1. Remote Sensing & Photogrammetry L7
Beata Hejmanowska
Building C4, room 212,
phone:

2. Photogrammetry
Marine resource mapping: an introductory manual - FAO Corporate Document Repository
8.  AERIAL PHOTOGRAPHS AND THEIR INTERPRETATION

3. 8.3 Terminology of Aerial Photographs
Basic terminology associated with aerial photographs includes the following:
i)  Format: the size of the photo;
ii)  Focal plane: the plane in which the film is held in the camera for photography (Figure 8.3);
iii)  Principal point (PP): the exact centre of the photo or focal point through which the optical axis passes. This is found by joining the fiducial or collimating marks which appear on every photo (Figure 8.4);
iv)  Conjugate principal point: image of the principal point on the overlapping photograph of a stereo pair;
v)  Optical axis: the line from the principal point through the centre of the lens. The optical axis is vertical to the focal plane (Figure 8.4);
vi)  Focal length (f): the distance from the lens along the optical axis to the focal point (Figure 8.3);
vii)  Plane of the equivalent positive: an imaginary plane at one focal length from the principal point, along the optical axis, on the opposite side of the lens from the focal plane (Figure 8.3);
viii)  Flying height (H): height of the lens above sea level at the instant of exposure. The height of a specified feature above sea level is designated “h” (Figure 8.3);
ix)  Plumb point (Nadir or vertical point): the point vertically beneath the lens at the instant of exposure (Figure 8.5);
x)  Angle of tilt: the angle subtended at the lens by rays to the principal point and the plumb point (Figure 8.5).

4. Focal plane
Focal plane: the plane in which the film is held in the camera for photography
Focal length (f): the distance from the lens along the optical axis to the focal point
Flying height (H): height of the lens above sea level at the instant of exposure. The height of a specified feature above sea level is designated “h”

5. The principal point, fiducial marks and optical axis of aerial photographs
Principal point (PP): the exact centre of the photo or focal point through which the optical axis passes. This is found by joining the fiducial or collimating marks which appear on every photo
Optical axis: the line from the principal point through the centre of the lens. The optical axis is vertical to the focal plane

6. Plum point and angle of tilt of aerial photographs
Plumb point (Nadir or vertical point): the point vertically beneath the lens at the instant of exposure
Angle of tilt: the angle subtended at the lens by rays to the principal point and the plumb point

7. The effect of topography on photo scale: photo scale increases with an increase in elevation of terrain

8. Variations in scale in relation to aircraft attitude. (After C. H
Variations in scale in relation to aircraft attitude. (After C.H. Strandberg, 1967)

9. An undistorted aerial photograph (a); distorted (b); and rectified (c)
An undistorted aerial photograph (a); distorted (b); and rectified (c). (After P.J. Oxtoby and A. Brown, 1976)

10.  Grid for transference of detail form an aerial photographs to a map: (a) polar grid; (b) polygonal grids (After G.C. Dickinsin, 1969)

11. Theory of Close Range Photogrammetry, Ch.2 of [Atkinson90]

12. Why photo is not a map? ck wb wa R - error on the map coused by DTM B
A defines refernce level A
RB-A

13. Radial dispacement an example
r = 100 mm
ck= 150 mm
Dh = 1m DR = 0.67m
Dh = 5m DR = 3.33m
r = 100 mm
ck= 300 mm
Dh = 1m DR = 0.33m
Dh = 5m DR = 1.67m

14. Airborne photo as a map - is it possible ?
On the airborne photo: errors caused by DTM and photo oblige
There is not possible to generate vertical airborhe photo, so even if the terrain is flat we are the errors caused by the oblige photo
How to remove it?

15. If terrain is flat the errors on the image can be removed by the projective transformation
A∙X+B∙Y+C
x =
D∙X+E∙Y+1
F∙X+G∙Y+H
y = y x
8 unknown coefficients (A...E)
One point = two equations
4 points – unique solution
(any three points must not lay on the one line) X Y Z

16. When terrain can be treated as a level?
Each map is produced with given accuracy if
R - error on the map caused by DTM is less then allowed map accuracy
then
Terain can be terated as plane (level)

17. When terrain can be treated as a level?ck
Rmax ?
Mean erro ± 0.3 mm in map scale B h A R
Map scale : mm = 30 cm in terrain
1: mm = 60 cm in terrain
1: mm = 3 m in terrain
1: mm = 7.5 m in terrain

18. If terrain is ca. plane projective transformation can be applied
rmax y x
Assuming reference plane in the middle of layer we have the thikness of the layer of ± Δhmax X Y Z
< 2Δhmax (maximum hight difference)

19. example hmax Map scale = 1:1000; photo: ck = 100 mm rmax = 150 mm
Rmax = 0.30 m hmax = 0.20m 2hmax = 0.40m
Map scale = 1:1000; photo : ck = 300 mm rmax = 150 mm
Rmax = 0.30 m hmax = 0.60m 2hmax =1.20m
Map scale = 1:10 000; photo : ck = 200 mm rmax = 150 mm
Rmax = 3.00 m hmax = 4.0 m hmax = 8.0 m

20. Coordinate system of airborne photox y
Fiducial points
Principal point

21. Coordinate system of airborne photox y
Proncipal point

22. External orientation of airborne photo
Vertical line
Coordinate of perspective center in terrain coordinate system X0, Y0, Z0
Projective center
angle κ determines yaw of the airborne image
(angle betwee x axis of the image and X axis of the terrain coordinate system) x y κ X Z Y
angles
φ(in plane XZ),
w (in plane YZ) deterimne tills of vertical camera axis φ ω
Camera axis
Terrain coordinate system

23. Collineartity equation
Fiducial coordinate image system z x y
x x
r = y = y
0 - ck ck O P R r
X0, Y0, Z0 ck O’ P’
XP – X0
R = YP – Y0
ZP – Z0 X Y Z
Terrain system
Vertical line
XP, YP, ZP

24. Collineartity equationck X Y Z
Terrain system
Image system z x y
Vertical line R P’ P O r O’
Collineartity equation
R =  • A • r
where: A – transformation atrix:   κ
λ – scale cofficient ( λ = )

25. Collineartity equation
R =  • A • r
A – rotation matrix describes orientation of fiducial system in relation to the terrain system
where: a11= cos κ cos φ
a12= sin ω sin φ cos κ + cos ω sin κ
a13= -cos ω sin φ cos κ + sin ω sin κ
itd

26. Collineartity equation
R =  • A • r
r = 1/ • A-1 • R
r = 1/ • AT • R 33 23 13 32 22 12 31 21 11 a AT =
A-1=

27. Collineartity equation
r = 1/ • AT • R
xP a11 a21 a XP - X0
yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a ZP - Z0
XP -X0
xP = 1/ • [a11 a21 a31] • YP -Y yP = , ck =
ZP -Z0
xP = 1/ • (a11 • (XP - X0) + a21 • (YP – Y0) + a31 • (ZP – Z0))
yP = 1/ • (a12 • (XP - X0) + a22 • (YP - Y0) + a32 • (ZP - Z0))
ck = - 1/ • (a13 • (XP - X0) + a23 • (YP - Y0) + a33 • (ZP - Z0))

28. Collineartity equation
r = 1/ • AT • R
ck = - 1/ • (a13 • (XP - X0) + a23 • (YP - Y0) + a33 • (ZP - Z0))
hence
1/ = - ck / (a13 • (XP - X0) + a23 • (YP - Y0) + a33 • (ZP - Z0))

29. xP, yP on the image and ck so together: r X0, Y0, Z0 (in vector R)
Collineartity equation terrain coordinate determination based on the point register on the image
xP a11 a21 a XP - X0
yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a ZP - Z0
known:
xP, yP on the image and ck so together: r
X0, Y0, Z0 (in vector R)
   (elements aij of matrix A)
calculated:
XP, YP, ZP (in vector R)

30. Collineartity equation terrain coordinate determination based on the point register on the image
xP a11 a21 a XP - X0
yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a ZP - Z0
Collinearity equation contained three unknowns: XP, YP, ZP, after separation to the component equation - we obtain two equations (xP=, yP=) not enough to the three unknowns calculation

31. xP’ a11’ a21’ a31’ XP – X0’ xP” a11” a21” a31” XP – X0”
Collineartity equation terrain coordinate determination based on the point register on the image
xP’ a11’ a21’ a31’ XP – X0’
yP’ = 1/’ • a12’ a22’ a32’ • YP - Y0’
-ck a13’ a23’ a33’ ZP - Z0’
xP” a11” a21” a31” XP – X0”
yP” = 1/” • a12” a22” a32” • YP - Y0”
-ck a13” a23” a33” ZP - Z0”
For coordinates XP, YP, ZP calculation from collinearity equation we have to measure the point on the two photos
In this case we obtaine two times of two equations (4 equations) and we calculate three unknowns (XP, YP, ZP)

32. ORTHOPHOTOMAP GENERATION

33. If terrain is ca. plane projective transformation can be applied
photomap - from projective transformation
assuming terrain is ca. plane y x X Y Z
< 2Δhmax (maximum hight difference)

34. Orthophoto – in terrain is not flaty x
Part of the photo
(pixel system) Z
DTM Y
Orthophotomap X

35. Orthophotomap
Assumptions:
Known elements of interior and external photo orientation
Known DTM
Orthophotomap if the map in photographical way but without errors caused by DTM and tilled airborne camera

36. Image rectification
Image rectification – image processing to the metric form and presented in terrain coordinate system
Rectification result is called by photographical map, because map content is in photographical form by the geometry is changed – new artificial image is generated, like we obtain in orthogonal projection
Photographical maps are categorized by photomaps and orthophotomaps, depending of the rectification method
If terrain is flat or almost flat projective transformation is applied and the result is called photomap
In the case if the applying of DTM is needed, because of the map accuracy, more complex process is involved, we called it orthophotorectification, and the result - orthophotomap KP

37. Mapping 2D on 2D – projective transformation mapping 3D on 2D –
With collinearity equations
Analythical relations
Linearization needed
simple 1 2 3 4 1’ 2’ 3’ 4’ 3 4 2 1 1’ 2’ 3’ 4’
unknowns
A, B,…, H (8)
(6)
needed for unknowns determination at least
4 points points
x,y x,y
X,Y X,Y,Z
x,y in any image coordinate system
x,y in fiducial coordinate system
5 pont and nexts are additional
4 point and nexts are additional

38. Data needed for image rectification
Photomap - 4 points of known x,y,X,Y
Orthophotomap:
camera calibration certification (for performing the interior orientation)
elements of external image orientation (or generation of the elements of external image orientation on teh base of minimum 3 points of known x,y,X,Y,Z)
Digital Terrain Model
Data can be obtained from:
aerotriangulation adjustements (will be lectured later)
measurements of the points on the image and in situ

39. Projective transformation
Digital image B
Projective transformation
Photomap on the image plane
Brighthess assign
(digital image A)
Digital fotomap generation

40. Orthorectification Brighthess assign Digital image B
ortofotomapa odwzorowana na płaszczyźnie zdjęcia
Brighthess assign
(digital image A)
Digital fotomap generation

41. Pixels of image A (photomap/orthophotomap) mapped on the image and their centres
image B pixels
New image (A) generation on the base of brightness of source image B is called resampling
Image A pixels

42. Mosaic