Merging Different Data Sets Based on Matching and Adjustment Techniques
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1 Technische Universität Berlin Merging Different Data Sets Based on Matching and djustment Techniques Lothar Gruendig, TU Berlin Frank Gielsdorf, Bernd schoff technet GmbH, Berlin L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques GDI - Reality Matching and Searching Matching: Finding of identical objects in different data sets - corners - distances - straight lines - points - Searching: Finding of geometrical conditions within one data set - right angles - straight lines - parallel lines - parallel lines with given distance - 3 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 4 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Geometrical harmony? Subdivision of a plot greek: harmonia (bringing into agreement) Unification of contradictable facts to a common entirety contradictable facts inconsistency remove inconsistencies adjustment harmonization adjustment Preserve local neighborhood 5 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 6 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
2 Distance depending correlations x x + cov( x, x ) cov(x,x E ) 0! x E x xe x E Integration of relative geometry Case 1: Original observations are unknown solution: djustment based on pseuobservables, i.e. simulating a rubber membrane, geometrical conditions ρ 1 cov( x, xe ) ρ x, xe x xe f ( se ) s reasoning: 1. Measurement following the principle of neighborhood. Mapping following the principle of neighborhood 7 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 8 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Integration of relative Geometry Integration of relative geometry Case : original observations given solution: adjustment of original (and pseudo) observations Membrane elements Straight lines General Case Right angles Parallel lines Circularity conditions Global coordinates Locale coordinates Distances L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 10 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Identical points pproach: Identity observations Functional model v X v Y... X i X X k k Y Y X Y Yk i i Stochastic model (FFG) + X i Yi 0 X k Yk + Identity observation 11 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 1 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
3 Identical straight lines Result of matching procedure n ρ d x ρ Observed identities for the analysis however no topological constraints! Identity is modelled geometrically not topologically. n ρ 0 Functional model ρ ρ v n x d Stochastic model FFG: xyi o 0 d x ρ 13 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 14 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Graphs Nodes Links Corners 15 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 16 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Extraction of partial graphs Geometrical parameterization example: corner Node-branch-matrix Incidence-matrix C link node Node Point X, Y link node C Link Straight line Point-direction n x, n y, d X, Y, r x, r y Node-node-matrix djacence-matrix C T C node C T Point-Point X, Y, X E, Y E link Dyadic product I, j, k are indices of corner points djacence-tensor i j k Corner Point-directions 3 Points X, Y, r, r, r E, r E X, Y, X M, Y M, X E, Y E 17 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 18 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
4 Stochastic model example: straight line Role of the datum Datum dependent matching given: Point-Point Searched for: Point-Direction Corner Point-Directions X, Y, r, r, r E, r E x y xk x E ye mit x CKK 0 y xe 0 ye x y xr r x ry mit x CRR y rx cov( x, ry ) ry Datum invariant matching Datum dependent parameters x pplying error propagation to solve for the transition R K R K RR KK f( x ) d x F d x C F C F T traverse s 1 s s 3 α 1 α s 1, s, s 3, α 1, α Datum invariant parameters resp. (s /s 1 ), (s 3 /s 1 ), α 1, α 19 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 0 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Principle of interconnected transformation How to find matching candidates? example: two data sets with corners each Flur 1 Flur Flur 1 Flur 1. possibility: to compare every corner with every corner n*m Operations of comparison * corners comparisons * corners comparisons 1 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques How to find matching candidates? Test referring to identity. possibility: Multi dimensional search trees Every corner has 6 geometrical parameters (x, y, rx, ry, rx E, ry E ) and therefore can be seen as point in a 6D space. Setting up a 64-Tree ( 6 64 Quadrants ) given.: two random vectors x1 y1 r x1 x 1 und ry 1 and the corresponding covariance matrices rxe1 (singular with rang defect of ) rye1 x y r x x ry rxe rye Search in 6D-window n*log d m Operations of comparison * corners comparisons result: 0 n matching-candidates C xx1 x1 cov( x, rye rye1 ) and C xx x cov( x, rye rye ) 3 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 4 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
5 Test referring to identity Hypothesis: x 1 x x 1 x d 0 FFG to d: C dd C xx1 + C xx check: d T C dd d ~ χ (f4) Boundary value: χ s χ s (f,α) for f 4 and α 5% χ s 9,5 Test decision: χ < χ s corners are identical χ > χ s corners are not identical 5 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 6 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Treatment of multiple choice possibilities Treatment of multiple choice possibilities Corner is present Corner-operator Straight line-operator Search for matchingcandidates No candidates found n candidates found Identiy test no identity one single identity Several identities Create identity observation Reject all candidates 7 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 8 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Process chain Matching-djustment Process chain Matching-djustment Several not georeferenced vector data sets are present Vector data sets are roughly geo-referenced djustment Datum invariant matching Flur 1 Flur Flur 1 Flur Datum dependent matching consistent adjustment result Point identies were generated more identical objects found False identities recognized Interconnected transformation Switch off the identity with largest NV Vector data sets are roughly geo-referenced No more identical objects found Identity with largest NV switched off 9 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 30 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
6 SYSTR software package observational types maps field record restrictions new survey Experience based on real projects > coordinates without distortions > unique result of analysis 31 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 3 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques SYSMTCH routine Wimmera Mallee Project Matching: - corners point identities - straight lines local systems - points point identies CRC-SI Corporative Research Centre Spatial Information - University of Melbourne - Department of Sustainability and Environment - Logica CMG Searching: - right angles observed right angles - straight lines observed straight lines extension: North-South East-West 170 km 138 km Cadastral points: GPS points: links: given point identities: 5 Corners in cadastre: Corners in GPS data: L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 34 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Starting situation Corner- matching 35 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 36 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
7 Geometrical Harmonization Straight line - matching 37 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 38 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques Matching-result Summary Geometrical harmonization does not work without adjustment detected point identities: 5 straight line identities: Prerequisite for the adjustment are information with respect to identical objects Matching-algorithms are efficient tools to find identity-information Matching and adjustment can not be separated 39 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques 40 L. Gruendig Merging Different Data Sets Based on Matching and djustment Techniques
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