data handling ii - transformation · 3/41 transformation - definition query a data handling class...
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1011© Wageningen UR
Data Handling II - transformation
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How to make different datasets comparable?
TransformationSynonymsThematicGeometric
• Vector – vector• Vector – raster• Raster – vector
Geo-data cycle
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Transformation - definitionQuery a data handling class of operators
which doesn’t change the thematic and geometric meaning of the original geo-datawhich doesn’t change the (geo-)reference or data structureit only selects a subset out of the whole data set
Transform a data handling class of operators
which doesn’t change the thematic and geometric meaning of the original geo-datawhich changes the (geo-)reference or data structure
Alter/Process a data handling class of operators
which changes the thematic and geometric meaning of the original geo-datawhich doesn’t change the (geo-)reference and data structure
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Transformation - synonyms
Conversionfrom analogue into digitalfrom data structure (.txt into .doc)from carrying medium (tape to CD)
Projection3D into 2D2D into another 2D 2D into 3D
RectifyingGeometrically wrong into geometrically correct
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Thematic transformationsNominal
TranslationExample:
• aardappelen = potatoes = kartoffeln• You to = U2, For you = 4U (SMS language)
OrdinalOther codingExample:
• 1 = bad / 2 = ok / 3 = good
Interval / ratioOther unitExample:
• Inch into cm• Joule into Kcal
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Geometric transformations
3D into 2D2D into 2D
Map to Map transformationSketch to Map transformationImage to Map transformation
2D into 3D
Data structurevector – vector raster – raster vector – rasterraster – vector
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Raster or Vector?VectorAdvantages
Compact data structureExplicit description of topologyCoordinate transformation Accurate graphic presentation
DisadvantagesComplex data structureCombining data setsSpatial analysis within basic units
Burrough, McDonnel, 1986/1998
RasterAdvantages
Location specific manipulationSimple data structureMathematical modeling is easy
DisadvantagesLarge data volumesCoordinate transformation Spatial resolution
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Exercise vector - raster: 1
cityhighwayforest
lake
Legend:
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Exercise vector - raster: 2
cityhighwayforest
lake
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Exercise vector - raster: 3
Cell_id Village Road Forest Lake7 0 0 0 08 0 0 1 09 0 1 1 0
10 1 1 1 011 0 1 1 012 0 0 1 013 0 0 0 0
7 8 9 10 11 1213
cityhighwayforest
lake
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Vector - raster: point 1
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Vector - raster: point 2
?
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Vector - raster: lines 1
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Vector - raster: lines 2
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Vector - raster: polygon 1
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Vector - raster: polygon 2
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Vector- raster: summaryObject/Feature selection
Priority rulesPoint-, Line- Or Area-
objectsOr Weighted
Allocation ruleseg. - Feature area % in cell- Shortest path OR
real geometry
BEWARE!!!
PointsPoint extension: area sizeNr. of points in one cell
LinesLine widening: area sizeNr. of lines in one cell
PolygonsBoundary extension: area changeNr. of polygons in one cell
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Vector raster conversion
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Grid Topology
1 2
6
3
45
7
8
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How many objects ?2 0
0
10
0 2
2
0
2
1
3
0
1
0
1
3
3
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Raster – Vector: 1
Object / Feature approach
1. Object / Feature type - point, line or area
2. Object / Feature construction rules - thematic classes (grid value)- topology (side / corner connection)
3. Transformation into data structure (with topology)
4. Geometric cosmetics
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Raster- vector: 2
1
2
3
4
1. Object / Feature type
2. Construction rules
3. Transformation
4. Geometric cosmetics
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Raster - vector: 3
21
3 4
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Summary:
Vector - Raster (priority rules, allocation rules)Raster - Vector (object definition based on topology/thematic rules)
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Exercise
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2D-2D: Geometric Transformation
Process of image registration- using a set of control points –, geometric transformation- equations to estimate coordinates of a sketch, digitized map, (satellite) image or photograph –
onto a projected Cartesian coordinate system by determined transformation coefficients
and validation
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2D into 2D - coefficients
Definition of a 2D coordinate system
Position of the origin (X+, Y+)Orientation of the system (Xo, Yo)Units of the axes (Xm, Yn)
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Vector-Vector example
s o
r
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Vector-Vector: coordinate transformation
s [scaling] (X * m, Y * n){ m eq n OR m neq N} o [orienting /translating] (X+s, Y+t){ x eq y OR x neq y} r [rotating] (X+uo, Y+vo){ u eq v OR u neq v}
Formal description:• X’ = srX + srY + s• Y’ = srX + srY + t
• X’ = AX + BX + C• Y’ = DX + EY + F
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Vector - vector transformations 1
Equal area
Similarity (equal shape)
Affine (parallelism )
Projective
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Similarity transformation 1
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Similarity transformation 2
• constraints• axis perpendicular • axis with equal units
• transformations• orienting/translate: X and Y differ { s neq t }• scaling: X and Y equal { m eq n }• rotating (inc skew): X and Y equal { u eq v }
• procedure• 4 parameters (unknown) • 2 tic points• extension of tic points
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Vector - vector: operators
• X’ = Ax + By + C Y’ = Dx + Ey + F
SkewnessAffine transformation most general used
Rotate (incl skew), scale
Translate
• procedure• 6 parameters (unknown) • >= 4 tic points
[See: Chang, 7.1.3-7.2 / 6.1.3 – 6.2 : Affine transformation]
Formal description:• X’ = srX + srY + s• Y’ = srX + srY + t
• X’ = AX + BX + C• Y’ = DX + EY + F
A= Sx cos (t)B= Sy [k cos (t) – sin (t) ]D= Sx Sx sin (t)E= Sy [k sin (t) – cos (t) ]
Sx, Sy (scaling)t (rotation angle)k (shear factor)
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Vector – vector: step 1
1 image registrationground control / tic / reference points in FROM - and TO – geodata set
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Example – image registration
Control or Tic points
a measure pair of coordinates of unprojected sketch, scan (FROM)
b measure related pair of coordinates of projected (TO)
c connect
FROM TO
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Vector – vector: step 2
1 image registrationground control / tic / reference points in FROM - and TO – geodata set
2 geometric transformationrun transformation on tic points and
Error validation by Root Mean SquareI/O Error for control point = √ ( XFROM (act) – XTO (est) ) 2 + (YFROM (act) -YTO (est) ) 2
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Error validation
FROM TO
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Vector – vector: step 3
1 image registrationground control / tic / reference points in FROM - and TO – geodata set
2 geometric transformationrun transformation on tic points and
Error validation by Root Mean Square
If RMS is acceptable then continue with 3if RMS is not acceptable then repeat 1
3 apply transformation on to FROM geodata set
I/O Error for control point = √ ( XFROM (act) – XTO (est) ) 2 + (YFROM (act) -YTO (est) ) 2
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Positional Accuracy
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Summary – geometric transformation
2D (sketch, images) into projected geodataimage registrationgeometric transformation- similarity - affinepositional error
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Study materials:
2007© Wageningen UR
Theory Chang, 2006 - 2008 [ 5th ]
Chapter 5.5:‘Data Conversion’ [ 4.5 ]
Chapter 7: ‘Geometric transformations’ [ 6 ]
(except 7.4 [ 6.1.4 and 6.3])
Practical: GRS-10306 practical manual, 2006Module 6: ‘Transformations’ Part 2
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Vector – vector transformations 2type
equi area
similarity
affine
projective
non-linear
Accepted Not-Accepted