GNR607 Principles of Satellite Image Processing Instructor: Prof. - - PowerPoint PPT Presentation

GNR607 Principles of Satellite Image Processing

Instructor: Prof. B. Krishna Mohan CSRE, IIT Bombay bkmohan@csre.iitb.ac.in

Slot 4 Lecture 21-23 Image Corrections

• Sept. 15-18, 2014 9.30 – 10.25 AM, 10.35 AM – 11.30 AM,

11.35 – 12.30 PM

Computation of Spatial Transformation

• The first order affine transformation is adequate

to account for a several forms of distortions:

– Skew – Rotation – Scale changes in x and y directions – Translation in x and y directions IIT Bombay Slide 47 GNR607 Lecture 21-23 B. Krishna Mohan

Control Point Selection

Reproduced with permission from the lecture notes of Prof. John Jensen, University of South Carolina

IIT Bombay Slide 46 GNR607 Lecture 21-23 B. Krishna

Source of Ground Control Points

• GCPs are obtained from:

– Survey of India topographic maps (digital

• r paper) at 1:25,000 or 1:50,000 scale

– Other maps with ground reference – Global Positioning Systems (GPS)

• It is important to choose GCPs that are

invariant with time since the map and image are often years apart in time

IIT Bombay Slide 45 GNR607 Lecture 21-23 B. Krishna Mohan

Computation of Spatial Transformation

• Given a map reference, we define the pixel size

such that after geometric correction, the image aligns with the map reference, with a pixel size chosen by the user.

• It may be noted that the size of pixel as

acquired by the satellite can be selected different from the pixel size after geometric correction

IIT Bombay Slide 48 GNR607 Lecture 21-23 B. Krishna Mohan

Spatial Transformation

Reproduced with permission from the lecture notes of

• Prof. John

Jensen, University of South Carolina

IIT Bombay Slide 49 GNR607 Lecture 21-23 B. Krishna Mohan

Errors in Transformation

• If the GCPs selected are in error, the

transformation maps the points in the image inaccurately onto the reference. The error can be measured in terms of the Root Mean Squared (RMS) Error

• RMSerror =

' ' 2 ' ' 2 1

1 ( ) ( )

N

• rig

comp

• rig

comp i

x x y y N

=

− + −

∑

IIT Bombay Slide 50 GNR607 Lecture 21-23 B. Krishna Mohan

Effect of Errors in Transformation Coefficients

• Error for each point is given by
• It is common to select initially more GCPs and

choose those that result in the smallest RMS error

' ' 2 ' ' 2

( ) ( )

• rig

comp

• rig

comp

x x y y − + −

IIT Bombay Slide 51 GNR607 Lecture 21-23 B. Krishna Mohan

Higher Order Transformations

• Sometimes the 1st order affine transformation may not

accurately transform the image onto the map in which case one can choose a higher order polynomial transformation such as

2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2

' ' x a x b xy c y d x e y f y a x b xy c y d x e y f = + + + + + = + + + + +

Based on the order of transformation, the number of coefficients vary. Accordingly the number of minimum GCPs also vary. Commercial products support 1st – 5th order transformations. IIT Bombay Slide 52 GNR607 Lecture 21-23 B. Krishna Mohan

Resampling or Intensity Interpolation

• The transformation is of two types:

– Forward mapping or input to output mapping, i.e., for every pixel in the input image find the corresponding location in the reference map according to the determined transformation – Reverse mapping or output to input mapping, i.e., for every pixel in the output frame find the corresponding location in the input image according to the determined transformation IIT Bombay Slide 53 GNR607 Lecture 21-23 B. Krishna Mohan

Intensity Transformation

Reproduced with permission from the lecture notes

• f Prof. John

Jensen, University

• f South Carolina

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 54

Intensity Interpolation

• In this phase, gray level values are

computed for the transformed pixels since they are now at different locations from where they collected the reflected energy

• This step involves intensity interpolation

since the computed values are weighted averages of existing measured values

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 55

Interpolation Strategy

• It is more convenient to use reverse

mapping or output to input mapping when geometrically correcting multispectral images

• The reference frame can be assigned a

given pixel size, and each pixel can then be located in the input image through the spatial transformation

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 56

Intensity Interpolation

Reference frame To be corrected

• •
• GNR607 Lecture 21-23 B. Krishna

Mohan IIT Bombay Slide 57

Nearest Neighbor Interpolation

P ● A B C D

Standard Interpolation Methods:

• Nearest Neighbor
• Bilinear

Interpolation

• Higher order

interpolation (bicubic) GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 58

Nearest Neighbor Interpolation

• P is the location to which a point from the

reference frame gets transformed

• Measured values exist at A, B, C and D
• Let DAP be the distance of P from A, likewise DBP,

DCP, and DDP

• P is assigned the value of

element K {A,B,C,D} ∈ in case of Nearest Neighbor Interpolation where DKP = Min{DAP, DBP, DCP, DDP}

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 59

Issues in NN Interpolation

• Fastest to compute
• No new values introduced – only the same

values recorded by the sensors retained

• Renders the image blocky if large pixel

size to small pixel size resampling is performed

• e.g., resampling an IRS-1D LISS-III image

to 1 metre pixel size

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 60

Bilinear Interpolation

• As opposed to nearest neighbor

interpolation, all the four known points are employed in estimating the value at the unknown point

• The weightages assigned to the four

points are dependent on the proximity of the unknown point to these known points.

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 61

Bilinear Interpolation Principle

P ● A B C D

Bilinear Interpolation

d(C,P)

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 62

Bilinear Interpolation

• Denoting the estimated gray level at point

P by f(P), and the known values by f(A), f(B), f(C) and f(D),

• The weight wA = 1/d(A,P), where d(A,P) is

the distance between point A and point P.

( ) ( ) ( ) ( ) ( )

A B C D A B C D

w f A w f B w f C w f D f P w w w w + + + = + + +

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 63

Cubic Convolution

• Use of a bigger neighborhood to estimate

the pixel gray level allows a smooth image since local differences are averaged out.

• O—O—O—O
• O—O—O—O
• O—O—O—O
• O—O—O—O

For the location marked by the colored circle, the neighboring 16 elements are employed. Location XR, YR Pixel (i,j) GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 64

Cubic Convolution Technique

• The estimated value at location (XR, YR) is given by

VR = V(i–1,j+n–2)× f(d(i–1,j+n–2)+ 1) + V(i, j + n – 2)× f(d(i, j + n – 2)) + V(i+1,j+n–2)× f(d(i+1,j+n–2)– 1) + V(i+2,j+n–2)× f(d(i+2,j+n–2)– 2)

4 1 n=

∑

V(m,n) is the value of the pixel at location (m,n) f(x) is weight function d(x,y) is the (Euclidean) distance between pixels x and y. GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 65

Cubic Convolution Kernel

• The weighting function f(x) is defined as

(Ref: ERDAS Field Guide)

3 2 3 2

f(x) = (a+2)|x | - (a+3)|x | +1 if x < 1 a |x | - 5a |x | +8a|x| - 4a if 1 < x < 2 0 Otherwise

a = -1 (constant) GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 66

Comments on Cubic Convolution

• Strengths
• Due to larger

neighborhoods, the mean and variance of input image and the output image match closely

• Useful to filter out noise

and improve the image

• Well suited when image

is resampled from a large pixel size to a small pixel

• Weaknesses
• Does produce new values

due to averaging of the

• riginal recorded values
• Extremely slow compared

to other methods GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 67

Comments on Intensity Interpolation

• The choice of order of transformation, and the

type of resampling method used will affect the image quality

• The distribution of control points is very

important to ensure that the image is properly registered to the map frame on all sides

• Nearest neighbor method is adequate if the

resolution of the input image and the corrected image are the same

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 68

Comments on Interpolation

• Bilinear interpolation is adequate if the

resampled image and the input image have only a small difference in the pixel size

• Cubic convolution is best to produce a smooth

resampled image, and is ideal when the pixel size of the resampled image is very different from that of the input image

• Nearest neighborhood is fastest, and cubic

convolution is slowest.

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 69

Image to Image Registration

• When a reference image is available to be used

instead of the map, we register the input image to the reference image.

• Registration is the process of making an

image conform to another image. If image A is not geo-referenced and it is being used with image B, then image B must be registered to image A so that they conform to each other.

• In this example, image A is not rectified to a

particular map projection, so there is no need to rectify image B to a map projection.

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 70

Image Registration

• Much of the procedure remains the same

except that if the pixel sizes of the input and references are different, then one should be first zoomed in / zoomed out to bring it to the size of the other.

• This step is vital when images from

different sensors are to be fused into one data set.

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 71

Image Mosaicing

• If the study area is large, it may be

covered by two adjoining scenes.

• Remote sensing data providers always

keep a small overlap between adjacent scenes.

• Mosaicing is the procedure of joining
• verlapping images into a single large

image

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 72

Image Mosaicing

• It is possible that the two adjoining images

are acquired on two different dates due to which the atmospheric conditions may vary

• The brightness levels of the images may

be different, and the place where the two images are joined, called the seam will be quite visible

• Example:Google Earth images

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 73

S e a m

• f

M

• s

a i c

GNR607 Lecture 21-23 B. Krishna IIT Bombay Slide 8774

Mosaicing Process

• Geo-referencing both images
• Identification of the overlap area
• Adjustment of the brightness levels of the

two images

• Adjustment of brightness across the
• verlap area (called feathering)
• Filling out the blank areas with black/white

values

GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 75

Mosaicing Process

Overlap Area Mosaic is the union image that contains both the input images GNR607 Lecture 21-23 B. Krishna Mohan IIT Bombay Slide 76

E x a m p l e

Reproduced with permission from the lecture notes

• f Prof. John

Jensen, University

• f South Carolina

GNR607 Lecture 21-23 B. Krishna IIT Bombay Slide 77

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