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