• Arithmetic algorithm

• Multiplicative

• Wavelet Transform method



RGB-HSI Transform Method• In color images, the spectral information is

contained in the hue and the saturation.

• Hue denotes the basic dominant wavelength of the radiation

• Saturation denotes the purity of the color or is a function of the amount of dilution of the color with white light

• Intensity is an indicator of the strength of the color or the magnitude of the energy that reaches our eye



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RGB-HSI Transform Method• The philosophy in HSI based fusion is to replace

the intensity with the new data set first and then compute the inverse transform of the HSI data set to the RGB coordinate system

• The spatial resolution of the added component and the spectral information in the hue and saturation together provide an enhanced data set compared to the original low resolution multispectral and high resolution panchromatic data sets.



Inp

ut H

igh

Reso

lutio

n Im

ag

eIIT Bombay Slide 104


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Input Multispectral Image



IHS

Reso

lutio

n M

erg

eIIT Bombay Slide 106


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IHS

Reso

lutio

n M

erg

e -

FC

C



TO BE CONTINUED!

neighborhood and multiband operations

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