Transcript Geometric Correction

Geometric Correction
It is vital for many applications using remotely sensed images to know the ground
locations for points in the image. There are two similar processes that can help
build the link between images and real world locations: image-to-map rectification
and image-to-image registration.
Image-to-map rectification: a process by which the geometry of an image is made
planimetric with reference to a projected map.
Image-to-image registration: a process which translate the geometry of one image
to another (usually projected) image so that corresponding elements of the same
ground area appear in the same place on the registered images. The image used as
reference (with known projection and coordinates) is called the master image, and
the image to be registered is called the subject image.
It is important that the reference map or image is rendered in a standard map
projection and coordinate systems.
Map Projection
Map projection is the process of systematic transformation of points on the Earth’s
surface to corresponding points on a plane surface.
Cylindrical
Conical
Planar
Commonly Used Spheroid in Map Projection
Ellipsoids
Clarke
WGS72
GRS80
WGS84
…
Date Semi-major axis Semi-minor axis Ellipticity
1866
1972
1980
1984
6,378,206.4
6,378,135
6,378,137
6,378,137
6,356,583.6
6,356,750
6,356,752
6,356,752
1/294.98
1/298.26
1/298.257
1/298.257
Many of the earlier US maps are based on Clarke 1866 ellipsoid which
was determined by Sir Alexander Clarke in 1866. The World Geodetic
System (WGS72 and 84) ellipsoids, determined from satellite orbital
data are considered more accurate.
GRS80 (Geodetic Reference System) ellipsoid is adopted by the International
Association of Geodesy
The Global Coordinate System
spherical coordinate system
unprojected!
expressed in terms of two angles (latitude &
longitude)
longitude: angle formed by a line going from the
intersection of the prime meridian and the
equator to the center of the earth, and a second
line from the center of the earth to the point in
question
latitude: angle formed by a line from the equator
toward the center of the earth, and a second
line perpendicular to the reference ellipsoid at
the point in question
Origin of Geographic Coordinate System
latitude
positive in n. hemisphere
negative in s. hemisphere
longitude
positive east of Prime Meridian
negative west of Prime Meridian
Global Coordinate System
The Universal Transverse Mercator Coordinate System
60 zones, each 6° longitude wide
Starting from 180 degrees eastward
zones run from 80° S to 84° N
poles covered by Universal Polar System (UPS
UTM Zone Projection
Transverse Mercator Projection
applied to each 6o zone to
minimize distortion
UTM Coordinate Parameters
Unit:
meters
Zones:
6o longititue
N and S zones:
separate coord
X-origin:
500,000 m east
of central meridian
Y-origin:
equator
USA In The UTM Zones
State Plane Coordinate System
• Each state has one or
more zones
• Zones are either N-S
or E-W oriented
(except Alaska)
• Each zone has separate
coordinate system and
appropriate projection
• Unit: feet
no negative numbers
Map Projections for State Plane Coordinate System
E-W zones:
Lambert conformal conic projection
N-S zones:
Transverse Mercator Projection
Geometric Correction
map
image
GCP
y’
y
x’
GCP
x  f1 ( x, y )
y   f 2 ( x, y )
Note: Coordinates must be in file
coordinates (lines, samples).
x
Ground Control Points
Master x
Master y
Subject x
Subject y
x1
y1
x1
y1
x2
y2
x2
y2
x3
y3
x3
y3
…
…
…
…
First order polynomial:
x  a0  a1 x  a2 y
y  b0  b1 x  b2 y
Second order polynomial:
x  a0  a1 x  a2 y  a3 xy  a4 x 2  a5 y 2
y  b0  b1 x  b2 y  b3 xy  b4 x 2  b5 y 2
Third order polynomial …
Goodness of fit:
1 n
RMSE   ( xi  xi ) 2  ( yi  yi ) 2
n i 1
Unit of RMSE: pixels
Image Grids on Reference Grids
The output of geometric
correction is a grid that
exactly overlays the
reference grid.
Image-to-image registration:
Reference grids already exist.
Image-to-map rectification:
Need to create a reference
grid first.
(1). Specify an origin
(2). Translate map coordinates
to image coordinates based
on pixel size.
Resampling Methods
1.
Nearest Neighbor: The DN values in the output grid takes from the pixel that
is nearest in the input grid. The output grid maintains all the original DN values
in the input grid.
4
2.
Bilinear Interpolation:
Inverse distance weighted average
of the four nearest pixels to the
output pixel.
3. Cubic Convolution:
Inverse distance weighted average
of the 16 nearest pixels to the
output pixel.
DN k

2
D
BV  k 14 k
1

2
D
k 1
k
16
DN k

2
k 1 Dk
BV  16
1

2
k 1 Dk