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