P.1

1
Sensor Modeling and Triangulation for an
Airborne Three Line Scanner lt 2008 ASPRS Annual
Conference gt

• JAMES S. Bethel
• Wonjo Jung
• Geomatics Engineering
• School of Civil Engineering
• Purdue University
• APR-30-2008

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Outline

• Introduction
• Dataset
• Camera Design
• Flight and observations (3-OC Atlanta, GA)
• Sensor Model
• Trajectory Model
• Pseudo Observation Equations
• Data Ajustment
• Implementation
• Results
• Conclusions
• Future plans

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1. Introduction
MAIN OBJECTIVE
Developing an algorithm to recover orientation
parameters for an airborne three line scanner
4
1. Introduction - Types of three line scanners
Three separate cameras
Linear arrays on the same focal plane
Lens
5
1. Introduction
Instantaneous gimbal rotation center
flight trajectory

• While ADS40, TLS and JAS placed CCD arrays on the
  focal plane in a single optical system, 3-DAS-1
  and 3-OC use three optical systems, rigidly fixed
  to each other.
• For this reason, we need to develop a
  photogrammetirc model for three different cameras
  moving together along a single flight trajectory

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1. Introduction

• Parameters to be estimated
• Exterior orientation parameters
• 6 parameters per an image line
• Additional external parameters
• Translation vector between a gimbal center to
  perspective centers
• Rotation angles between gimbal axis and sensor
  coordinate systems
• Interior orientation parameters
• Focal lengths
• Principal points
• Radial distortions

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1. Introduction

• There have been two kinds of approaches.
• Reducing number of unknown parameters
• Piece-wise polynomials
• Providing fictitious observations in addition to
  the real observations
• Stochastic models

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1. Introduction

• Reducing number of unknown parameters
• Piecewise polynomials

3618
estimated
100066000
given
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1. Introduction

• Providing fictitious observations in addition to
  the real observations
• 1st-Order Gauss-Markov Model

observations
estimated
given
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1. Introduction

• Self-calibration
• Partial camera calibration information is
  provided.
• focal length, aperture ratio, shift of the
  distortion center, radial distortion
• Coordinates of projection center of the camera
  relative to the gimbal center is not measured.
  Just design values are provided.
• Need to refine some of the parameters

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2. DATASET

• Camera Design (3-OC)

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2. DATASET
Strip ID Heading Altitude
2 E 5,500ft
3 W 5,500ft
4 E 5,500ft
5 W 5,500ft
6 S 5,500ft
8 N 5,500ft
9 S 5,500ft
10 N 5,500ft
11 S 10,500ft
12 N 10,500ft
13 S 10,500ft
14 N 10,500ft
15 E 10,500ft
16 W 10,500ft
17 E 10,500ft
18 W 10,500ft
20 GCPs
8Check points
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3. Sensor Model

• Collinearity Equation a line scanner

Sensor Coordinate System (SCS)
Perspective Center
scan line
flight direction
SCS
column
row
Ground
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3. Sensor Model

• Collinearity Equation - oblique camera

perspective Center
scan line
flight direction
Ground
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3. Sensor Model

• Collinearity in a three line scanner

three angles should be considered
flight direction
gimbal center
B
N
F
plumb line
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4. Trajectory Model

• 1st order Gauss-Markov trajectory model
• Probability density function f(x(t)) at a certain
  time is dependent only upon previous point
• Probability density function is assumed to be
  Gaussian
• Autocorrelation function becomes

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4. Trajectory Model

• 1st order Gauss-Markov trajectory model

autocorrelation function
Parameters are highly correlated!
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5. Pseudo Observation equations
One-sided equation
Symmetric pseudo observation equation
t
autocorrelation function
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6. Data Adjustment

• the Unified Least Squares Adjustment

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7. Implementation

• To reduce the number of parameters, only the
  parameters of lines containing image observations
  are implemented.
• For the memory management, IMSL Ver. 6.0 library
  is used. IMSL contains a sparse matrix solver.
• riptide.ecn.purdue.edu
• Red Hat Enterprise Linux 4 operating systems
• 16 multi core processors
• 64GB of system memory

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8. Results

• Processing time 49 seconds
• (16 core x86_64 Linux with 64GB ram)
• Number of iteration 7
• Converged at 0.58 pixels
• RMSE 1.08 pixels for 8 check points

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8. Results

• Interior Orientation parameters are
  self-calibrated

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9. Conclusions

• We could successfully recover the orientation
  parameters using stochastic trajectory model
• Interior orientation parameters of three cameras
  can be refined through the self calibration
  process

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9. Future Plans

• Analysis on the model properties
• Adding pass points
• Automated passpoints generation