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Lecture 17 Content. Aerotriangulation (AO). Defined as the procedure of establishing the geometric relationships among overlapping and side lapping photographs for determining the positions of supplemental horizontal control points Reduces substantially the control required by field methods.

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Lecture 17 content

Lecture 17 Content

Aerotriangulation (AO)

Lecture 17 content

  • Defined as the procedure of establishing the geometric relationships among overlapping and side lapping photographs for determining the positions of supplemental horizontal control points

  • Reduces substantially the control required by field methods



  • Triangulation calculates:

    • The position and rotation of the camera each time an image was exposed (Exterior Orientation Parameters)

  • The X, Y and Z coordinates of tie points

Overlap between runs or swaths

30% overlap between

runs or swaths

Run #1

Run #2

Overlap between Runs or Swaths

What is a block

  • 1. Photographs or images

  • 2. Camera information


  • 3. Control

What is a BLOCK?

  • A BLOCK is all the information needed to triangulate a set of air photographs in one process

  • This must include:

  • 4. Projection, Spheroid, Datum Information

What is a block1

60% Overlap

What is a BLOCK?

  • A Block created in Stereo Analyst contains two overlapping images (a Stereo Pair).

Lecture 17 content

  • Aeotriangulation adopts photogrammteric triangulation which establishes the geometric relationships among overlapping and sidelapping photographs to determine supplemental horizontal and vertical control points

  • Aeotriangulation is performed using one of two methods:

    • Semianalytical (or independent model triangulation)

    • Analytical (or bundle block)

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  • Semianalytical

    • passes control from one model to the next

    • Model’s relative orientation is done instrumentally on the plotter or analytically using a computer program, but the scale transfer between successive models is accomplished analytically

    • Hence each model are independently generated

    • Each model will have at least 3 tie points in common

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  • Relative orientation is done for each model and absolute orientation is done for the first model

  • Use is made of the coordinates of the perspective centers of both photos (using the same coordinate system) as tie points

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  • Coordinates for the second overlap is transformed mathematically by making coordinates of the left-hand perspective center of the first overlap and then rotating the second coordinate system about its three axes to make the points coincide with the first overlap

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  • The perspective center coordinate provides a strong geometric tie between the models

  • Tie points are computed using computer program that implements a transformation involving 7 parameters:

    • 3 translations

    • 3 rotations

    • One scale change

Tie points

Tie points

  • A TIE point is the image coordinate position of an object appearing on 2 or more images

  • The X, Y and Z coordinates of a tie point are unknown and are determined by OrthoBASE during the aerial triangulation procedure

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  • Analytical

    • This is the second method of aerotriangulation

    • Image point-measuring instruments (comparator, analytical plotter, workstation) are used to measure the x-y plate coordinates of each tie point and control point in each photograph

    • Sequence of mathematical models are formed from which strip coordinates are derived

    • Mathematical model represent the geometric relations between object space, perspective centers, and photographic images

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  • Image points are represented by their photographic coordinates measured

  • Input are photographic coordinates, camera parameters, and ground control points

  • Use is made of the collinearity and coplanarity equations to manipulate the coordinates in a high speed computer

  • Output of the computations are ground coordinates and elevations of the tie points

  • Ideal tie points are the same points used in relative orientation

  • Ability to correct for all possible systematic errors, such as film shrinkage, lens distortion, atmospheric refraction, and so on

Block residuals

Block Residuals

  • Block of eight images…

  • Image & ground measurements

Least Squares Adjustment calculates new points based on distributing and minimizing residuals throughout the ENTIRE block

  • There are RESIDUALS for:

  • Each ground point

  • Each image point

  • Each perspective center

Spreading error

Predicted Location

Standard Deviation



Spreading Error

  • The adjustment distributes error throughout the block trying to minimize all the residuals

  • You can control the adjustment process with the quality estimates

When to stop

When to stop?

  • Least Squares is an iterative process. So, how does the process know when to stop adjusting the points and recalculating residuals?

  • We define a threshold value in meters

    Convergence Value

  • Once the process reaches convergence it stops

  • What is convergence?…

The convergence value














The Convergence Value

  • After each iteration residuals calculated for each measurement

If every difference between these values is less than the Convergence value, the iterations will STOP












Indicates that the triangulation has met the required accuracy




Scba how it works

Self Calibrating and Bundle Adjustment

  • Focal length

  • Principal Point

SCBA: How it works

  • More GCPs an advantage (6 per overlap)

  • SCBA will estimate the Interior Geometry of the sensor

Self calibrating bundle adjustment scba

Self-Calibrating Bundle Adjustment (SCBA)

  • Cameras not designed for photogrammetry:

    • Non-metric camera, digital camera or videography

  • Cameras with outdated or no calibration reports

  • Will estimate the interior orientation parameters of the camera/sensor

    • Focal length

    • Principal Point in the x direction

    • Principal Point in the y direction

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… The End …

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