View
217
Download
0
Category
Tags:
Preview:
Citation preview
Remote Sensing & Photogrammetry
L7
Beata HejmanowskaBuilding C4, room 212, phone: +4812 617 22 72
605 061 510galia@agh.edu.pl
Photogrammetry
• Marine resource mapping: an introductory manual - FAO Corporate Document Repository http://www.fao.org/DOCREP/003/T0390E/T0390E00.htm#Toc
• 8. AERIAL PHOTOGRAPHS AND THEIR INTERPRETATION http://www.fao.org/DOCREP/003/T0390E/T0390E08.htm
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).
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”
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
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
The effect of topography on photo scale: photo scale increases with an increase in elevation of terrain
Variations in scale in relation to aircraft attitude. (After C.H. Strandberg, 1967)
An undistorted aerial photograph (a); distorted (b); and rectified (c).
(After P.J. Oxtoby and A. Brown, 1976)
Grid for transference of detail form an aerial photographs to a map: (a)
polar grid; (b) polygonal grids(After G.C. Dickinsin, 1969)
• Theory of Close Range Photogrammetry, Ch.2 of [Atkinson90]
• http://www.lems.brown.edu/vision/people/leymarie/Refs/Photogrammetry/Atkinson90/Ch2Theory.html
Why photo is not a map?
ck
wb
wa
A
B
A defines refernce level RB-A
kc
r
h
R
kc
rh=R
R - error on the map coused by DTM
r
h
Radial dispacementan example
R =h
c k
r
r = 100 mm
ck= 150 mm
h = 1m R = 0.67m
h = 5m R = 3.33m
r = 100 mm
ck= 300 mm
h = 1m R = 0.33m
h = 5m R = 1.67m
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?
If terrain is flat the errors on the image can be removed by the projective transformation
x
y
X
YZ
A∙X+B∙Y+Cx = D∙X+E∙Y+1
F∙X+G∙Y+Hy = D∙X+E∙Y+1
8 unknown coefficients (A...E)
One point = two equations
4 points – unique solution
(any three points must not lay on the one line)
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)
When terrain can be treated as a level?
kcr
hR
max
kmaxmax r
cR=h
r
A
B
R
h
ck
Rmax ?
Mean erro ± 0.3 mm in map scale
Map scale 1:1000 0.3 mm = 30 cm in terrain
1:2 000 0.3 mm = 60 cm in terrain
1:10 000 0.3 mm = 3 m in terrain
1:25 000 0.3 mm = 7.5 m in terrain
If terrain is ca. plane projective transformation can be applied
max
maxmax r
cRh k
rmax
< 2Δhmax (maximum
hight difference)
x
y
X
YZ
Assuming reference plane in the middle of layer we have the
thikness of the layer of ± Δhmax
example hmax
Map scale = 1:1000; photo: ck = 100 mm rmax = 150 mm
Rmax = 0.30 m hmax = 0.20m 2hmax = 0.40m
Map scale = 1:1000; photo : ck = 300 mm rmax = 150 mm
Rmax = 0.30 m hmax = 0.60m 2hmax =1.20m
Map scale = 1:10 000; photo : ck = 200 mm rmax = 150 mm
Rmax = 3.00 m hmax = 4.0 m 2hmax = 8.0 m
Coordinate system of airborne photo
Fiducial points
Principal pointx
y
Coordinate system of airborne photo
Proncipal point
x
y
External orientation of airborne photo
Terrain coordinate system X
Z
Y
Projective center
Coordinate of perspective center in terrain coordinate system X0, Y0, Z0
Vertical line
angles φ(in plane XZ), (in plane YZ) deterimne tills of vertical camera axis
ω
φ
κ
angle κ determines yaw of the airborne image(angle betwee x axis of the image and X axis of the terrain coordinate system)
Camera axis
x
y
Collineartity equation
X
Y
Z
Terrain system
Fiducial coordinate image system
z
x
y
Vertical line
R
P’
XP – X0
R = YP – Y0
ZP – Z0
P
O
r
x - 0 xr = y - 0 = y 0 - ck - ck
O’
X0, Y0, Z0
XP, YP, ZP
ck
Collineartity equation
ck
X
Y
Z
Terrain system
Image systemz
x
y
Vertical line
R
P’
P
O
rO’
R = • A • r
where: A – transformation atrix: κ
λ – scale cofficient ( λ = )|r||R|
R = • A • r
333231
232221
131211
aaa
aaa
aaa
A
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. .......
A – rotation matrix describes orientation of fiducial system in relation to the terrain system
Collineartity equation
R = • A • r
333231
232221
131211
aaa
aaa
aaa
A
Collineartity equation
r = 1/ • A-1 • R
r = 1/ • AT • R
332313
322212
312111
aaa
aaa
aaa
AT =A-1=
Collineartity equationr = 1/ • AT • R
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))
XP -X0
xP = 1/ • [a11 a21 a31] • YP -Y0 yP = ...... , -ck = ....... ZP -Z0
xP a11 a21 a31 XP - X0 yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a33 ZP - Z0
Collineartity equation r = 1/ • AT • R
ck = - 1/ • (a13 • (XP - X0) + a23 • (YP - Y0) + a33 • (ZP - Z0))
hence
)Z - (Z • a )Y - (Y • a ) X- (X • a)Z - (Z • a )Y - (Y • a ) X- (X • a
cx0P330P230P13
0P310P210P11kP
)Z - (Z • a )Y - (Y • a ) X- (X • a)Z - (Z • a )Y - (Y • a ) X- (X • a
cy0P330P230P13
0P320P220P12kP
1/ = - ck / (a13 • (XP - X0) + a23 • (YP - Y0) + a33 • (ZP - Z0))
Collineartity equation terrain coordinate determination based on
the point register on the image
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)
xP a11 a21 a31 XP - X0 yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a33 ZP - Z0
Collineartity equation terrain coordinate determination based on
the point register on the image
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
xP a11 a21 a31 XP - X0 yP = 1/ • a12 a22 a32 • YP - Y0
-ck a13 a23 a33 ZP - Z0
Collineartity equation terrain coordinate determination based
on the point register on the image
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)
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”
ORTHOPHOTOMAP GENERATION
If terrain is ca. plane projective transformation can be applied
< 2Δhmax (maximum
hight difference)
x
y
X
YZ
photomap - from projective transformation
assuming terrain is ca. plane
Orthophoto – in terrain is not flat
DTM
Orthophotomap
Part of the photo(pixel system)
X
Z
Y
x
y
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
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
Mapping 2D on 2D – projective transformation
mapping 3D on 2D –With collinearity equations
1
EYDX
CBYAXx
1
EYDX
HGYFXy
1
2
3
4
1’2’
3’4’
)()()()()()(
332313
312111
OOO
OOO
ZZaYYaXXaZZaYYaXXa
cx
)()()()()()(
332313
322212
OOO
OOO
ZZaYYaXXaZZaYYaXXa
cy
unknowns
,,,,, OOO ZYXA, B,…, H (8)
3
42
1
1’2’
3’4’
(6)
needed for unknowns determination at least
4 points 3 points
x,y x,y
X,Y X,Y,Z
Analythical relations
5 pont and nexts are additional 4 point and nexts are additional
simple Linearization needed
x,y in any image coordinate system
x,y in fiducial coordinate system
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
Projective transformation
Digital fotomap generation
Photomap on the image plane
Digital image B
(digital image A)Brig
hthe
ss a
ssig
n
OrthorectificationDigital image B
(digital image A)
ortofotomapaodwzorowanana płaszczyźnie
zdjęcia
Brig
hthe
ss a
ssig
n
Digital fotomap generation
image B pixels
Pixels of image A (photomap/orthophotomap) mapped on the image and their centres
New image (A) generation on the base of brightness of source image B is called resampling
Image A pixels
Mosaic
Recommended