Intro Geo informationScience (GRS 10306) · 2009. 9. 28. · 2 Introduction Geo information Science...
Transcript of Intro Geo informationScience (GRS 10306) · 2009. 9. 28. · 2 Introduction Geo information Science...
Intro Geoinformation Science
(GRS10306)
Data handling 2: Transformations
2009/2010
CGIGIRS©
Introduction Geo information Science (GRS 10306)2
Transformation definition� Query a data handling class of operators
� which doesn’t change the thematic and geometric meaning of the original geodata
� which doesn’t change the (geo)reference or data structure
� it 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 geodata
� which 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 geodata
� which doesn’t change the (geo)reference and data structure
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Overview
� Transformation� Synonyms� Thematic� Geometric
• Vector – vector• Vector – raster• Raster – vector
Geo information process
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Transformation synonyms
� ConversionConversionConversionConversion� from analogue into digital� from data structure (.txt into .doc)� from carrying medium (tape to CD)
� ProjectionProjectionProjectionProjection� 3D into 2D� 2D into another 2D � 2D into 3D
� RectifyingRectifyingRectifyingRectifying� Geometrically wrong into geometrically correct
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Thematic transformations� Nominal Nominal Nominal Nominal
� Translation� Example:
• aardappelen = potatoes = kartoffeln• You to = U2, for you = 4U (SMS language)
� OrdinalOrdinalOrdinalOrdinal� Other coding� Example:
• 1 = bad / 2 = ok / 3 = good
� Interval / ratioInterval / ratioInterval / ratioInterval / ratio� Other unit� Example:
• Inch into cm• Joule into Kcal
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Geometric transformations
� 3D into 2D
� 2D into 2D
� Map to Map Transformation
� Sketch to Map transformations
� Image to Map transformation
� 2D into 3D
� Data structure
� vector – vector
� raster – raster
� vector – raster
� raster – vector
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Exercise
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Geometric Transformation
� Process of using a set of control points and transformation equations to register a map, satellite image or photograph onto a Cartesian coordinate system
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2D into 2D
Definition of a 2D coordinate system:
� Position of the origin (X, Y)
� Orientation of the system (X, Y)
� Units of the axes (m, m)
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VectorVector example
s o
r
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Vector vector: operators
co-ordinate transformations
• linear• X’ = aX + b • Y’ = eY+ f
example:• similarity• affine
• higher order (non linear)• X’ = aX3 + bX2 + cX + d
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VectorVector: parameters
Transformation parameters:
� s [scaling] (X, Y)
� o [orienting /translating] (X, Y)
� r [rotating] (X, Y)
� Estimated using control points (see box 7.1 Chang)
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Vector vector transformations 1
� Equiarea
� Similarity
� Affine
� Projective
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Similarity transformation 1
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Similarity transformation 2
• constraints• axis perpendicular • axis with equal units
• transformations• orienting: X and Y differ• scaling: X and Y equal• rotating: X and Y equal
• procedure• 4 parameters (unknown) • 2 tic points• extension of tic points
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Vector vector: operators
• X’ = Ax + By + C • Y’ = Dy + Ey + F
� Skewness
� Affine transformation most general used
� Available ArcGis (use transform tool in arcinfo)
Rotate, skew, scale
Translate
• procedure• 6 parameters (unknown) • >= 4 tic points
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Real problems
� Try warping (rubber sheeting)
� Use higher order polynomials (non linear)
X’ = aX3 + bX2 + cX + d
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Vector – vector: procedure
1 ground control / tic / reference points in FROM - and TO – geodata set
2 run transformation on tic points (RMS-value)
1 again OR Continue with 3
3 apply transformation to FROM geodata set
Error for control point = √ ( Xact – Xest) 2 + (Yact-Yest) 2
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Transforming coordinates for coverage in_cov_name
Scale (X,Y) = (246.140,255.702) Skew (degrees) = (-0.061)Rotation (degrees) = (0.334) Translation = (2890.267,3679.906)RMS Error (input, output) = (0.084,20.592)
Affine X = Ax + By + C
Y = Dx + Ey + F
A = 246.135 B = -1.763 C = 2890.267
D = 1.434 E = 255.696 F = 3679.906
Example output
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Introduction Geo information Science (GRS 10306)21
Raster or Vector?VectorAdvantages
� Compact data structure� Explicit description of
topology� Coordinate transformation � Accurate graphic presentation
Disadvantages� Complex data structure� Combining data sets� Spatial analysis within basic
units
Burrough, McDonnel, 1986/1998
RasterAdvantages
� Location specific manipulation
� Simple data structure
� Mathematical modeling is easy
Disadvantages
� Large data volumes
� Coordinate transformation
� Spatial resolution
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Exercise vector raster: 1
city
highway
forest
lake
Legend:
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Exercise vector raster: 2
city
highway
forest
lake
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Exercise vector raster: 3
Cell_id Village Road Forest Lake
7 0 0 0 0
8 0 0 1 0
9 0 1 1 0
10 1 1 1 0
11 0 1 1 0
12 0 0 1 0
13 0 0 0 0
7 8 9 10 11 12
13
village
highway
forest
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: summary
� Object selection
� Priority rules� Points, lines, areas� Weight values
� Allocation ruleseg. - Object area percentage in cell- Shortest path OR real geometry
BEWARE!!!
� Points� Point extension
� Nr. of points
� Lines� Line widening
� Nr. of lines
� Polygons� Boundary extension
� Nr. of polygons
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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 approach
1. Object type - point, line or area
2. Object 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 type
2. Object construction rules
3. Transformation
4. Geometric cosmetics
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Raster vector: 3
21
3 4
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Summary:
� Geometric transformations
� Affine transformation
� ‘ 2Dplane’ into ‘2Dplane’
� Vector Vector
• (coordinate transformations: equiarea, similarity, affine, projective)
� Vector Raster (priority rules, allocation rules)
� Raster Vector (object definition)
Study materials:
2007© Wageningen UR
Theory Chang, 2006
Chapter 5.5:‘Data Conversion’
Chapter 7: ‘Geometric transformations’
Practical: GRS10306 practical manual, 2006
Module 6: ‘Transformations’ Part 2
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Vector – vector transformations 2
type
equi area
similarity
affine
projective
non-linear
Accepted Not-Accepted