1. Collinearity Condition
The collinearity condition is illustrated in the figure below. The exposure station of a photograph, an object point and its photo image all lie along a straight line. Based on this condition we can develop complex mathematical relationships.
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Appendix D

2. Collinearity Condition Equations
Let:
Coordinates of exposure station be XL, YL, ZL wrt object (ground) coordinate system XYZ
Coordinates of object point A be XA, YA, ZA wrt ground coordinate system XYZ
Coordinates of image point a of object point A be xa, ya, za wrt xy photo coordinate system (of which the principal point o is the origin; correction compensation for it is applied later)
Coordinates of image point a be xa’, ya’, za’ in a rotated image plane x’y’z’ which is parallel to the object coordinate system
Transformation of (xa’, ya’, za’) to (xa, ya, za) is accomplished using rotation equations, which we derive next.
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Appendix D

3. Rotation Equations Omega rotation about x’ axis:
New coordinates (x1,y1,z1) of a point (x’,y’,z’) after rotation of the original coordinate reference frame about the x axis by angle ω are given by:
x1 = x’
y1 = y’ cos ω + z’ sin ω
z1 = -y’sin ω + z’ cos ω
Similarly, we obtain equations for phi rotation about y axis:
x2 = -z1sin Ф + x1 cos Ф
y2 = y1
z2 = z1 cos Ф + x1 sin Ф
And equations for kappa rotation about z axis:
x = x2 cos қ + y2 sin қ
y = -x2 sin қ + y2 cos қ
z = z2
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Appendix C

4. Final Rotation Equations
We substitute the equations at each stage to get the following:
x = m11 x’ + m12 y’ + m13 z’
y = m21 x’ + m22 y’ + m23 z’
z = m31 x’ + m32 y’ + m33 z’
Where m’s are function of rotation angles ω,Ф and қ
In matrix form: X = M X’
where
Are we not rotating x,y,z to the prime x,y and z?
Properties of rotation matrix M:
Sum of squares of the 3 direction cosines (elements of M) in any row or column is unity.
M is orthogonal, i.e. M-1 = MT
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Appendix C

5. Coming back to the collinearity condition…
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6. Collinearity Equations
Using property of similar triangles:
Substitute this into rotation formula:
Now,
factor out za’/(ZA-ZL), divide xa, ya by za
add corrections for offset of principal point (xo,yo)
and equate za=-f, to get:
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Appendix D

7. Review of Collinearity Equations
are nonlinear and
involve 9 unknowns:
omega, phi, kappa inherent in the m’s
Object coordinates (XA, YA, ZA )
Exposure station coordinates (XL, YL, ZL )
Where,
xa, ya are the photo coordinates of image point a
XA, YA, ZA are object space coordinates of object/ground point A
XL, YL, ZL are object space coordinates of exposure station location
f is the camera focal length
xo, yo are the offsets of the principal point coordinates
m’s are functions of rotation angles omega, phi, kappa (as derived earlier)
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Ch. 11 & App D

8. First, we need to know what it is that we need to find…
Now that we know about the collinearity condition, lets see where we need to apply it.
First, we need to know what it is that we need to find…
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9. Elements of Exterior Orientation
As already mentioned, the collinearity conditions involve 9 unknowns:
Exposure station attitude (omega, phi, kappa),
Exposure station coordinates (XL, YL, ZL ), and
Object point coordinates (XA, YA, ZA).
Of these, we first need to compute the position and attitude of the exposure station, also known as the elements of exterior orientation.
Thus the 6 elements of exterior orientation are:
spatial position (XL, YL, ZL) of the camera and
angular orientation (omega, phi, kappa) of the camera
All methods to determine elements of exterior orientation of a single tilted photograph, require:
photographic images of at least three control points whose X, Y and Z ground coordinates are known, and
calibrated focal length of the camera.
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Chapter 10

10. Elements of Interior Orientation
As an aside, from earlier discussion:
Elements of Interior Orientation
Elements of interior orientation which can be determined through camera calibration are as follows:
Calibrated focal length (CFL), the focal length that produces an overall mean distribution of lens distortion. Better termed calibrated principal distance since it represents the distance from the rear nodal point of the lens to the principal point of the photograph, which is set as close to optical focal length of the lens as possible.
Principal point location, specified by coordinates of a principal point given wrt x and y coordinates of the fiducial marks.
Fiducial mark coordinates: x and y coordinates of the fiducial marks which provide the 2D positional reference for the principal point as well as images on the photograph.
Symmetric radial lens distortion, the symmetric component of distortion that occurs along radial lines from the principal point. Although negligible, theoretically always present.
Decentering lens distortion, distortion that remains after compensating for symmetric radial lens distortion. Components: asymmetric radial and tangential lens distortion.
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Chapter 3

11. Next, we look at space resection which is used for determining the camera station coordinates from a single, vertical/low oblique aerial photograph…
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12. Space Resection By Collinearity
Space resection by collinearity involves formulating the “collinearity equations” for a number of control points whose X, Y, and Z ground coordinates are known and whose images appear in the vertical/tilted photo.
The equations are then solved for the six unknown elements of exterior orientation that appear in them.
2 equations are formed for each control point
3 control points (min) give 6 equations: solution is unique, while 4 or more control points (more than 6 equations) allows a least squares solution (residual terms will exist)
Initial approximations are required for the unknown orientation parameters, since the collinearity equations are nonlinear, and have been linearized using Taylor’s theorem.
No. of points
No. of equations
Unknown ext. orientation parameters 1 2 6 4 3 8
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Chapter 10 & 11

13. Coplanarity Condition
A similar condition to the collinearity condition, is coplanarity, which 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.
Like collinearity equations, the coplanarity equation is nonlinear and must be linearized by using Taylor’s theorem. Linearization of the coplanarity equation is somewhat more difficult than that of the collinearity equations.
But, coplanarity is not used nearly as extensively as collinearity in analytical photogrammetry.
Space resection by collinearity is the only method still commonly used to determine the elements of exterior orientation.
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14. Initial Approximations for Space Resection
We need initial approximations for all six exterior orientation parameters.
Omega and Phi angles: For the typical case of near-vertical photography, initial values of omega and phi can be taken as zeros. H:
Altimeter reading for rough calculations
Compute ZL (height H about datum plane) using ground line of known length appearing on the photograph
To compute H, only 2 control points are required, rest are redundant. Approximation can be improved by averaging several values of H.
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Chapter 11 & 6

15. Calculating Flying Height (H)
Flying height H can be calculated using a ground line of known length that appears on the photograph.
Ground line should be on fairly level terrain as difference in elevation of endpoints results in error in computed flying height.
Accurate results can be obtained despite this though, if the images of the end points are approximately equidistant from the principal point of the photograph and on a line through the principal point.
H can be calculated using equations for scale of a photograph:
S = ab/AB = f/H
(scale of photograph over flat terrain) Or
S = f/(H-h)
(scale of photograph at any point whose elevation above datum is h)
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Chapter 6

16. As an explanation of the equations from which H is calculated:
Photographic Scale
S = ab/AB = f/H
SAB = ab/AB = La/LA = Lo/LO = f/(H-h)
where
S is scale of vertical photograph over a flat terrain
SAB is scale of vertical photograph over variable terrain
ab is distance between images of points A and B on the photograph
AB is actual distance between points A and B
f is focal length
La is distance between exposure station L & image a of point A on the photo positive
LA is distance between exposure station L and point A
Lo = f is the distance from L to principal point on the photograph
LO = H-h is the distance from L to projection of o onto the horizontal plane containing point A with h being height of point A from the datum plane
Note: For vertical photographs taken over variable terrain, there are an infinite number of different scales.
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Chapter 6

17. Initial Approx. for XL, YL and k
x’ and y’ ground coordinates of any point can be obtained by simply multiplying x and y photo coordinates by the inverse of photo scale at that point.
This requires knowing
f, H and
elevation of the object point Z or h.
A 2D conformal coordinate transformation (comprising rotation and translation) can then be performed, which relates these ground coordinates computed from the vertical photo equations to the control values:
X = a.x’ – b.y’ + TX; Y = a.y’ + b.x’ + TY
We know (x,y) and (x’,y’) for n sets are known giving us 2n equations.
The 4 unknown transformation parameters (a, b, TX, TY) can therefore be calculated by least squares. So essentially we are running the resection equations in a diluted mode with initial values of as many parameters as we can find, to calculate the initial parameters of those that cannot be easily estimated.
TX and TY are used as initial approximation for XL and YL, resp.
Rotation angle θ = tan-1(b/a) is used as approximation for κ (kappa).
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Chapter 11

18. Space Resection by Collinearity: Summary
(To determine the 6 elements of exterior orientation using collinearity condition)
Summary of steps:
Calculate H (ZL)
Compute ground coordinates from assumed vertical photo for the control points.
Compute 2D conformal coordinate transformation parameters by a least squares solution using the control points (whose coordinates are known in both photo coordinate system and the ground control cood sys)
Form linearized observation equations
Form and solve normal equations.
Add corrections and iterate till corrections become negligible.
Summary of Initializations:
Omega, Phi -> zero, zero
Kappa -> Theta
XL, YL -> TX, TY
ZL ->flying height H
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Chapter 11

19. 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 by the procedure known as space intersection…
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20. Space Intersection By Collinearity
Use: To determine object point coordinates for points that lie in the stereo overlap area of two photographs that make up a stereopair.
Principle: Corresponding rays to the same object point from two photos of a stereopair must intersect at the point.
For a ground point A:
Collinearity equations are written for image point a1 of the left photo (of the stereopair), and for image point a2 of the right photo, giving 4 equations.
The only unknowns are XA, YA and ZA.
Since equations have been linearized using Taylor’s theorem, initial approximations are required for each point whose object space coordinates are to be computed.
Initial approximations are determined using the parallax equations.
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Chapter 11

21. Parallax Equations Parallax Equations: pa = xa – x’a hA = H – B.f/pa
XA = B.xa/pa
YA = B.ya/pa
where
hA is the elevation of point A above datum
H is the flying height above datum
B is the air base (distance between the exposure stations)
f is the focal length of the camera
pa is the parallax of point A
XA and YA are ground coordinates of point A in the coordinate system with origin at the datum point P of the Lpho, X axis is in same vertical plane as x and x’ flight axes and Y axis passes through the datum point of the Lpho and is perpendicular to the X axis
xa and ya are the photo coordinates of point a measured wrt the flight line axes on the left photo
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Chapter 8

22. Applying Parallax Equations to Space Intersection
For applying parallax equations, H and B have to be determined:
Since X, Y, Z coordinates for both exposure stations are known,
H is taken as average of ZL1 and ZL2 and
B = [ (XL2-XL1)2 + (YL2-YL1)2 ]1/2
The resulting coordinates from the parallax equations are in the arbitrary ground coordinate system.
To convert them to, for instance WGS84, a conformal coordinate transformation is used.
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Chapter 11

23. Now that we know how to determine object space coordinates of a common point in a stereopair, we can examine the overall procedure for all the points in the stereopair...
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24. Analytical Stereomodel
Aerial photographs for most applications are taken so that adjacent photos overlap by more than 50%. Two adjacent photographs that overlap in this manner form a stereopair.
Object points that appear in the overlap area of a stereopair constitute a stereomodel.
The mathematical calculation of 3D ground coordinates of points in the stereomodel by analytical photogrammetric techniques forms an analytical stereomodel.
The process of forming an analytical stereomodel involves 3 primary steps:
Interior orientation (also called “photo coordinate refinement”): Mathematically recreates the geometry that existed in the camera when a particular photograph was exposed.
Relative (exterior) orientation: Determines the relative angular attitude and positional displacement between the photographs that existed when the photos were taken.
Absolute (exterior) orientation: Determines the absolute angular attitude and positions of both photographs.
After these three steps are achieved, points in the analytical stereomodel will have object coordinates in the ground coordinate system.
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Chapter 11

25. Analytical Relative Orientation
Analytical relative orientation involves defining (assuming) certain elements of exterior orientation and calculating the remaining ones.
Initialization:
If the parameters are set to the values mentioned (i.e., ω1=Ф1=қ1=XL1=YL1=0, ZL1=f, XL2=b),
Then the scale of the stereomodel is approximately equal to photo scale.
Now, x and y photo coordinates of the left photo are good approximations for X and Y object space coordinates, and
zeros are good approximations for Z object space coordinates.
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Chapter 11

26. Analytical Relative Orientation
All exterior orientation elements, excluding ZL1 of the left photo of the stereopair are set to zero values.
For convenience, ZL of left photo (ZL1) is set to f and XL of right photo (XL2) is set to photo base b.
This leaves 5 elements of the right photo that must be determined.
Using collinearity condition, min of 5 object points are required to solve for the unknowns, since each point used in relative orientation is net gain of one equation for the overall solution (since their X,Y and Z coordinates are unknowns too)
No. of points in overlap
No. of equations
No. of unknowns 1
4 (2+2)
5 + 3 = 8 2
4 + 4 = 8
8 + 3 = 11 3
8 + 4 = 12
= 14 4
= 16
= 17 5
=20
=20 6
= 24
= 23
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Chapter 11

27. Analytical Absolute Orientation
Stereomodel coordinates of tie points are related to their 3D coordinates in a (real, earth based) ground coordinate system. For small stereomodel such as that computed from one stereopair, analytical absolute orientation can be performed using a 3D conformal coordinate transformation.
Requires minimum of two horizontal and three vertical control points. (20 equations with 8 unknowns plus the 12 exposure station parameters for the two photos:closed form solution). Additional control points provide redundancy, enabling a least squares solution.
(horizontal control: the position of the point in object space is known wrt a horizontal datum;
vertical control: the elevation of the point is known wrt a vertical datum)
Once the transformation parameters have been computed, they can be applied to the remaining stereomodel points, including the XL, YL and ZL coordinates of the left and right photographs. This gives the coordinates of all stereomodel points in the ground system.
No. of equations
No. of additional unknowns
Total no. of unknowns
1 horizontal control point
2 per photo =>total 4
1 unknown Z value
12 exterior orientation parameters + 1 = 13
1 vertical control point
2 equations per photo => 4 equations total
2 unknown X and Y values
= 14
2 horizontal control points
4 * 2 = 8 equations
1 * 2 = 2
3 vertical control points
4 * 3 = 12 equations
2 * 3 = 6
= 18
2 horizontal + 3 vertical control points
= 20 equations
2 + 6 = 8
= 20
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Chapter 16 & 11

28. As already mentioned while covering camera calibration, camera calibration can also be included in a combined interior-relative-absolute orientation. This is known as analytical self-calibration…
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29. 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-absolute orientation.
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 lens distortion.
In addition, the equations might include corrections for atmospheric refraction.
With the inclusion of the extra unknowns, it follows that additional independent equations will be needed to obtain a solution.
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Chapter 11

30. So far we have assumed that a certain amount of ground control is available to us for using in space resection, etc. Lets take a look at the acquisition of these ground control points…
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31. Ground Control for Aerial Photogrammetry
Ground control consists of any points
whose positions are known in an object-space coordinate system and
whose images can be positively identified in the photographs.
Classification of photogrammetric control:
Horizontal control: the position of the point in object space is known wrt a horizontal datum
Vertical control: the elevation of the point is known wrt a vertical datum
Images of acceptable photo control points must satisfy two requirements:
They must be sharp, well defined and positively identified on all photos, and
They must lie in favorable locations in the photographs .
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Chapter 16

32. Photo Control Points for Aerotriangulation
The Number of ground-surveyed photo control needed varies with
size, shape and nature of area,
accuracy required, and
procedures, instruments, and personnel to be used.
In general, more dense the ground control, the better the accuracy in the supplemental control determined by aerotriangulation. – thesis of our targeting project!!
There is an optimum number, which affords maximum economic benefit and maintains a satisfactory standard of accuracy.
The methods used for establishing ground control are:
Traditional land surveying techniques
Using Global Positioning System (GPS)
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Chapter 16

33. Having covered processing techniques for single points, we examine the process at a higher level, for all the photographs…
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34. Aerotriangulation
It is the process of determining the X, Y, and Z ground coordinates of individual points based on photo coordinate measurements.
consists of photo measurement followed by numerical interior, relative, and absolute orientation from which ground coordinates are computed.
For large projects, the number of control points needed is extensive
cost can be extremely high
. Much of this needed control can be established by aerotriangulation for only a sparse network of field surveyed ground control.
Using GPS in the aircraft to provide coordinates of the camera eliminates the need for ground control entirely
in practice a small amount of ground control is still used to strengthen the solution.
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Chapter 17

35. Pass Points for Aerotriangulation
selected as 9 points in a format of 3 rows X 3 columns, equally spaced over photo.
The points may be images of natural, well-defined objects that appear in the required photo areas
if such points are not available, pass points may be artificially marked.
Digital image matching can be used to select points in the overlap areas of digital images and automatically match them between adjacent images.
essential step of “automatic aerotriangulation”.
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Chapter 17

36. Analytical Aerotriangulation
The most elementary approach consists of the following basic steps:
relative orientation of each stereomodel
connection of adjacent models to form continuous strips and/or blocks, and
simultaneous adjustment of the photos from the strips and/or blocks to field-surveyed ground control
X and Y coordinates of pass points can be located to an accuracy of 1/15,000 of the flying height, and Z coordinates can be located to an accuracy of 1/10,000 of the flying height.
With specialized equipment and procedures, planimetric accuracy of 1/350,000 of the flying height and vertical accuracy of 1/180,000 have been achieved.
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Chapter 17

37. Analytical Aerotriangulation Technique
Several variations exist.
Basically, all methods consist of writing equations that express the unknown elements of exterior orientation of each photo in terms of camera constants, measured photo coordinates, and ground coordinates.
The equations are solved to determine the unknown orientation parameters and either simultaneously or subsequently, coordinates of pass points are calculated.
By far the most common condition equations used are the collinearity equations.
Analytical procedures like Bundle Adjustment can simultaneously enforce collinearity condition on to 100s of photographs.
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Chapter 17

38. Simultaneous Bundle Adjustment
Adjusting all photogrammetric measurements to ground control values in a single solution is known as a bundle adjustment. The process is so named because of the many light rays that pass through each lens position constituting a bundle of rays.
The bundles from all photos are adjusted simultaneously so that corresponding light rays intersect at positions of the pass points and control points on the ground.
After the normal equations have been formed, they are solved for the unknown corrections to the initial approximations for exterior orientation parameters and object space coordinates.
The corrections are then added to the approximations, and the procedure is repeated until the estimated standard deviation of unit weight converges.
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Chapter 17

39. Quantities in Bundle Adjustment
The unknown quantities to be obtained in a bundle adjustment consist of:
The X, Y and Z object space coordinates of all object points, and
The exterior orientation parameters of all photographs
The observed quantities (measured) associated with a bundle adjustment are:
x and y photo coordinates of images of object points,
X, Y and/or Z coordinates of ground control points,
direct observations of exterior orientation parameters of the photographs.
The first group of observations, photo coordinates, is the fundamental photogrammetric measurements.
The next group of observations is coordinates of control points determined through field survey.
The final set of observations can be estimated using airborne GPS control system as well as inertial navigation systems (INSs) which have the capability of measuring the angular attitude of a photograph.
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Chapter 17

40. Bundle Adjustment on a Photo Block
Consider a small block consisting of 2 strips with 4 photos per strip, with 20 pass points and 6 control points, totaling 26 object points; with 6 of those also serving as tie points connecting the two adjacent strips.
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Chapter 17

41. Bundle Adjustment on a Photo Block
To repeat, consider a small block consisting of 2 strips with 4 photos per strip, with 20 pass points and 6 control points, totaling 26 object points; with 6 of those also serving as tie points connecting the two adjacent strips.
In this case,
The number of unknown object coordinates
= no. of object points X no. of coordinates per object point = 26X3 = 78
The number of unknown exterior orientation parameters
= no. of photos X no. of exterior orientation parameters per photo = 8X6 = 48
Total number of unknowns = = 126
The number of photo coordinate observations
= no. of imaged points X no. of photo coordinates per point = 76 X 2 = 152
The number of ground control observations
= no. of 3D control points X no. of coordinates per point = 6X3 = 18
The number of exterior orientation parameters
If all 3 types of observations are included, there will be a total of =218 observations; but if only the first two types are included, there will be only =170 observations
Thus, regardless of whether exterior orientation parameters were observed, a least squares solution is possible since the number of observations in either case (218 and 170) is greater than the number of unknowns (126 and 78, respectively).
No. of imaged points = 4 X 8
(photos 1, 4, 5 & 8 have 8 imaged points each) +
4 X 11
(photos 2, 3, 6 & 7 have 11 imaged points each)
= total 76 point images
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Chapter 17

42. Linearization of our non-linear equation set
Our Least Squares Solution was for a linear set of equations
Remember in all our photogrammetric equations we have sines, cosines etc.
Need to linearize
Use Taylor Series Expansion
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43. Review of Collinearity Equations
are nonlinear and
involve 9 unknowns:
omega, phi, kappa inherent in the m’s
Object point coordinates (XA, YA, ZA )
Exposure station coordinates (XL, YL, ZL )
Where,
xa, ya are the photo coordinates of image point a
XA, YA, ZA are object space coordinates of object/ground point A
XL, YL, ZL are object space coordinates of exposure station location
f is the camera focal length
xo, yo are the coordinates of the principal point
m’s are functions of rotation angles omega, phi, kappa (as derived earlier)
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Ch. 11 & App D

44. Linearization of Collinearity Equations
Rewriting the collinearity equations:
where
Applying Taylor’s theorem to these equations (using only upto first order partial derivatives), we get…
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Appendix D

45. Linearized Collinearity Equations Terms
where
F0, G0: functions of F and G evaluated at the initial approximations for the 9 unknowns;
are partial derivatives of F and G wrt the indicated unknowns evaluated at the initial approximation
are unknown corrections to be applied to the initial approximations. (angles are in radians)
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Appendix D

46. Simplified Linearized Collinearity Equations
Since photo coordinates xa and ya are measured values, if the equations are to be used in a least squares solution, residual terms must be included to make the equations consistent.
The following simplified forms of the linearized collinearity equations include these residuals:
where J = xa – F0, K = ya - G0 and the b’s are coefficients equal to the partial derivatives
In linearization using Taylor’s series, higher order terms are ignored, hence these equations are approximations.
They are solved iteratively, until the magnitudes of corrections to initial approximations become negligible.
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Chapter 11

47. Lets first generalize and then express the equations in matrix form…
We need to generalize and rewrite the linearized collinearity conditions in matrix form.
While looking at the collinearity condition, we were only concerned with one object space point (point A).
Lets first generalize and then express the equations in matrix form…
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48. Generalizing Collinearity Equations
The observation equations which are the foundation of a bundle adjustment are the collinearity equations:
These non-linear equations involve 9 unknowns: omega, phi, kappa inherent in the m’s, object point coordinates (Xj, Yj, Zj ) and exposure station coordinates (XLi, YLi, ZLi )
Where,
xij, yij are the measured photo coordinates of the image of point j on photo i related to the fiducial axis system
Xj, Yj, Zj are coordinates of point j in object space
XLi, YLi, ZLi are the coordinates of the eyepoint of the camera
f is the camera focal length
xo, yo are the coordinates of the principal point
m11i, m12i, ..., m33i are the rotation matrix terms for photo i
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Ch. 11 & App D

49. Coming to the actual observations in the observation equations (collinearity conditions), first we consider the photo coordinate observations, then ground control and finally exterior orientation parameters…
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50. Now that we have all our observation equations and the observations, the next step in applying least squares, is to form the normal equations…
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51. Now that we have the equations ready to solve, we can solve them with the initial approximations and iterate till the iterated solutions do not change in value.
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52. Summary The mathematical concepts covered today were:
Least squares adjustment (formulating observation equations and reducing to normal equations)
Collinearity condition equations (derivation and linearization)
Space Resection (finding exterior orientation parameters)
Space Intersection (finding object space coordinates of common point in stereopair)
Analytical Stereomodel (interior, relative and absolute orientation)
Ground control for Aerial photogrammetry
Aerotriangulation
Bundle adjustment (adjusting all photogrammetric measurements to ground control values in a single solution)- conventional and RPC based
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53. Terms
A lot of the terminology is such that can sometimes cause confusion. For instance, while pass points and tie points mean the same thing, (ground) control points refer to tie points whose coordinates in the object space/ground control coordinate system are known, while the term check points refers to points that are treated as tie points, but whose actual ground coordinates are very accurately known.
Below are some more terms used in photogrammetry, along with their brief descriptions:
stereopair: two adjacent photographs that overlap by more than 50%
space resection: finding the 6 elements of exterior orientation
space intersection: finding object point coordinates for points in stereo overlap
stereomodel: object points that appear in the overlap area of a stereopair
analytical stereopair: 3D ground coordinates of points in stereomodel, mathematically calculated using analytical photogrammetric techniques
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54. Terms
interior orientation: photo coordinate refinement, including corrections for film distortions, lens distortion, atmospheric refraction, etc.
relative orientation: relative angular attitude and positional displacement of two photographs.
absolute orientation: exposure station orientations related to a ground based coordinate system.
aerotriangulation: determination of X, Y and Z ground coordinates of individual points based on photo measurements.
bundle adjustment: adjusting all photogrammetric measurements to ground control values in a single solution
horizontal tie points: tie pts whose X and Y coordinates are known.
vertical tie points: tie pts whose Z coordinate is known
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55. References
Wolf, Dewitt: “Elements of Photogrammetry”, McGraw Hill, 2000
Dial, Grodecki: “Block Adjustment with Rational Polynomial Camera Models”, ACSM-ASPRS 2002 Annual Conference Proceedings, 2002
Grodecki, Dial: “Block Adjustment of High-Resolution Satellite Images described by Rational Polynomials”, PE&RS Jan 2003
Wikipedia
Other online resources
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Thank You!
9/10/2018
P Maunga(MSU)