A Review on Analytical Photogrammetry

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1M. Saadat Seresht M. Saadat Seresht Dept. of Surveying Engineering and GeomaticsDept. of Surveying Engineering and GeomaticsThe University of TehranThe University of Tehran

A Review onA Review on

Analytical PhotogrammetryAnalytical Photogrammetry

CHAPTER TWOCHAPTER TWO

Feb. 2004Feb. 2004

Photogrammetry IVPhotogrammetry IV


ContentContent

CHAPTER TWO

A Review on Analytical Photogrammetry

Mono Image

Stereo Images

Photography Planning




Mono ImageMono Image


Single Camera GeometrySingle Camera Geometry

• Central perspective projection

– Projection plane

– Perspective axis POp

– Principal point p

– Principal distance c

– Homologous points a and A

• Coordinate systems:

– Object coordinate systems XYZ

– Image coordinate systems xyz

X

Z

Y

z

x

y

y

p

P

a

r

Oc

A




Geometric ModelGeometric Model

• X A

=XO+S

• S=-uRtxa

• xa=u-1R(XO-X A)

−

−

=

c

y

x

r r r

r r r

r r r

u

Z

Y

X

Z

Y

X

a

a

O

O

O

A

A

A

332313

322212

312111

X

Z

Y

z

x

y

a

O

A

X A

S

XO

x

y

Rt

xa

−

−

−

=

−

−

O A

O A

O A

a

a

Z Z

Y Y

X X

r r r

r r r

r r r

u

c

y

x

333231

232221

131211

1


The CoThe Co--linearity Conditionlinearity Condition

Perfect solution:

Linear solution: DLT

1

1

11109

8765

11109

4321

+++

+++=

+++

+++=

Z LY L X L

L Z LY L X L y

Z LY L X L

L Z LY L X L x




Camera CalibrationCamera Calibration

• Difference between real geometry of image

formation and ideal central perspective

projection

• The most discrepancy is lens.

• Calibration methods:

– Self calibration

– One the job calibration

– Analytical plumb-line calibration

• Fraser (1197), Digital camera self calibration, ISPRS Journal ofPhotogrammetry & Remote Sensing , 52:149-159.


Lens DistortionLens Distortion

• Lens performance and stability – Gaussian and Balanced radial distortion

• Radial lens distortion: – Polynomial function of radial distance from point of

symmetry

– dr =K1r 3+K1r 5+K1r 7 – dx=dr x/r and dx=dr y/r

• Tangential lens distortion: – Misalignment of lens components => image point

displacement

– dx=P1[r 2+2x]+2P2xy

– dy=P2[r 2+2y]+2P1xy




Film DeformationFilm Deformation

• Film unfastens• Film distortion

• Reseau plate and vacuum device

• Fiducial marks

• 2D transformations – 2D conformal

– 2D affine

– 2D projective


Earth CurvatureEarth Curvature

A

A’

aa’




Image ResectionImage Resection

• 3 Rotations – Physical: Euler

– Analytical: Rodrigues

• 3 Positions

• Min 3 GCP

• Methods:

– Co-linearity condition

– DLT


Image RectificationImage Rectification

• In Flat area Z=aX+bY+c

• 2D projective transformation is proper!

1

1

87

654

87

321

++

++=

++

++

=

Y L X L

LY L X L y

Y L X L

LY L X L

x




Stereo ImageStereo Image


CoplanarityCoplanarity ConditionCondition

• Relative orientation

• Epipolar plane

• 5 variable 1 equation

• Min 5 stereo points

O1O2

A0

222

111

=

z y x bbb

z y x

z y x




Image IntersectionImage Intersection

• 1 Stereo point measurement = 4 equations• 3D point = 3 variable

• Solution methods:

– Resection + Intersection

– Resection/Intersection

• Model:

– DLT

– Co-linearity condition


Photography PlanningPhotography Planning




Photography PlanningPhotography Planning


Image ScaleImage Scale

• Topographic map scale: mi=K sqrt(mm)

– Standard equipments: K=200

– Modern equipments: K=300-350

• Forward motion compensation

• Restitution accuracy: – Planimetric

– Height :

Hg =11500sz Mi=1000Hg/f

]005.0[

][1000][

'mm

mmmm

xy

xy

i=

=σ

σ




OverlapOverlap

D=d hg /c


Side lapSide lap

The highest ground level should be considered!




Classification of PointsClassification of Points

• According to identification – Signalized point

– Natural point

– Artificial point

• According to their use in adjustment – Control point

– Tie point

– Single point

Documents

A Review on Analytical Photogrammetry