Mapping forest plots: An efficient method combining photogrammetry and field triangulation/trilateration
Download ReportTranscript Mapping forest plots: An efficient method combining photogrammetry and field triangulation/trilateration
Mapping forest plots: An efficient method combining photogrammetry and field triangulation/trilateration
MMVAR-Colloquim May 4, 2007 Korpela, Tuomola and Välimäki
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
Existing methods: Case: Tree mapping in a forest plot
Objective: Stem/Butt positions in XYZ GLOBAL Phases 1. XYZ LOCAL 2. XYZ LOCAL mapping → XYZ GLOBAL 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.
: use Network-RTK satellite positioning. One investigator – cm-level accuracy
New method: Point (Tree) mapping directly in XYZ GLOBAL
Objective: Stem/Butt positions in XYZ GLOBAL Phases XYZ LOCAL mapping and XYZ LOCAL → XYZ GLOBAL transformation combined.
Assumptions
1) Up-to-date (with respect to events in the forest) orientated (XYZ GLOBAL ) aerial photography is available. Large scale > 1:15000. 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 XYZ GLOBAL treetop positions, called points P A . These are considered as XY control points.
4) Points P A can be found in the field and used for the positioning of other targets.
New method: Point (Tree) mapping directly in XYZ GLOBAL Background
“Points P A can be used for positioning of other points” - Points P A are treetops observed in the aerial images with coordinates (X A ,Y A ) - For non-slanted trees (X A ,Y A ) ~ 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-positions Forward ray intersection in plane - Observe angles or bearings/azimuths between the unknown point P 0 and known points P A . Use LS-adjustment of angles to compute the XY-position of point P 0 (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.
Background - MATHEMATICS - LS-adjustment of intertree azimuths and distance observations
Objective: Obtain XY-position for P0 We have: - Photogrammetric observations of control points PA (X A ,Y A ) with XA YA - Field observations of intertree azimuths ( ) and distances (
d
) - Initial approximation (guess) of (X 0 ,Y 0 ) - Unknowns are non-linear functions of the observations → non-linear regression
Background - MATHEMATICS - LS-adjustment of 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
, It’s 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 = (A T PA) -1 A T Py
- if ||
x
|| is small stop, otherwise add
x
and continue
Background - MATHEMATICS - LS-adjustment of intertree azimuths and distance observations
0
y T Py
r
Q xx
Xi
(A T PA)
1
0
diag
(Q xx )
Standard errors of unknowns eig(
Q xx
) => Error ellipses in XY
Q vv
P
1
AQ xx A T
w j
0
y j q j
Search for gross errors in observations
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.
Simulation results
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
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
Practical issues – accuracy of photogrammetric obs
Practical issues – some results
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!
Young stands: use Network-RTK satellite positioning.
One investigator – cm-level accuracy