photogrammetry2 ghadi zakarneh
TRANSCRIPT
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Palestine Polytechnic University
College of Engineering & Technology
Civil and Architectural Engineering Department
Surveying & Geomatics Engineering
PHOTOGRAMMETRY II
Text Book:
lements of Photogrammetry
Paul R. Wolf
Bon A. Dewitt
Lecturer:
Eng Ghadi Zakarneh
Hebron-Palestine
2007
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TABLE OF CONTENTS
Chapter 1:
Tilted Photographs
Chapter 2:
Analytical Photogrammetry
Chapter 3:
Stereoplotters
Chapter 4:
Close Range Photogrammetry
Chapter 5:
Ground Control
Chapter 6:
Aerotriangulation
Chapter 7:
Project Planning
Appendix:
Accuracy Standards
Units Conversions
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
Ch01
Tilted Photographs
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
TILTED PHOTOGRAPHS
1- Introduction
1. In practice it is impossible to maintain the optical axis of the camera truly vertical.
2.
Unavoidable aircraft tilts cause photographs to be exposed with the camera axistilted slightly from vertical, and the resulting pictures are called tilted
photographs.3. Optical axis deviates from vertical is usually less than 1 and it rarely exceeds 3.
Six independent parameters called the elements of exterior orientation express thespatial position and angular orientation of a tilted photograph.
1. The spatial position: XL, yL,and ZL
The three-dimensional coordinates of the exposure station in a ground
coordinate system.
2. Angular orientation:
The amount and direction of tilt in the photo. Three angles are sufficient
to define angular orientation,
1. the tilt-swing-azimuth (t-s-) system
2. The omega-phi-kappa (, , ) system.
2- Angular Orientation In Tilt, Swing, and Azimuth
In the following figure:
exposure stationL principle pointo
camera axisLo
the vertical lineLn The photographic nadir point n
The ground nadir point gN
The datum nadir point dN
Principal plane (vertical planeLno)
Princip l line noa Tiltt :is the anglet, ornLobetween the optical axis and vertical lineLn.
Swings:is defined as clockwise angle measured in the plane of the photographfrom the positive y-axis to downward or nadir end of the principal line. Azimuth :is the clockwise angle measured from the ground Y axis (usually
North) to the datum principal line.
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
3- Coordinates systems for tilted photographs
In the following figure the yx coordinates system is an auxiliary coordinates system
used in tilted photographs.
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
its origin at the photographic nadir point n
axis coincides with the principle line (positive in the direction from n to o).y
Positive is 90 clockwise from positivex y
Conversion from the xy fiducial system to yx coordinates system:
-Rotation
-a translation of origin fromoton.
The coordinates of image point a after rotation are x and y , depending on the
measured fiducial coordinates of pointa( :aa yx , )
Auxiliary coordinates -x y is obtained by adding the translation distance on
to ,y :
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
4- Angular Orientation In Omega-phi-kappa
As previously stated, besides the tilt-swing-azimuth system, angular orientation of atilted photograph can be expressed in terms of three rotation angles:
1. Omega
2.
Phi3. Kappa
(a) Rotation about the x axis through angle omega.
(b) Rotation about the y axis through angle phi.(c) Rotation about the z2 axis through angle kappa.
5- Scale of tilted photographs
Vertical Photo: Variations in object distances were caused only by topographic
relief.
Tilted Photo: Relief variations also cause changes in scale, but scale in various parts
f the photo is further affected by the ma nitude and angular orientation of the tile.o g
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
Scale on a tilted photograph for any point:
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
6- Ground coordinates from Tilted photographs
Using the above figure we have for X:
And for X:
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
7- Relief Displacement on A Tilted Photograph
1. Tilted Photo:Image displacements on tilted photographs caused by topographicrelief occur much the same as they do on vertical photos, except that relief
displacements on tilted photographs occur along radial lines from the nadir point.
2. Vertical Photo: Relief displacements on a truly vertical photograph are also
radial from the nadir point, but in that special case the nadir point coincides with
the principal point.
3. Relief displacement is zero for images at the nadir point and increases withincreased radial distances from the nadir.
Magnitude of relief displacement depends upon flying height,
height of object,
amount of tilt, and Location of the image in the photograph.
8- Determining the elements of the exterior orientation
The most common method is called space resection, using the collinearity equations, the
condition of collinearity is that the the exposure station of a photograph, object point, andits photo image all lie in a straight line.
Where the collinearity equations are:
)()()(
)()()(
333231
131211
LALALA
LALALA
oaZZmYYmXXm
ZZmYYmXXmfxx
++
++=
)()()(
)()()(
333231
232221
LALALA
LALALAoa
ZZmYYmXXm
ZZmYYmXXmfyy
++
++=
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
Where ms in term of Omega ,Phi , and kappa . and Tilt, Swing , and Azimuth are :
The collinearity equations development:
The image coordinates x-y in the tilted photo with respect their correspondingcoordinates in the rotated image(vertical image):
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
If , divide D-2 and D-3 by D-4 , thenfza = is cancelled, and we
add corrections of the principle point ( ). We get:00 ,yx
)()()(
)()()(
333231
131211
LALALA
LALALA
oaZZmYYmXXm
ZZmYYmXXmfxx
++
++=
)()()(
)()()(
333231
232221
LALALA
LALALAoa
ZZmYYmXXm
ZZmYYmXXmfyy
++
++=
Or can be written as:
The values of Omega , Phi , kappa, tilt , swing and azimuth can be calculated asfollows:
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
9- Rectification of Tilted Photographs
Rectification is the process of making equivalent vertical photographsfrom tilted photo negatives.
The resulting equivalent vertical photos are called rectifiedphotographs.
Rectified photos theoretically are truly vertical photos, and as suchthey are free from displacements of images due to tilt.
Orthophoto rectification & Differential rectificationThese relief displacements and scale variations can also be removed ina process called differential rectification or orthorectification. the
resulting products are then called orthophotos. Orthophotosare often
preferred over rectified photos because of their superior geometric
quality.
10- Rectification Methods
1. Geometry of Rectification
This methods in never used
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
2. Analytic rectification
There are several methods available for performing analytical rectification each ofthe analytical methods performs rectification point by point, and each requires that
sufficient ground control appear in the tilted photo. One method is the 2D projective
coordinates transformations that remove the effects of the small tilts.
XY: ground coordinates
_xy: photo coordinates
3. Optical-Mechanical Rectification
In practice, the optical-mechanical method is widely used, although digital methods are
rapidly surpassing this approach. The optical-mechanical method relies on instrumentscalledRectifiers.
4. Digital rectificationRectified photos can be produced by digital techniques that incorporate a
photogrammetric scanner and computer processing. This procedure is a special case of
the more general concept of georeferencing.
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
11- Correction of Relief for Ground Control Points used in Rectification
This procedure requires that the coordinates which can be computed from
space resection, the X, Y, and Z (or h) coordinates for each ground control point be
known:
LLL ZYX ,,
Coordinates of the displaced (image) point are computed by:
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
12- Atmospheric Correction in Tilted Photographs
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
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Photogrammetry II Ch01: Tilted Photographs By: Eng.Ghadi Zakarneh
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
Ch02
Analytical
Photogrammetry
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
ANALYTICAL PHOTOGRAMMETRY
1- Introduction
1. Analytical photogrammetryis a term used to describe the rigorous mathematical
calculation of coordinates of points in object space based upon cameraparameters, measured photo coordinates and ground control.
2. Unlike the elementary methods presented in earlier chapters, this process
rigorously accounts for any tilts that exist in the photos. Analytical
photogrammetry generally involves the solution of large, complex systems of
redundant equations by themethod of least squares.
3. Analytical photogrammetry forms the basis of many modem hardware and
software systems, including: stereoplotters (analytical and softcopy), digitalterrain model generation, orthophoto production, digital photo rectification, and
aerotriangulation.
4. This chapter presents an introduction to some fundamental topics and elementary
applications in analytical photogrammetry.
5. The coverage here is limited to computations involving single photos andstereopairs
2- Image Measurements
1.
A fundamental type of measurement used in analytical photogrammetry is an xand y photo coordinate pair.
2. Since mathematical relationships in analytical photogrammetry are based on
assumptions such as "light rays travel in straight lines" and "the focal plane of aframe camera is flat," various coordinate refinements may be required to correct
measured photo coordinates for distortion effects that otherwise cause these
assumptions to be violated.3. A number of instruments and techniques are available for making photo
coordinate measurements.
3- Control Points
Object space coordinates of ground control points, which may be either image-
identifiable features, are generally determined via some type of field survey technique
such as GPS.
It is important that the object space coordinates be based on a three-dimensional
Cartesian systemwhich has straight, mutually perpendicular axes.
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
4- Collinearity Condition
Perhaps the most fundamentaland useful relationshipin analytical photogrammetry is
the collinearity condition. Collinearity is the condition that the exposure station, any
object point, and its photo image all lie along a straight linein three-dimensional space.
)()()(
)()()(
333231
1312110
LALALA
LALALAa
ZZmYYmXXm
ZZmYYmXXmfxx
++
++=
)()()(
)()()(
333231
2322210
LALALA
LALALAa
ZZmYYmXXm
ZZmYYmXXmfyy
++++
=
Or written as:
rfqxF a+== 0
sfqyG a+== 0Where:
)()()( 333231 LALALA ZZmYYmXXmq ++=
)()()( 131211 LALALA ZZmYYmXXmr ++=
)()()( 232221 LALALA ZZmYYmXXms ++=
Using Taylor theorem the previous equations are linearized according to the
following form:
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
A
A
A
A
A
A
L
L
L
L
L
L
a
a
dZdZ
FdY
dY
FdX
X
FdZ
Z
FdY
Y
F
dXX
Fd
Fd
Fd
Fdx
x
FF
00000
00000
0)(0
+
+
+
+
+
+
+
+
+
+=
A
A
A
A
A
A
L
L
L
L
L
L
a
a
dZdZ
GdY
dY
GdX
X
GdZ
Z
GdY
Y
G
dXX
Gd
Gd
Gd
Gdx
y
GG
00000
00000
0)(0
+
+
+
+
+
+
+
+
+
+=
To simplify the solution, the following arrangements are applied to the equations
above:
1-
dxaand dyaare corrections forxaandyameasurements, so that they are treated
as residuals.
2- (F)oand (G)oare the evaluations of F and G using initial estimates for relative
orientation parameters.
This enables us to write equations (4-12-a) and (4-13-a) in the following form:
JdZbdYbdXbdZb
dYbdXbdbdbdbv
AAAL
LLxa
++++
++=
16151416
1514131211
KdZbdYbdXbdZb
dYbdXbdbdbdbv
AAAL
LLya
++++
++=
26252426
2524232221
Where,
( ) ( )ZmYmq
fZmYm
q
xb 1213323311 +++=
[ ] [
])coscoscos()coscos(sin
)cossin()cossin()sin(sincos12
+
++++=
ZY
X
q
fZYX
q
xb
( )ZmYmXmq
fb ++= 23222113
)()( 113114 mq
fm
q
xb +=
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
)()( 123215 mq
fm
q
xb +=
)()( 133316 mq
fm
q
xb +=
q
rfqx
q
FJ
)()( 0 +==
( ) ( )ZmYmq
fZmYm
q
yb 2223323321 +++=
[ ] [
])sincos(cos)coscossin(
)sin(sin)sincos()sin(sincos22
ZY
Xq
fZYX
q
yb
++
+++=
( )ZmYmXm
q
fb +=
13121123
)()( 213124 mq
fm
q
yb +=
)()( 223225 mq
fm
q
yb +=
)()( 233326 mq
fm
q
yb +=
q
sfqy
q
GK
)()(0
+==
Where,
LA XXX =
LA YYY =
LA ZZZ =
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
5- Coplanarity Condition
Coplanarity is the condition that the two exposure stations of a stereopair, any object
point, and its corresponding image points on the two photos all lie in a common plane. In
the figure below, points L1, L2, a1, a2 and A all lie in the same plane.
Epipolar plane:any plane containing the two exposure stations and an object point, in
this instance plane L1AL2
Epopolar line:the intersection of the epipolar plane with the left and right photoplanes.
Given the left photo location of image a1, its corresponding point a2 on the right photo is
known to lie along the right epipolar line. The coplanarity condition equation is:
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
6- Space Resection By Collinearity
Space resection is a method of determining the six elements of exterior
orientation (, , , XL, YL, and ZL) of a photograph.
This method requires a minimum of three control points, with known
XYZ object space coordinates, to be imaged in the photograph.
If the ground control coordinates are assumed to be known and fixed, then the linearized
forms of the space resection collinearity equations for a point A are :
axLLL vJdZbdYbdXbdbdbdb +=++ 161514131211
ayLLL vJdZbdYbdXbdbdbdb +=++ 262524232221
Since the collinearity equations are nonlinear, and have been linearized using
Taylor's theorem, initial approximations are required for the unknown orientation
parameters.
For the typical case of near-vertical photography, zero values can be used as
initial approximations for and .
0===
meanL
meanL
YY
XX
=
=
1
1
HZL =1
For the photograph, we have 6 unknowns, and each control point has 2-observations
(x,y), so 3 controlpoints give us exact solution, 4 controlpoints or more we can apply
least squaressolution. The matrix form for the solution, if we have four control points A,
B, C, and D, is:
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
=V=A =X =L
Use ?6500 =LZ
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
7- Space Intersection By Collinearity
If space resection is used to determine the elements of exterior orientation for both photos
of a stereopair, then object point coordinates for points that lie in the stereo overlap area
can be calculated.
The procedure is known as space intersection, so called because corresponding rays tothe same object point from the two photos must intersect at the point. So common point
with unknown ground coordinates (pass points) can be used in addition to the ground
control points that are still required for scaling and rotation of the model:
JdZbdYbdXbdZb
dYbdXbdbdbdbv
AAAL
LLxa
++++
++=
16151416
1514131211
KdZbdYbdXbdZb
dYbdXbdbdbdbv
AAAL
LLya
++++
++=
26252426
2524232221
Each control point has 2-observations (x,y) in each photograph, this means in two
photographs we have 4-observations for each control or pass point. For each
photograph we have 6 unknowns, this means we have 12 unknowns for both
photographs, in addition for each pass point we have 3unknowns (X,Y,Z).
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
8- Analytical Stereomodel
1. Aerial photographs for most applications are taken so that adjacent photos overlap
by more than 55 percent. Two adjacent photographs that overlap in this manner
form a stereopair; and object points that appear in the overlap area constitute a
stereomodel.
2. The mathematical calculation of three-dimensional ground coordinates of points
in the stereomodel by analytical photogrammetric techniques forms an analytical
stereomodel
The process of forming an analytical stereomodel involves three primary steps:
1.
Interior orientation,
2.
Relative orientation, and3. Absolute orientation.
After these three steps are achieved, points in the analytical stereomodel will have object
coordinates in the ground coordinate system.
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
9- Analytical Interior Orientation
Interior orientation for analytical photogrammetry is the step which mathematically
recreates the geometry that existed in the camera when a particular photograph was
exposed.
This requires camera calibration information as well as quantification of the effects of
atmospheric refraction. These procedures, commonly called photo coordinate
refinement.
The processare
1. With coordinates of fiducials and image pointswhich have been measured by a
comparator or related device.
2. A 2D coordinate transformation is used to relate the comparator coordinates to the
fiducial coordinate system as well as to correct for film distortion.
3. The lens distortion and principal-point information from camera calibration are
then used to refine the coordinates so that they are correctly related to the
principal point and free from lens distortion.
4. Atmospheric refraction corrections can be applied to the photo coordinates to
complete the refinement,
5. Finish the interior orientation.
The observation equations for this mathematical model are:
xVXcbyax +=++
yVYfeydx +=++
where,
x and y are the machine coordinates.
X and Y are the fiducial coordinates.
XV and are the residuals in the observed values.YV
athroughf are the transformation parameters.
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
The following matrix form represents the mathematical model of the two
dimensional affine coordinate transformation, when 4 fiducial points are used:
AX=L+V
Where,
=
1000
0001
1000
0001
1000
0001
1000
0001
44
44
33
33
22
22
11
11
yx
yx
yx
yx
yx
yx
yx
yx
A , , ,
=
f
e
d
c
b
a
X
=
4
4
3
3
2
2
1
1
Y
X
Y
X
Y
X
Y
X
L
=
4
4
3
3
2
2
1
1
y
x
y
x
y
x
y
x
v
v
v
v
v
v
v
v
V
The least squares solution for the above parameters in matrixXis given by:
X= (ATA)
-1A
TL
10- Analytical Relative Orientation
Analytical relative orientationis the process of determining the relative angular attitudeand positional displacement between the photographs that existed when the photos were
taken. This involves defining certain elements of exterior orientation and calculating the
remaining ones. The resulting exterior orientation parameters will not be the actual values
that existed when the photographs were exposed; however, they will be correct in a
"relative sense" between the photos.
1. In analytical relative orientation, it is common practice to fix the exterior
orientation elements , , , XL, and YL of the left photo of the stereopair to zero
values.
2. Also for convenience, ZL of the left photo (ZL1) is set equal f of, and XL of the
right photo (XL2) is set equal to the photo base b.
3. This leaves five elements of the right photo that must be determined
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
Using collinearity equations and, with the input data of the coordinates of image
point in each photo, each point gives two equations in the left photo and two equations in
the right photo. Each point has three unknown model coordinates X, Y, and Z, in addition
to the five relative orientation unknown parameters ( 2, 2 , k2,YL2, and ZL2). To solve
this system of equations the least number of pass points needed is n. The nis calculated
as follows:
4n=3n+5
Then
n=5 (minimum number of pass points)
The following matrix form is used:
AX=L+V
The least squares solution for parameter is solved using the following equation:
X= (ATA)
-1A
TL
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
If six pass points were used (A through F) for the solution, then matrix A is formed as
shown in the next page. X and L are as follows:
123
2
2
2
2
2
=
F
F
F
E
E
E
D
D
D
C
C
C
B
B
B
A
A
A
L
L
dZ
dY
dX
dZdY
dX
dZ
dY
dX
dZ
dY
dX
dZ
dY
dX
dZ
dY
dX
dZ
dY
d
d
d
X
( )( )( )( )( )( )( )( )
( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )
1242
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
=
f
f
e
e
d
d
c
c
b
b
a
a
f
f
e
e
d
d
c
c
b
b
a
a
K
J
K
J
K
J
K
J
K
J
K
J
K
J
KJ
K
J
K
J
K
J
K
J
L
( )
( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )( )
( )( )( )( )( )
1242
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
=
yf
xf
ye
xe
yd
xd
yc
xc
yb
xb
ya
xa
yf
xf
ye
xe
yd
xd
yc
xc
yb
xb
ya
xa
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
V
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
Where,
1, denotes the left photo.
2, denotes the right photo.
Showing the zero elements we have
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
11- Calculating model coordinates
After the solution of relative orientation parameters for the stereopair, the model
coordinates of any point can be calculated by using the collinearity equations. Since the
collinearity equations are non-linear equations, they have to be linearized to their model
coordinates, as described below:
++++
=)()()(
)()()(
333231
131211
LALALA
LALALAa
ZZmYYmXXm
ZZmYYmXXmfx
++++
=)()()(
)()()(
333231
232221
LALALA
LALALAa
ZZmYYmXXm
ZZmYYmXXmfy
The above Equations are rearranged in following form:
q
rfVxF xaa =+=
q
sfVyG yaa =+=
Where,
)()()( 333231 LALALA ZZmYYmXXmq ++=
)()()( 131211 LALALA ZZmYYmXXmr ++=
)()()( 232221 LALALA ZZmYYmXXms ++=
Those equations can be solved for X, Y, and Z using least squares solution, since
there are four equations for x and y for any point in the two photos. The solution by using
least squares can be solved as follows:
AX=L+V
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
Where,
142
2
1
1
1422
22
11
11
13
34
222
222
111
111
,,,
0
0
0
0
=
=
=
=
y
x
y
x
V
V
V
V
V
GG
FF
GG
FF
LdZdY
dX
X
Z
G
Y
G
X
GZ
F
Y
F
X
F Z
G
Y
G
X
GZ
F
Y
F
X
F
A
Where,
( )2
3111
q
mrmqf
X
F =
( )2
3212
q
mrmqf
Y
F =
( )2
3313
q
mrmqf
Z
F =
( )2
3121
q
msmqf
X
G =
( )2
3222
q
msmqf
Y
G =
( )23323
qmsmqf
ZG =
As discussed above the collinearity equations are non-linear equations, and can be
solved iteratively. The initial coordinates of the model points are calculated from the first
photo(with assumption of verticallity)as follows:
xf
HX
im
=
yf
HY
im
=
avem ZZ i =
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
12- Analytical Absolute Orientation
1. For a stereomodel computed from one stereopair, analytical absolute orientation
can be performed using a 3D conformal coordinate transformation.
2.
This requires at least two horizontal and three vertical control points, but
additional control points provide redundancy, which enables a least squares
solution.
3. In the process of absolute orientation, stereomodel coordinates of control points
are related to their 3D coordinates in a ground based system. It is important for
the ground system to be a true Cartesian coordinate system, such as local vertical,
since the 3D conformal coordinate transformation is based on straight, orthogonal
axes.
In the three dimensional conformal coordinates transformation there are three
rotations , , and k about the three axes x, y, and z respectively(This is shown in the
figure below). Also, there are three translations Tx, Ty, and Tz, and a scale factor, thus
giving seven parameters. The transformation equations are developed as the follows:
Omega Phi Kappa
xpppP TzmymxmsX +++= )( 312111
ypppP TzmymxmsY +++= )( 322212
zpppP TzmymxmsZ +++= )( 332313
Where,
sis the scale factor. Tx,Ty, and Tzare the translations in x, y, and z directions.
m's are functions of rotation angles , , andk.Their values are computed from the
following equations:
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
coscos11=m
sincoscossinsin12 +=m
sinsincossincos13 +=m
sincos21 =m
coscossinsinsin22 +=m
cossinsinsincos23 +=m
sin31=m
cossin32 =m
coscos33 =m
If three full control points were used, the matrices form solution is:
AX=L+V
=
97969594939291
87868584838281
77767574737271
67666564636261
57565554535251
47464544434241
37363534333231
27262524232221
17161514131211
aaaaaaa
aaaaaaa
aaaaaaaaaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
aaaaaaa
A
17
=
z
y
x
dT
dTdT
d
d
d
ds
X
, ,
190
0
0
0
0
0
0
0
0
)(
)(
)()(
)(
)(
)(
)(
)(
=
RR
RR
RR
QQ
QQ
QQ
PP
PP
PP
ZZ
YY
XXZZ
YY
XX
ZZ
YY
XX
L
19
=
ZR
YR
XR
ZQ
YQ
XQ
Zp
Yp
Xp
V
V
VV
V
V
V
V
V
V
The least squares solution for the above system is:
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
X= (ATA)
-1A
TL
where,
)()()( 31211111 ppp zmymxms
Xa ++=
=
012 ==
Xa
[ ]szyxX ppp )(cos)(sinsin))(cossin(
++=a13
=
1=
=xT
X15
a
016 =
=yT
Xa
017 =
=zT
Xa
)()()( 32221221 ppp zmymxms
Ya ++=
=
[ ]szmymxmYa ppp )()()( 33231322 =
=
[ ]szyxYa ppp ))(sin(sin)(sincossin())(coscossin(23
++=
=
[ ]symxmYa pp )()( 122224 =
=
025 =
=xT
Ya
126 =
=yT
Ya
027
=
=
zT
Ya
)()()( 33231331 ppp zmymxms
Za ++=
=
[ ]szmymxmZa ppp )()()( 32221232 ++=
=
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
[ ]szyxZa ppp ))(sincos()(sincos(cos))(coscoscos(33
++=
=
[ ]symxmZa pp )()( 132334 =
=
035 ==
xTZa
036 =
=yT
Za
137 =
=ZT
Za
XpV , , , .., and are the residuals in the coordinates of the control points.YpV ZpV ZRV
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Photogrammetry II Ch02: Analytical Photogrammetry By: Eng.Ghadi Zakarneh
13- Analytical Self-Calibration
Analytical self-calibration is a computational process wherein camera calibration
parameters are included in the photogrammetric solution, generally in a combined
interior-relative-absoluteorientation.
The process uses collinearity equations that have been augmented with additional terms
to account for adjustment of the calibrated focal length, principal-point offsets, and
symmetric radial and decentering lensdistortion. In addition, the equations might
include corrections foratmospheric refractionas presented.
Where,
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Ch03
Stereoscopic
Plotting Instruments
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
STEREOPLOTTERS
1- Introduction
Stereoplotters (Stereoscopic plotting instruments) are instruments designed to
provide a rigorous solutions for object point positions from their corresponding image
positions on overlapping pairs of photos. In general, stereoplotters are manufactured to a
high degree of precision and accurate results may be obtained from them.
Transparencies or diapositives are prepared to exacting standards from the
negatives. Then, they are placed in two stereoplotter projectors, this process is called
interior orientation.
Through, a process calledrelative orientation,the two projectors are oriented sothat the diapositives bear the exact relative angular orientation to one another in the
projectors that the negatives had in the camera at the instant they were exposed. So that
light rays projected through the photos from the corresponding images on the left and
right photos intersect below. Thus, a stereo model is created.
After relative orientation is completed,absolute orientationis performed. In this
process the model is brought to the desired scale and leveled with respect to a reference
datum.
The stereoplotters combine three distinct systems:
(1)A projection system, which creates the true three-dimensional stereomodel.
(2)A viewing system, which makes it possible for an operator to see that model
(3) A measuring (or tracing) system, which enables measurements of the
stereomodel to be made and recorded.
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
2- Classifications of stereoplotters
Classifications methods of stereoplotters depend on common characteristics of
plotters, some of these methods are the following:
1-Classifications based on projections system:
A-Direct optical projection instruments: these instruments create
models using direct optical projection, and the operator can see themodel directly by his eyes.
B-Mechanical or optical-mechanical projections instruments: these
instruments create the three dimensional model using combinations of
optical and mechanical methods, and the operator can see the model
stereoscopically.
2-Clasifications based on accuracy capability: (first, second, third ), and this
classification is rarely used because accuracy is not a function of instrument only.
3-Clasifications based on analogue solution type:
A-approximate: these instruments assume a vertical photos, to create a three
dimensional model. When the photos were tilted accurate solution is not
achieved.
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
B-theoretically correct: these instruments deal with photos through the
operations of interior, relative and absolute orientation, accurate solution can
be achieved whether the photos were vertical or tilted.
4-Analytical stereoplotters: see item 3-4
5-Digital stereoplotters: see item 3-5
3- Direct Optical Projection Stereoplotters
The main parts are:
1. Main frame
2. Reference table
3. Tracing table
4. Platen
5. Guide rods
6. Projectors
7. Illumination lamps
8. Diapositives
9. Leveling screws
10. Projector bar
11. Tracing pencil
4- Projection System
Light rays projected through projector objective l
and intercepted below on platen
enses
Requires operation in dark room
Lens formula must be satisfied
Intersection must occur within depth of field of
projector lens
To recreate relative angular relationships
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Projectors must have rotational and translational movement capabilities
6 possible for each projector
5- Viewing Systems
Anaglyphic system: using color filters usually red and green, to separate the right
and the left projectors. If the green filter in the left projector and the red filter in
the right project, then if the user uses green glass in left eye and red glass in the
right eye, he will see 3D stereomodel.
- Simple and cheap.
- Using colored diapositives is precluded. And there is a Loss in model
color (model is not bright).
Stereo-image alternator (SIA): shutters are used in the left and right projectors.
These shutters run simultaneously with shutters in the corresponding eyes.
Polarized Viewing systems(PPV): similar to anaglyphic system but the use of
polarizing filters
6- Interior Orientation
Recreates geometry of the taking camera
Four steps
1. Centering diapositives on the projectors
2. Setting off the proper principal distance3. Preparation of the diapositive
4. Compensation for image distortions
Preparation of the diapositive
Direct contact printing
Principal distance will equal focal length of taking camera
Projection printing
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Seldom used today
Necessary for reduced-sized diapositives
Must meet the following:
Compensation for lens distortion
Use a correction plate in projection printing of diapositive, followed
by use of distortion-free lens
Vary the projector principal distance by means of a cam
Reconstructing true geometry
Use projector lens whose distortion characteristics negate cameras
distortion
7- Relative Orientation
Recreate the same relative relationship between diapositives that existed at the
time of the photography
Condition: each model point and the two projection centers form a plane in
miniature
Just like that which existed for the corresponding ground point and the
two exposure stations
Since px is a function of elevation, it can be removed by raising or lowering
platen (Z-wheel)
What remains is py removed using a rotational or translational element to a
projector on the stereoplotter
6 von Gruber points (pass points) used to clear y-parallax
5 points used to clear the model
6th point used to check the model
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
The possible movements of the projectors are:
There are two method to apply the relative orientation:
1- Independent method:
Both right and left projectors are used:
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
2- Dependent method:
8- Absolute Orientation
After relative orientation, a true 3-D model is formed, we have to Level model with
respect to datum, and the Unknown scale of model is fixed to the desired scale for
mapping
Selecting model scale:
Model scale constrained by scale of photography and limitations of stereoplotter
Model scale represented by
Recalling scale of photography, model scale can be represented as
When model scale determined, initial model air base is set off
More convenient before relative orientation
Scale closer to required model scale
Initial model base obtained by multiplying photo base by actual
enlargement ratio
Model scale changed by varying model base
If by and bz settings same for each projector, model base consists only of bx
motion
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Scaling the model:
Minimum of 2 horizontal control points are needed
Unique solution no check
Place floating mark over point A and mark location on plotting sheet
Similarly for point B
Distance shown as AB
If AB does not equal AB, compute change to bx
-If by and bz not equal, need to move the right projector from position II
to II
Leveling the model:
Requires minimum of 3 vertical control pts.
No check
Proper gears must be placed in instrument for consistent vertical scale
Two components of tilt
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Iterative procedures for leveling the models:
1. Set floating mare on model point A and index tracing table dial to read control
elevation of point
2. Read model elevation of control point D
3. If difference exists, X-tilt () applied
If model elevation is higher than control elevation, model is tilted up in
near
4. Repeat steps 1-3 until model is level in the direction from A to D
5. Reindex tracing table dial to read control elevation of point A with floating
mark set on model point A
6. Read model elevation of control point B
7. If model elevation does not agree with control elevation, introduce Y-tilt ( )
in similar fashion as set 3
8. Repeat steps 5-7 until model is level in that direction
9. Check point D to see if model elevation still conforms to control elevation
If line AD is not parallel to Y-axis of stereoplotter then it will be likelynot to conform
10.Check point C to see if model elevation conforms to control elevation
If elevation does not conform, may indicate an error in relative
orientation or blunder in the vertical control
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Methods of introducing corrective tilts instrument dependent
Reference table may be tilted in X and Y directions making them
parallel to model datum
Using leveling screws to rotate projector bar
Introducing corrective tilts to each projector individually
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
9- Analytical stereoplotters
Most of operation in photogrammetry have been automated because of the use of
computers, which enabled to solve most of mathematics for photogrammetry, examples
of these operations are reading data from comparators digitally, and recording the output
data digitally. By linking encoders servo systems and computers, the analytical
stereoplotter had been developed.
The basic components of the analytical stereoplotters are as follows, see fig. (3-9):
1- Precise stereocomparator.
2- Coordinatograph.
3- Computer.
4- Servomotors and encoders to enable the computer to drive the other
components of analytical stereoplotter for photogrammetric operations.
Figure: Analytical stereoplotter
Analytical stereoplotters compute mathematical models using collinearity
equations, instead of using mechanical or optical models.
The input of analytical stereoplotter to solve collinearity equation can be classified into:
1- External input: to solve collinearity equations which consists of camera
interior orientation parameters and ground coordinates of control points.
2- Internal input: using the instrument itself to enter the image coordinates.
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Then using these data and collinearity the computer calculates model and ground
coordinates and the output data are displayed on a screen or they are printed on a hard
copy, or transmitted to the coordinatograph.
Advantages of Analytical stereoplotters:
1- No optical and mechanical limitations.
2- Capable of using vertical, tilted, oblique, and high oblique photographs.
3- More accuracy is achieved because intersections of light rays do not use optical
or mechanical projections. They can also correct for camera lens distortions and
photo shrinkage and expansion, and they can consider atmospheric and earth
curvature corrections.
Analytical stereoplotters orientations
Similar to analogue instruments analytical plotters are oriented in three steps;
interior, relative and absolute orientation. The difference in these types of instruments lies
in the fact that these steps are simulated mathematically. In the analytical stereoplotters
computers guide the user to enter the necessary data for all operations, using the
keyboard for external data and stereocomparators for internal data.
Orientation of analytical stereoplotter is shown in the following steps, and described in
figure below:
A- Interior Orientation
Interior orientation using analytical stereoplotter can be implemented in the order below :
1- Stereopair of photos with (x,y) and ( yx , ) fiducial coordinates are placed in
stereocomparators stages (x1,y1) and (x2,y2).
2- Principle distances and fiducial coordinates are entered to the computers.
3- Using stereocomparator pointing mark at least three fiducials are needed,
and its preferred to use more fiducial points for least squares solutions.
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
4- Tow dimensional coordinates transformation is applied to convert
comparator stages coordinates (x1,y1) and (x2,y2) to fiducial coordinates
systems (x,y) and ( yx , ).
5-
Corrections of shrinkage and expansion are included in the coordinates
transformation.
6- Principle point and lens distortion correction can also be considered.
7- The calculated parameters of coordinates transformations are stored in the
computer.
Figure: Analytical Stereoplotter concepts
B- Relative Orientation
The following steps of relative orientation are implemented:
1. (x,y) and ( ) coordinates of at least five points are entered using the
stereocomparator stages .
yx ,
2. The collinearity equations are then solved to find out the relative orientation
parameters by using least squares solution.
3. Relative orientation parameters are stored in the computer.
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
Using the relative orientation parameters the model coordinates ( ZYX ,, ) of any point
can be calculated by entering its fiducial coordinates (x,y) and ( ) by using the
stereocomparator .
yx ,
C- Absolute Orientation
At least two horizontal control points and three vertical control points are needed to
transform the model coordinates into ground coordinates through what is known as the
absolute Orientation step. Absolute orientation in the analytical stereoplotters is carried
out as follows:
1. Ground coordinates of control points are input to computer manually .
2. Their corresponding images (x,y) and (x,y) coordinates are input using the
stereocomparator .
3. The computer calculates the model coordinates of the control points.
4. Three dimensional coordinates transformations are applied to covert model
coordinates to ground coordinates.
5. Parameters of absolute orientation are stored in the computer.
After computing the orientation parameters, ground coordinates (Xg,Yg,Zg) of any point
can be calculated by entering its fiducial coordinates (x,y) and ( yx , ).
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Photogrammetry II Ch03: Stereoplotters By: Eng.Ghadi Zakarneh
10- Digital stereoplotter
The digital stereoplotter is a stereoplotter with digital input and output. They use
scanned image instead of hardcopy. The fundamental features are the fully digital
environment using digital images and the production of digital output in an interactive
and automated fashion.
A digital stereoplotter is definitely something other than an Analytical Plotter. In
1981 Sarjakoski defined the digital stereoplotter as analytical stereoplotter with images
stored in digital format. The concept goes much further and the major difference is the
availability of the image information in the computer and the potential for automating the
photogrammetric measurement and interpretation tasks in the fully digital system.
Digital photogrammetric workstation is not necessarily a part of a GIS system,
although some users prefer it to be a part of the GIS system. The output of digital
stereoplotter can be used as an input to the GIS.
The fundamental components of the digital stereoplotter are:
1- Computer, databases and graphics systems.
2- Interaction and automation.
3-
The peripheral input and output devices.
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Photogrammetry II Ch04: Close Range Photogrammetry By: Eng.Ghadi Zakarneh
4 -1
Ch04
Close Range
Photogrammetry
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Photogrammetry II Ch04: Close Range Photogrammetry By: Eng.Ghadi Zakarneh
4 -2
CLOSE RANGE PHOTOGRAMMETRY
1- Introduction
Terrestrial photogrammetryis an important branch of the science of photogrammetry. Itdeals with photographs taken with cameras located on the surface of the earth.
The term close-range photogrammetry is generally used for terrestrial photographshaving object distances up to about 300 m.
Terrestrial photography may be:
Static: photos of stationary objects. Stereopairs can be obtained by using a singlecamera and making exposures at both ends of a baseline.
Or dynamic: photos of moving objects. Two cameras located at the ends of abaseline must make simultaneous exposures.
2- Applications of Close Range photogrammetry
Surveying Industry(e.g. aircraft manufacture) Archeology Medicine ..etc
H.W: write a report about an application of close range photogrammetry?- Group of 2 students.
- Copy past from the internet is not allowed (your own writing).- Students have to prepare a 10 minutes presentation.- A 10 minutes discussion will be held.
- The report has 10% of your final result.
3- Terrestrial Cameras
Two general classifications:
Metric: for photogrammetric applications. They have fiducial marks. Theyare completely calibrated before use. Their calibration values for focal
length, principal- point coordinates, and lens distortions can be applied
with confidence over long periods. Non-metric: manufactured for amateur or professional photograph) where
pictorial quality is important but geometric accuracy requirements aregenerally not considered paramount.
A phototheodolite is an instrument that incorporates a metric camera with a surveyors
theodolite. With this instrument, precise establishment of the direction of the optical axiscan be made.
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Photogrammetry II Ch04: Close Range Photogrammetry By: Eng.Ghadi Zakarneh
A stereometric camera system consists of two identical metric cameras which are
mounted at the ends of a bar of known length. The optical axes of the cameras areoriented perpendicular to the bar and parallel with each other. The length of the bar
provides a known baseline length between the cameras, which is important for
controlling scale.
4- Horizantal and Oblique Terrestrial Photos
Classification of terrestrial photos depending on the orientation of the camera :
Horizontal: if the camera axis is horizontal when the exposure is made. , the plane
of the photo is vertical. So if metric camera is used the x-axis is horizontal and thethe y-axis is vertical.
Oblique: the camera axis is inclined either up or down in an angle fromhorizontal. If is upward is called elevation angle. If its downward it called
depressing angle.
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5- Camera Inclination
Determining the angle of inclination of the camera axis of a terrestrial photo relies on thefollowing two fundamental principles of perspective geometry(as in the figure below):
1. Horizontal parallel lines intersect at a vanishing point on the horizon v.2. Vertical parallel lines intersect at the nadirn(or zenith).
3. The line from n through the principal point o intersects the horizon at a rightangle at pointk.
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The phot coordinates system can be established as in the following figure, where:
1. The origin isk.2.
The x-axis is positive in the right side of the origin in the horizon line.
3. The y-axis is positive perpendicularly to x-axis upwards.
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Two ways to determine the the depression angle:
First:
=
f
yotan
koyo =
is depression angle if is negative(as in the figure above), else it is an
elevation angle.
koyo =
Second:
For the depression angle:
Where, n is the nadir point.
If the angle is elevation angle:
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6- Horizontal and Vertical Angles
Horizontal angle between the vertical planes, (Laa), containing image pointaand thevertical plane,Lko, containing the camera axis is:
is positive if it is clockwise, and negative if it is counter clockwise.
Vertical angle a to image pointacan be calculated from the following equation:
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Photogrammetry II Ch04: Close Range Photogrammetry By: Eng.Ghadi Zakarneh
7- Camera axis and exposure station position
The method as explained in the figure below is calledthree point resection.
This needs the following steps:
1. Three known points horizontal positions (A,B,C) drawn to scale on a map plate.
2. has to be known.3. The angles between the three points have to be calculated.
4. Graphical three-point resection procedure, using transparent template containing
the three rays and the camera axis.5. The template is placed on the base map and adjusted in position and rotation until
the three rays simultaneously pass through their respective plotted control points.
6. the position of L is fixed according to the map coordinates system.
Other method, the position of L can be calculated resection problem numerically, as in
surveying.
The elevation of the exposure station is the height of the camera lens above the datum.
Assume that the position and elevation of point A are known. And a is calculated, then:
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8- Location points by intersection from two photos
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and can be determined by three points resection. , , ,and a can be calculated as explained before.
Then the position of a point A is calculated as follows:
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9- Analytical solution for close range photogrammetry
The analytical solution for close range photogrammetry can be applied using the same
methods in aerial photogrammetry, and this need the following steps:
1. Interior orientation using affine coordinates transformations, we
get xy-coordinates in the fiducial coordinates system.2. Relative Orientation using collinearity equations, we get model
coordinates.3. Absolute Orientation using 3D conformal coordinates
transformations. We ground coordinates X,Y, and elevations.
Important NOTE: in the relative orientation the X-axis is in the base between theexposure stations. And the Z-axis is the line Vertical to the image plane. The Y-axis is
perpendicular to the XZ-plane, positive upwards. See figure below.
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Photogrammetry II Ch05: Ground Control By: Eng.Ghadi Zakarneh
Ch05
Ground Control
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Photogrammetry II Ch05: Ground Control By: Eng.Ghadi Zakarneh
GROUND CONTROL
1- Introduction
Photogrammetric control or ground control consists of any points whose positions areknown in an object- space reference coordinate system and whose images can be
positively identified in the photographs.
Photogrammetric control can be:
- Full control: X, Y, Z ground coordinates is known.- Horizontal control: X, Y ground coordinates are only known.
- Vertical control: Z (elevations) is known.
Requirements of ground control:- They should be sharp.
- They should be in favorable locations.
For Horizontal control, their horizontal positions on the photographs must be precisely
measured; images of horizontal control points must be very sharp and well defined.
Horizontal control are intersections of sidewalks, intersections of roads, manhole covers,small lone bushes, isolated rocks, corners of buildings, fence corners, power poles, points
on bridges, intersections of small trails or watercourses, etc.
Images for vertical control need not be as sharp and well defined horizontally. Pointsselected should be well defined vertically. Best vertical control points are small, flat or
slightly crowned areas. The small areas should have some natural features nearby, such
as trees or rocks, which help to strengthen stereoscopic depth perception. Large, openareas such as the tops of grassy hills or open fields should be avoided.
2- Number and Location of Ground ControlSpace resection problem: for determining the position and orientation of a tilted photo, aminimum of three XYZ control points is required. The images of the control points
should ideally form a large, nearly equilateral triangle. Although three control points are
the required minimum for space resection, redundant control is recommended to increasethe accuracy of the Photogrammetric solution and to help detecting mistakes.
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In astripit is recommended to have 2 horizontal and 3 vertical control points at each fifth
model.
In case ofblock adjustment, it is recommended to full control points at the beginningand the end of each strip, horizontal and vertical control have to be well distributed
within the block.
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Photogrammetry II Ch05: Ground Control By: Eng.Ghadi Zakarneh
3- Planning the Control Survey
The control points should have accuracy much better than required accuracy of the
produced map. One method is usingNational map accuracy standards (NMAS):
1. Horizontal control:
-
At least 90% of the palnimetric features are required to be plotted within
inch
30
1or (0.8mm) of their true position. If the map scale is larger than
1:20,000.
- At least 90% of the palnimetric features are required to be plotted within
inch
50
1or (0.5mm) of their true position. If the map scale is smaller
than 1:20,000
- The Horizantal control accuracy should not be greater than4
1or
3
1of the
map accuracy.
Example:
If it is required to have a map plotted with scale 1:600, what is the required horizontal
control accuracy?
0.8 mm is equivalent to 0.48m
This mean the accuracy of the Horizontal control should be m16.0m
2. Vertical control: 90% of the points should be within 0.5 of the contour interval.
The vertical control should be better than 0.2 or 0.1 of the contour interval.
4- Field Survey methods
Traverse
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Photogrammetry II Ch05: Ground Control By: Eng.Ghadi Zakarneh
Triangulation
GPS
Differential Leveling
Trigonometric leveling
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5- Artificial Targets
In some areas such as prairies, forests, and deserts, natural points suitable for
Photogrammetric control may not exist. In these cases artificial points calledpanel points
may be placed on the ground prior to taking the aerial photography. Their positions are
then determined by field survey or in some cases by aerotriangulation. This procedure iscalledpremarking or paneling.
Advantages of artificial targets:
Excellent image quality. Unique appearance.
Disadvantages:
Extra work and expenses The can be moved before taking the photographs, the position is changed, this
leads to wrong solutions.
They may not appear in a favorable location in the photographs.
The targets should have a good color contrast. This can be achieved by using light colors
on dark backgrounds.
A typical shape is shown in the following figure.
The target has a central sizeD of 0.03 to 0.1 mmdepending on the photo scale. And the
legs have the size ofDX5D.
Example:
If the photo scale is 1:12000 is planned. What should be the artificial target size, if its
photo size is required to be 0.05mm?
0.05mm is equivalent 0.6m
Other known shapes of the artificial targets are shown in the figure below.
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
Ch06
Aerotriangulation
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
AEROTRIANGULATION
1- Introduction
Aerotriangulation is the term most frequently applied to the process of determining theX, Y, and Z ground coordinates of individual points based on photo coordinate
measurements.
The photogrammetric procedures discussed so far were restricted to one stereo model. It
is quite unlikely that a photogrammetric project is covered by only two photographs,
however. Most mapping projects require many models; large projects may involve asmany as one thousand photographs, medium sized projects hundreds of photographs.
Advantages of Aerotriangulation
1. Minimizing the field surveying by minimizing the number of required control
points.2. Most of work is done in laboratory.
3. Access to the property of project area is not required.4. Field survey in steep and high slope areas is minimized.
5. Accuracy of the field surveyed control points can easily be verified by
aerotriangulation.
Classifications of Aerotriangulation processes1. Analog: involved manual interior, relative, and absolute orientation of the
successive models of long strips of photos using stereoscopic plotting instruments
having several projectors.2. Semianalytical aerotriangulation: involves manual interior and relative orientation
of stereomodels within a stereoplotter, followed by measurement of model
coordinates. Absolute orientation is performed numerically hence the term
semianalytical aerotriangulation.3. Analytical methods :consist of photo coordinate measurement followed by
numerical interior, relative, and absolute orientation from which ground
coordinates are computed.
2- Pass points for aerotriangulation
The points may be images of natural, well-defined objects that appear in the required
photo areas, but if such points are not available, pass points may be artificially marked byusing a special stereoscopic point-marking device.
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3- Semianalytical Aerotriangulation
Often referred to as independent model aerotriangulation.
It is a partly analog and partly analytical procedure.
Manual relative orientation in a stereoplotter of each stereomodel of a strip or
block of photos.
Models are numerically adjusted to the ground system by either a sequential or a
simultaneous method.
3-1 Independent model Sequential method
In the sequential approach to semianalytical aerotriangulation, each stereopair of a
strip is relatively oriented in a stereoplotter, the coordinate system of each modelbeing independent of the others.
Model coordinates of all control points and pass points are read and recorded in
each individual stereomodel.
Coordinates of the perspective centers (model exposure stations) are alsomeasured to get good geometric solution. Each independent model and included
as common points in the transformation.
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
As in figure below of common points d, e, f, and of model 2-3 are made to
coincide with their corresponding model 1-2 coordinates. Once the parameters for
this transformation have been.
2O
Using these points the parameters of the 3D coordinates transformations are
calculated.
parameters are applied to the coordinates of points g, h, i, and in the system ofmodel 2-3 to obtain their coordinates in the model 1-2 system. These points are
used to apply the transformation between model 2-3 and 3-4.
3O
And repeat the process for successive models.
All models have the coordinate system of the first model.
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
Adjustment of strip model to ground coordinates
To transform from model coordinates to ground coordinates 3D conformal
coordinates transformation can applied. To find the parameters of the 3D conformal
coordinate transformation 3 full control points are needed as minimum, or at least 2
horizontal and 3 vertical control points.Random errors will accumulate in a systematic manner in long strips. So control
points in the first model are used to orient it to the ground system. The other control
points are used as check points to represent the errors as smooth curves.
An example of polynomial representation of the errors is shown in the equationbelow. These equations have 30 parameters, so we need at least 10 full control points
to find these parameters for the strip.
After calculating the parameters, for any new point, the adjusted coordinates are
calculated directly by measuring the model coordinates XYZ of the point.
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
3-2 Independent models Simultinuous Aerotriangulation
Simultaneous transformation method is applied using three dimensional coordinatestransformation:
This has 7 parameters:
- Scale factor S.
- Three rotations ),,( k .
- And three translations .),,(ZYXTTT
For the figure below we have 6 models, this means we have 6X7=42 parameters. Thisneeds at least 42 observation equations to solve for the unknown parameters.
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For the figure, each control point provides 3 observation equations. As follows:
We have 6 control control point A-F, this gives us 6X3=18 equation.
Other type of observation equations is for the pass or tie points and the exposure stations
points; these points coordinates are equal for the both common models. These equations
are written as follows:
The common points are as follows:- , , , are common points between 2 models , so we have 4X3=12
observation equations.
2O 3O 6O 7O
- Points 3,6,7,9,10,15,14,12,11,18 are common between 2 models, so we have
10X3=30 observation equations.
- Points B and E are common between 2 models, so we have 2X3=6 observationequations.
- points 8 and 13 are common between 4models, so we can make 6 model
combimations, so we have 2X6X3=36 observation equations.
The total number of observation equations=24+12+30+6+36=108 observation
equations.
4- Analytical Aerotriangulation
analytical aerotriangulation consist of the following basic steps:(1) Relative orientation of each stereomodel.
(2) Connection of adjacent models to form continuous strips and/or blocks.(3) Simultaneous adjustment of the photos from the strips and/or blocks to field-
surveyed ground control.
Advantages of Aerotriangulation: Analytical aerotriangulation tends to be more accurate than analog or
semianalytical methods, largely because analytical techniques can more
effectively eliminate systematic errors such as film shrinkage, atmosphericrefraction distortions, and camera lens distortions.
X and Ycoordinates of pass points can be located to an accuracy of within
about 1 / 15,000 of the flying height, and Z coordinates can be located to
an accuracy of about 1/10,000 of the flying height.
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Photogrammetry II Ch06: Aerotriangulation By: Eng.Ghadi Zakarneh
planmetric accuracy of 1/350,000 of the flying height and vertical
accuracy of 1 / 180,000 have been achieved.
Freedom from the mechanical or optical limitations imposed by
stereoplotters.
5- Simultaneous Bundle Adjustment
Bundle adjustment is The process to adjust all photogranimetric measurements to ground
control values in a single solution.
The process is so named because of the many light rays that pass through each lens
position constituting a bundle of rays. As shown in the figure below.
The solution depends basically on the collinearity condition, where the collinearity
equations are:
The solution of the above equations give the exterior orientation parameters of all imagesincluded in the adjustment (omega, phi, kappa, XL,YL,ZL).
For the adjustment we have:
- 2 observations(x,y) for any control or tie point in the photo.- 6 unknowns for each photo (omega, phi, kappa, XL, YL, ZL).
- 3 unknowns for each tie point; ground coordinates(X, Y, and Z).
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Example:
For the bundle adjustment of the following for images, what is the number of unknowns,observations, and how will the design matrix A appear?
Number of observations:
4 x 6 x 2 = 48 observations (collinearity equations). Number of unknowns:
4 x 6 + 3 x 4 = 36 unknowns
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Example:
For the following model what is the number of unknowns, observations, and how will thedesign matrix A appear?
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Photogrammetry II Ch07: Project Planning By: Eng.Ghadi Zakarneh
Ch07
Project Planning
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Photogrammetry II Ch07: Project Planning By: Eng.Ghadi Zakarneh
PROJECT PLANNING
1- Introduction
When a project is planned the following should be considered: Scales
Accuracies
The project planning has the following catogories:
Planning aerial photography
Planning ground control
Selecting instruments and procedures to achieve desired results
Estimating costs and delivery schedules
The flight planning has two part:
1.
Flight map : Shows where photos are to be taken2. Specifications : how the photos will be taken Camera and film requirements
Scale
Flying height End and side lap
Tilt and crab tolerances
2- Endlap and Sidelap
percent of Endlap : overlapping successive photos. Normally 60% and minimum value50%.
Percent of Sidelap: overlapping adjacent flight strips. Normally 30%.
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