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.

Young stands

: 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

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