SUG541 - Advanced Photogrammetry - Aerial Triangulation Method

MARA UNIVERSITY OF TECHNOLOGY JACK RUZAINI

BACHELOR OF GEOMATIC AND SURVEYING SCIENCE (AP220) [email protected] PHOTOGRAMMETRY (SUG541) Aerial Triangulation Method

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QUESTION

Briefly explain the following aerial triangulation (AT) method:

1. Aeropolygon using multi projector plotter for a short strip.

2. Aeropolygon using multi projector plotter for a long strip.

3. Aeropolygon using universal plotter for a short strip.

4. Aeropolygon using universal plotter for a long strip.

5. Aeropolygon using dual projector plotter for a short strip.

6. Aeropolygon using multi projector plotter for a small block (4 model/strip-4strips).

7. Independent Model Triangulation (IMT).

8. Cantilever IMT by simultaneous approach for a block of models.

9. Fully analytical AT by simultaneous bundle adjustment for a block of photo.

10. Digital AT by simultaneous bundle adjustment for a block of photo.

11. Integration of AT with GPS/INS with GCP.

12. Integration of AT with GCP/INS without GCP.

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ANSWER

1. Aeropolygon using a multi projectors plotter for a short strip.

This is an analogue method which uses a multi projectors plotter for a short strip of model.

This method use the concept of Direct Optical Projection Stereoplotter, which diapositive

of a stereopair are placed in projectors and being illuminated from above.

The instrument should be operated in a dark room and capable to make a rotational and

translational movement.

This Aeropolygon – method process is being setup on a scheme and the adjustments are

being made on a system.

The Absolute Orientation was suitable to be process in a graphical method.

The operation is done without computations and the ground coordinates (X, Y, Z) for the

Pass Points and Omega (Tilt), Phi (Tip), Kappa (Rotation) for the adjusted model were

obtained directly.

2. Aeropolygon using multi projectors plotter for a long strip.

This analogue method uses a multi projectors plotter for a long strip of model.

This method uses the concept of Direct Optical Projection Stereoplotter where a

diapositive of a stereopair is placed in projectors and being illuminated from the above.

The instrument is operated in dark room and it should have rotational and translational

movement capabilities.

The processing is based on Aeroplygon - method where all being setup on the scheme

and the adjustments were being made on the system.

The determination of coordinate is being done by Polynomial method. For a long strip it is

need to take the effect of curvature of the earth.

The Absolute Orientation is done using Numerical method where the equation of

transformation formula is determined.

The operation is done without computations and it creates a long striped model from which

coordinates of pass points could be read directly. The Omega (Tilt), Phi (Tip), Kappa

(Rotation) for the adjusted model also can be obtained.

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3. Aeropolygon using universal plotter for a short strip.

This analogue method of aerial triangulation is using a universal plotter for a short strip of

models.

The process is repeated for each new projector. The new model which has been brought

to scale cross tilting is checked, and the forward carry over point and past point are

selected and measured.

After instrumentation complete, the base sheet is generally oriented in a correct direction

referred to the control point. Then the strip model position of all control points is being

plotted on the base sheet.

This instrument used space rods instead of the complex mechanical system. The

instrument should have Base In and Base Out availability. It also should have the

processes of changing the optical path which is functioned to allow the operator to view

the left photograph with the right eye and the right photograph with the left eye.

The photographs were moved in X and Y tracks for the measurement process. It is

needed to apply a conformal method because for the short strip requirement, the earth

curvature effect is being neglected.

This method will produce an accurate coordinates (X, Y, Z) for the position of the image

when the model are properly oriented and calibrated.

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4. Aeropolygon using universal plotter for a long strip.

This is another analogue method which using a universal plotter in preparation for a long

strip of models. The Relative Orientation now performed in order to form a stereomodel.

The model is scaled and leveled.

When the model has been completely oriented, the past points were read to determine

their instrument coordinate. The physical orientation of space rod and optical trains in first

model are shown schematically. Left eye views left diapositive 1. Right eye views right

diapositive 2.

Now suppose that diapositive 1 is replaced with

diapositive 3. Space rod move upward as shown in

figure (Base-Out). Left eye views right diapositive

and right eye view left diapositive. Diapositive 3

effectively positioned to the right diapositive 2.

Diapositive 2 replaced by diapositive 4. Space rod

moved two Base-In positions. Left eye views left

diapositive and right eye views right diapositive.

Following the Relative Orientation of each new

model, scaling of the new model is performed by

changing the base component. It is to make an

elevation reading of the carry-over point agreed with

its reading in the previous model. This means that

the Z-counter must not be reindexed throughout the

strip.

The instrument should have Base-In and Base-Out

availability. It should consist the process to change the optical path which allows the

operator to view the left photograph with the right eye and right photograph with the left

eye. This instrument used space rods instead of the complex mechanical system.

To determine the coordinates, the use of conformal method will involved a calculation. So

the most suitable is by using polynomial method. And this will take on the effect of earth

curvature and are much simpler compared to the conformal method. This method will

produce accurate coordinates (X, Y, Z) for the position in the image when the model are

properly oriented and calibrated.

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5. Aeropolygon using dual projector plotter for a short strip.

This analogue method of Aerotriangulation is using a dual projector plotter for a short strip

of models.

To complete the system it needs a double projector, which offered a direct viewing of the

projected images.

In order to have a sharp focus when the negative and easel (positive) planes are not

parallel, the negative plane, easel plane and lens plane (plane perpendicular to the optical

axis) must intersect along one line.

The adjustment for the model involved the Relative and Absolute orientation. It is

necessity of redundant rays to recreate the proper geometry.

The adjustment is done using the conformal method. Conformal are used normally for

image that are less than 4. Conformal consist of multiplying each of the original coordinate

of points by scale factor.

This method will produce an accurate coordinates (X, Y, Z) for the position in the image

when the model are properly oriented and calibrated.

6. Aeropolygon using multi projector plotter for a small block (4 model/strip-4strips).

Model coordinate; stereoplotter measurement.

Derive coordinates of the perspective center.

Transformation using 3D conformal.

Linear equation where the unknown parameter transformation only the correction the

parameter.

Derive initial value for the transformation for unknown parameters.

Forming observed using Least Square Equation.

Correction will get to apply for initial value.

7. Independent Model Triangulation (IMT).

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i. IMT by a sequential method for a short strip of models;

Each stereopair of a strip is relatively oriented in a stereoplotter.

Adjustment using 3D conformal coordinate transformation and the coordinate system

of each model being independent of the others.

2 horizontal control point and 3 vertical control point.

Adjustment to transfer coordinates from model to the ground.

4 models

ii. IMT by a sequential method for a long strip of models;

More than 4 models.

3D conformal adjustment to transform model coordinates to the ground coordinate

system.

Most of 3D conformal in use of adjusting strips formed by aerotriangulation are

variations of the order equations.

8. Cantilever IMT by simultaneous approach for a block of models.

This approach avoids the accumulation of errors inherent in the sequential strip

forming process and thus requires no polynomial error modeling.

The basis of simultaneous independent model aerotriangulation is the 3D conformal

coordinates transformation.

All models in a strip or block are joined and adjusted to ground control in a single step,

much like the simultaneous transformation technique.

A more robust method for performing independent model aero triangulation is to

employ simultaneous transformation rather than sequential.

9. Fully analytical AT by simultaneous bundle adjustment for a block of photo.

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Simultaneous Bundle Adjustment is a principle that is used to adjust all photogrammetric

measurements to ground control values in a single solution.

The process is named because of many light rays that pass through each lens position

constituting a bundle of rays.

The bundles of ray from all photos were then adjusted simultaneously so that the

corresponding light rays intersect at positions of the pass and control points on the

ground.

The process is an extension of the principles of analytical photogrammetry was applied to

an unlimited number of overlapping photographs.

Fully analytical aerotriangulation must be adjusted by a weighted least square

adjustment method.

Adjustment software must be form the collinearity conditions equations for the entire photo

coordinate observation the black and solve for all photo orientation and ground point

coordinates in each iteration until the solution converges.

The exterior coordinate system used for the adjustment should be a local rectangular

coordinate system.

This coordinate system contains no earth curvature or map projection distortions.

These effects may be judged to be negligible for small project areas and low flying

heights, but they are significant factors for large projects areas and high flying heights.

The least square adjustment results should be examined to check the consistency of the

photo coordinate measurements and the ground control fit.

Residuals on the photo coordinates should be examined to see that they are

representative of the random error expected from the instrument used to measure them.

Residuals should be randomly plus or minus and have uniform magnitude. The residual

should be checked carefully for outliers and systematic trends.

The standard deviation of unit weight computed from the weight adjusted residuals should

not be more than 1.5 times the reference standard deviation used to computed the

weights for the adjustment.

10. Digital AT by simultaneous bundle adjustment for a block of photo.

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With the development of digital photogrammetric workstations - sometimes called softcopy

workstations - and high resolution image scanners, which both are offered at a highly

operational level, aerial triangulation should be automated.

The benefit working in a digital environment is its automation potential.

As far as digital aerotriangulation is concerned this is restricted only to the identification of

ground control points and signalized tie points, as well as the measurement of image

coordinates of these classes of points.

The difficulty of detecting (signalized) ground control points when working in a digital

image of reasonable resolution - let us assume 15 - 30µm pixel size - is the pixel width of

the point signal.

In order to be reliable more than 3 - 5 pixel should be used in any template matching

process, otherwise the matching algorithm is not able to match the template with its

image.

One solution to overcome this problem would be a pointwise improved resolution of the

scanning process, what means the scanner should automatically driven to points with

signals.

As a consequence the scanning software should include already template matching

algorithms to be autonomous in this respect.

The task of digital aerotriangulation is the complete process of aerial triangulation

including block adjustment, on the basis of digital imagery resp. scanned analogue images

by semi- and/or fully automated procedures.

11. Integration of AT with GPS/INS with GCP.

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Aerotriangulation is essentially an interpolation tool, capable of extending control points to

areas between ground survey control points using several contiguous uncontrolled

stereomodels.

An aerotriangulation solution should never be extended or cantilevered beyond the ground

control. Ground control should be located at the ends of single strips and along the

perimeter of block configurations.

Within a strip or block, ground control is added at intervals of several stereomodels to limit

error propagation in the adjusted pass point coordinates. Extending control by

aerotriangulation methods is often referred to as bridging since the spatial image ray

triangulation spans the gap between ground controls.

Ground control accuracy for aerotriangulation should be more stringent than for a project

fully controlled by field survey points. The aerotriangulation solution will contribute to the

propagated error in the pass point ground control values. Since the pass point coordinates

should meet the accuracy required for photo control, the photo identifiable ground control

points used to control the aerotriangulation should be more typical of the accuracy of the

basic control survey.

AREA AT WITH GCP INS – AT WITHOUT GCP

Position

RMS

Height

RMS

Position

RMS

Height

RMS

1 5cm 2cm 8cm 20cm

2 7cm 10cm 12cm 20cm

3 7cm 2cm 26cm 28cm

Comparison of a traditional aerotriangulation with ground control points (GCP) versus an AT

without GCPs based only on the DGPS and INS data.

Well designed blocks with good overlap and opposite flight lines can deliver sufficient

results, for low and mid level accuracies actually without GCPs.

The geo referencing is poor checked without any GCPs. Inaccuracies among the images

direction dependent errors can be avoided using the AT with sufficient tie points,

systematic errors of the whole block can not be finally excepted. This kind of problems can

be solved by using just 1 or 2 GCPs.

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The situation is much more complicated in single lines without cross track overlap. Some

test delivered results in an accuracy level of single images. If in anyway possible

additional overlap of the separate lines is recommended.

Whereas in usual AT the accuracy of the ground points (GCPs and tie points) are in the

center of attention, in the AT for boresight calibration the accuracy of the rotation angles is

the primary target. Some special requirements have to be considered:

a. A very good DGPS solution is necessary. All ambiguities have to be solved.

b. The offset of the antenna has to be measured with geodetic methods.

c. A simultaneous camera calibration has to be avoided. The calibration of the camera

has to be fixed.

d. The use of additional parameters has to be restrictive.

e. No shift or drift parameters for the separate lines can be used.

f. Overall shift parameters may be used, but no rotations.

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12. Integration of AT with GCP/INS without GCP.

Aerial triangulation controlled by GPS observations in the aircraft has been established as

a precise method of photogrammetric point determination without the need of ground

control. New developments of kinematic GPS processing yield accurate exposure

locations instantaneously.

Aerial triangulation can be carried out without any ground control points provided that

GPS observations are available for blocks of aerial photos. Unfortunately, this method

cannot be applied to single flight lines, since the GPS observations do not recover the roll

angle of the aircraft. Therefore, ground control is mandatory for GPS controlled strip

triangulation.

GPS aerotriangulation can be accomplished in two steps: relative and absolute

orientations. The relative orientation can be performed by measuring at least five tie points

in each stereo-pair. The resulting models can be joined together for the whole block or

strip, yielding one model in a local coordinate system. Performing this task does not

require any ground control.

On the other hand, in order to perform the absolute orientation, control is mandatory.

The minimum control requirement for the absolute orientation is three control points that

must not be collinear.

For GPS controlled block triangulation this condition is satisfied because the GPS

observations at the perspective centers, our control, are well distributed over the whole

block. On the other hand this condition is not satisfied for strip triangulation since the GPS

observations of the exposure stations are almost collinear. In that case, the roll angle

(around the flight direction) cannot be recovered, and ground control points are necessary

for solving the absolute orientation.

Basically, the following procedure is executed:

a. Measure image coordinates of a number of points along the linear feature in the

captured images; this can be done monoscopically.

b. Fit an analytical function through these points in the image. Each image has an

individual function representing the linear feature.

c. As constraint of the adjustment, the ground feature is projected into image space

and must belong to the corresponding function in the image; this serves as a

constraint in the least squares adjustment.

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SUG541 - Advanced Photogrammetry - Aerial Triangulation Method