correction of geometric distortions in line scanner imagery

Digital Imaging and Remote Sensing Laboratory

Correction of Geometric Distortions in Correction of Geometric Distortions in Line Scanner ImageryLine Scanner Imagery

Peter Kopacz

Dr. John Schott

Bryce Nordgren

Scott Brown

May 8, 1998


CoverageCoverage

• Line Scanner Background Theory

• Geometric Distortions

• Results

• Future Work / Recommendations


Line Scanner ExampleLine Scanner Example

across track

along track

FOV

IFOV

sampled ground pixel

• Airborne / Spaceborne EO Imaging Instrument

• Scanning mirror allows for collection of ground data

one line at a timegeometric distortions...


Geometric DistortionsGeometric Distortions

• Degradation in visual appearance of the

image

• Due to the Platform Attitude (orientation):

Roll, Pitch, and Yaw

• Due to the Sensor’s Design Characteristics:

Tangential, V/H

roll distortion….


Roll DistortionRoll Distortion

hypothetical output image

Nadir

direction of flight

Roll Distortion introduces a shift in the

acquired scan lines. tangent distortion….


h y p o th e ti c al o u tp u t im a g e

direction of flight

DnadirDedge

Tangent DistortionTangent Distortion

- All pixels collected at equal angular increments.

- Unequal ground representation between the collected

ground pixels (Dedge > Dnadir) V/H distortion….


Oversampling….

• V/H - ratio of aircraft velocity and altitude

• oversampling - scan rate is too fast when

compared to the ratio

• undersampling - scan rate is too slow when

compared to the ratio

V/H DistortionV/H Distortion



Nadir

direction of flight

V/H Distortion - oversamplingV/H Distortion - oversampling

Undersampling….

Scan lines are acquired too fast, causing an overlap


V/H Distortion - undersamplingV/H Distortion - undersampling


Nadir

direction of flight

proposed hypothesis….

Scan lines are acquired too slow, leaving gaps


HypothesisHypothesis

Develop a set of C algorithms to correct the

discussed geometric distortions in line

scanner imagery.

Research Progress….


Uncorrected InputUncorrected Input

512

512

Scan Parameters

512 scan lines

512 pixels per line

altitude = 1000 ft

Field of View = 45o


Corrected OutputCorrected Output

334

551

• Roll Correction - (shifting of scan lines rectifies the image)

• V/H Correction - (eliminated the stretching in scene objects)

• Tangent Correction - (pixels represent equal ground areas)


• Nearest Neighbor Resampling

• Mean Radiometry (DC Distribution) Preserved

Histogram ComparisonHistogram Comparison

Input Image (512 x 512) Output Image (551 x 334)



512

512

Scan Parameters

512 scan lines

512 pixels per line

altitude = 250 ft

Field of View = 45o

Distortions:

V/H (Undersampling)

Tangent



1336

541

• V/H Correction - (eliminated compression

effects in scene objects)

• Tangent Correction - (pixels represent

equal ground areas)

• Equal ground representation along and

across track (square ground pixels)


Input Image (512 x 512) Output Image (541 x 1336)

Histogram ComparisonHistogram Comparison

• Nearest Neighbor Resampling

• Mean Radiometry (DC) Preserved

Research Progress….



512

512

Scan Parameters

512 scan lines

512 pixels per line

altitude = 250 ft

Field of View = 45o

slant path (45 degrees)

Distortions:

V/H (Undersampling)

Tangent (ex:curvature

along the diagonal)



615

1025

• V/H Correction - (eliminated compression

effects in scene objects)

• Tangent Correction - (pixels represent

equal ground areas)

• Improvement in the appearance of the

diagonal


Algorithm ImprovementsAlgorithm Improvements

• Single resampling after Roll, Tangent, and V/H

corrections limits further image degradation (ex:

blurring due to bilinear resampling)

• Choice of Resampling Algorithms:

Nearest Neighbor or Bilinear

• Corrects multiple bands simultaneously

Error Analysis….


Scientific AnalysisScientific Analysis

• accurate determination of ground pixel’s position dictates

the appearance of the resulting image.

• determines which flight parameters are the largest

sources of error : aircraft velocity, aircraft altitude, roll

angle, start angle, IFOV?

How ? ...


Error Sensitivity AnalysisError Sensitivity Analysis

Based on the governing equations, estimate the errors across track (X) and along track (Y)

Starting ofCollection

Y (Along Track)

X (Across Track)

Error Across Track….


Error Across TrackError Across Track

direction of flight

DnadirDedge

H

start + roll

IFOV

ground pixel ctr[x] = H * tan ( start + roll + (IFOV*x) + (IFOV/2) )

Plots….


Roll Angle EffectsRoll Angle Effects

Across Track Error due to Roll Angle(altitude=1000 ft)

(roll=0 deg.)

0

5

10

15

20

25

30

35

40

45

500.

000

0.10

3

0.20

6

0.30

9

0.41

3

0.51

6

0.61

9

0.72

2

0.82

5

0.92

8

1.03

1

1.13

4

1.23

8

1.34

1

1.44

4

1.54

7

1.65

0

1.75

3

1.85

6

1.96

0

2.06

3

Uncertainty in Roll Angle (degrees)

Err

or

(pix

els)

edge pixel (45 deg.)

nadir pixel (0 deg.)

• Largest source of error across track

• Sensor’s ability to accurately determine a ground pixel’s

position decreases for pixels near the edges


Altitude EffectsAltitude Effects

Across Track Error Due to Altitude(altitude=1000 ft)

(roll=0)

0

5

10

15

20

250.

00

1.81

3.63

5.44

7.25

9.07

10.8

8

12.6

9

14.5

1

16.3

2

18.1

3

19.9

5

21.7

6

23.5

7

25.3

8

27.2

0

29.0

1

30.8

2

32.6

4

Uncertainty in Altitude (feet)

Err

or

(pix

els)


nadir pixel (0 deg.)

• Second Largest source of error across track

• Nadir pixel unaffected by the sources of error

Error Along Track….


Error Along TrackError Along Track

Nadir

Velocity

yH

ny= n * ( (H *IFOV) - (Velocity * time_per_scan) )

Plots….


Along Track Error Due to Uncertainties in Velocity(altitude=1000 ft)

(velocity=166 ft/sec)(scan rate=30 Hz)

0

5

10

15

20

250

1.62

3.24

4.86

6.48 8.1

9.72

11.3

4

12.9

6

14.5

8

16.2

17.8

2

19.4

4

21.0

6

22.6

8

24.3

25.9

2

27.5

4

29.1

6

30.7

8

32.4

Uncertainty in Aircraft Velocity (ft/sec)

Err

or

(pix

els)

1 pixel from nadir6 pixels from nadir32 pixels from nadir

Velocity EffectsVelocity Effects

• Largest source of error along track

• Position Error increases with aircraft velocity


Along Track Error due to Altitude(altitude=1000 ft)

(velocity=110 mph)(scan rate=30 Hz)

0

2

4

6

8

10

12

14

16

18

0.00

1.63

3.26

4.90

6.53

8.16

9.79

11.4

2

13.0

5

14.6

9

16.3

2

17.9

5

19.5

8

21.2

1

22.8

5

24.4

8

26.1

1

27.7

4

29.3

7

31.0

1

32.6

4

Uncertainty in Altitude (ft)

Err

or

(pix

els)

near nadir (0.1 deg.)


Altitude EffectsAltitude Effects

• Second Largest source of error along track

Future Work….


Conclusion - Future WorkConclusion - Future Work

• Correction algorithms successfully improve the

visual appearance of the image

• Incorporate the algorithms with (MISI) line

scanner

• Incorporate other geometric distortions, such as

pitch and yaw

Acknowledgments….


AcknowledgmentsAcknowledgments

I’d like to thank the following people for contributing to this

research:

• Dr. John Schott

• Bryce Nordgren

• Scott Brown

• Rolando Raqueño

www.cis.rit.edu/~pak2930

correction of geometric distortions in line scanner imagery

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