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 XYZGLOBAL Phases 1. XYZLOCAL mapping 2. 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) 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 XYZGLOBAL treetop positions, 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-adjustment of 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

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

Background - MATHEMATICS - LS-adjustment of intertree azimuths and distance observations 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 Young stands: use Network-RTK satellite positioning. One investigator – cm-level accuracy BACK