Mapping forest plots: An efficient method combining photogrammetry and field

triangulation/trilaterationMARV1 June 2007

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 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

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 > 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 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.

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-positions

Forward 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.

Background - MATHEMATICS - LS-adjustmentof intertree azimuths and distance observations

Objective: Obtain XY-position for P0

We 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

- 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 = (ATPA)-1ATPy- if ||x|| is small stop, otherwise add x and continue

Background - MATHEMATICS - LS-adjustmentof intertree azimuths and distance observations

Background - MATHEMATICS - LS-adjustmentof intertree azimuths and distance observations

r0

PyyT

)(Q

PA)(AQ

xx

1Txx

diagXi 0

j

jj

q

yw

0

Txx

1vv AAQPQ

Standard errors of unknowns

eig(Qxx) => Error ellipses in XY

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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