Mapping forest plots: An efficient method combining photogrammetry and field triangulation/trilateration

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Mapping forest plots An efficient method
combining photogrammetry and field
triangulation/trilateration
MMVAR-Colloquim May 4, 2007Korpela, Tuomola and
Välimäki
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• Point positioning in the forest
• - Mapping needs When the structure, position and
  geometric relations are somehow important ?
  ecological applications
• Accuracy precision Local and Global - Data
  acquisition for distance-dependant growth models
  - Data acquisition for Remote Sensing teaching,
  validation - Misalignment - offsets (bias
  in XYZ) - Distortions from Cartesian
• 2D and 3D mapping An issue of complexity?
• Existing methods Case Tree mapping in a forest
  plot

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Existing methods Case Tree mapping in a forest
plot Objective Stem/Butt positions in
XYZGLOBAL Phases1. XYZLOCAL mapping2. XYZLOCAL
? XYZGLOBAL transformation
Phase 1 - Options- Tacheometry (Spherical
coordinate system)- Theodolite (Triangulation
needed)- Compass EDM (Polar Coordinate system,
XY)- Grid-methods (Prism and tapes, XY)Phase 2
- Options- H for origin by levelling (Geodetic
infra)- XYZ / XY(H) for origin using GPS-
XY-orientation, compass, not good- Full rigid
7-parameter transformation XYZ-offset,
XYZ-rotations, scale, Control points. Young
stands use Network-RTK satellite positioning.
One investigator cm-level accuracy
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New method Point (Tree) mapping directly in
XYZGLOBAL Objective Stem/Butt positions in
XYZGLOBAL Phases XYZLOCAL mapping and XYZLOCAL ?
XYZGLOBAL transformation combined. Assumptions 1
) Up-to-date (with respect to events in the
forest) orientated (XYZGLOBAL) aerialphotography
is available. Large scale gt 115000. More than 1
view per target.Enough for XY-positioning. 2)
An accurate Digital Terrain Model (DTM) is
available. Enables Z / H positioning. 3)
Photogrammetric workstation software for
measuring XYZGLOBAL treetoppositions, called
points PA. These are considered as XY control
points. 4) Points PA can be found in the field
and used for the positioning of other targets.
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New method Point (Tree) mapping directly in
XYZGLOBAL

• Background Points PA can be used for positioning
  of other points
• Points PA are treetops observed in the aerial
  images with coordinates (XA,YA)- For
  non-slanted trees (XA,YA) stem position-
  Inaccuracy ?XA ? ?YA 0.25 m, Control points
  with observational error.
• Triangulation in plane
• - Create a base-line with exact distance, fix the
  datum or let it float, triangulate with angle
  observations between new points, use LS-
  adjustment of angle-observations for the
  computation of XY-positionsForward ray
  intersection in plane
• - Observe angles or bearings/azimuths between the
  unknown point P0 and known points PA. Use
  LS-adjustment of angles to compute the
  XY-position of point P0 (and, if needed, the
  orientation of the angle-device).
• Trilateration in space / plane
• - Measure distances from known points (e.g.
  satellite in its orbit) to the unknown point
  and use LS-adjustment of distance observations
  for computing the XY- or XYZ position.

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Background - MATHEMATICS - LS-adjustmentof
intertree azimuths and distance observations
Objective Obtain XY-position for P0We have -
Photogrammetric observations of control points
PA (XA,YA) with ?XA ? ?YA- Field observations of
intertree azimuths (?) and distances (d)-
Initial approximation (guess) of (X0,Y0)-
Unknowns are non-linear functions of the
observations ? non-linear regression
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Background - MATHEMATICS - LS-adjustmentof
intertree azimuths and distance observations

• Observations include coordinates m,
  distances m and azimuths rad ? normalizing
  and weighting required ? WLS adjustment
• Form a design matrix A, Its elements are
  partial derivates of the observations with
  respect to the unknowns- Form a diagonal weight
  matrix P, with 1/? elements a priori standard
  errors of observations
• Compute residuals in observations, y given the
  initial approximations of unknowns
• Solve x (ATPA)-1ATPy- if x is small stop,
  otherwise add x and continue

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Background - MATHEMATICS - LS-adjustmentof
intertree azimuths and distance observations
Standard errors of unknowns
eig(Qxx) gt Error ellipses
in XY
Search for gross errors in observations
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Geometric aspects
If measurements consist solely of intertree
azimuths or distances ? geometric constellation
is important, otherwise error ellipse is
elongated. If both azimuth and distance are
observed errors cancel each other ? always
circular error patterns (error ellipse), unless
the observation errors are considerable, or eq.
distance dependant. Monte-Carlo simulator well
suited for examining the potential and weaknesses.
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Simulation results
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Practical issues

• Preparatory work 1) photogrammetric
  measurements, 2) prepare maps, tree labels and
  tally sheets (here DTM is accurate)
• Work in the forest GPS brings you close, match
  tree pattern, use azimuth pencils to verify the
  photo-tree, label it, map finally other objects

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Practical issues

• - Recall assumptions (Imagery, DTM,
  photogrammetric software)
• WLS-adjustment and gross error detection should
  be done in the field, instantly after first
  redundant observation, requires a field
  computer of some sort ? Errror estimates on the
  fly continue observations untill the required
  accuracy is reached
• What if magnetic anomalies are present?
• Slanted trees, very dense stands perhaps
  problematic
• Good for large field plots with limited
  visibility, one person and low-cost equipment

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Practical issues accuracy of photogrammetric
obs
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Practical issues some results
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Some ideas of future work
GPS brings you within 5 m ? Measure a
ray-pencil (azimuths to trees) or set of
distances to trees ? Adjust position with
photogrammetric treemap i.e. obtain a position
fix down to 0.2 m under canopy. WORKS in
theory. THANK YOU!
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Young stands use Network-RTK satellite
positioning. One investigator cm-level
accuracy
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