Data handling 2: Transformations

Transcription

1 Intro Geo information Science (GRS 10306) Data handling 2: Transformations 2009/2010 CGI GIRS

2 Transformation definition Query a data handling class of operators which doesn t change the thematic and geometric meaning of the original geo data 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 geo data 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 geo data which doesn t change the (geo )reference and data structure 2

3 Overview Geo information process Transformation Synonyms Thematic Geometric Vector vector Vector raster Raster vector 3

4 Transformation synonyms Conversion from analogue into digital from data structure (.txt into.doc) from carrying medium (tape to CD) Projection 3D into 2D 2D into another 2D 2D into 3D Rectifying Geometrically wrong into geometrically correct 4

5 Thematic transformations Nominal Translation Example: aardappelen = potatoes = kartoffeln You to = U2, for you = 4U (SMS language) Ordinal Other coding Example: 1 = bad / 2 = ok / 3 = good Interval / ratio Other unit Example: Inch into cm Joule into Kcal 5

6 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 6

7 Exercise 7

8 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 8

9 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) 9

10 Vector Vector example r o s 10

11 Vector vector: operators co-ordinate transformations linear X = ax + b Y = ey+ f example: similarity affine higher order (non linear) X = ax 3 + bx 2 + cx + d 11

12 Vector Vector: 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) 12

13 Vector vector transformations 1 Equiarea Similarity Affine Projective 13

14 Similarity transformation 1 14

15 Similarity transformation 2 constraints axis perpendicular axis with equal units transformations orienting: scaling: rotating: X and Y differ X and Y equal X and Y equal procedure 4 parameters (unknown) 2 tic points extension of tic points 15

16 Vector vector: operators Skewness Affine transformation most general used Available ArcGis (use transform tool in arcinfo) X = Ax + By + C Y = Dy + Ey + F Translate procedure 6 parameters (unknown) >= 4 tic points Rotate, skew, scale 16

17 Real problems Try warping (rubber sheeting) Use higher order polynomials (non linear) X = ax 3 + bx 2 + cx + d 17

18 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 = ( X act X est ) 2 + (Y act -Y est ) 2 18

19 Example output Transforming coordinates for coverage in_cov_name Scale (X,Y) = ( , ) Skew (degrees) = ( )Rotation (degrees) = (0.334) Translation = ( , )RMS Error (input, output) = (0.084,20.592) Affine X = Ax + By + C Y = Dx + Ey + F A = B = C = D = E = F =

20 20

21 Raster or Vector? Vector Advantages Compact data structure Explicit description of topology Coordinate transformation Accurate graphic presentation Disadvantages Complex data structure Combining data sets Spatial analysis within basic units Raster Advantages Location specific manipulation Simple data structure Mathematical modeling is easy Disadvantages Large data volumes Coordinate transformation Spatial resolution Burrough, McDonnel, 1986/

22 Exercise vector raster: 1 Legend: city highway forest lake 22

23 Exercise vector raster: 2 city highway forest lake 23

24 Exercise vector raster: Cell_id Village Road Forest Lake village highway forest lake 24

25 Vector raster: point 1 25

26 Vector raster: point 2? 26

27 Vector raster: lines 1 27

28 Vector raster: lines 2 28

29 Vector raster: polygon 1 29

30 Vector raster: polygon 2 30

31 Vector raster: summary Object selection Priority rules Points, lines, areas Weight values Allocation rules eg. - 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 31

32 Grid Topology

33 How many objects?

34 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 34

35 Raster vector: 2 1. Object type 1 2. Object construction rules 2 3. Transformation 3 4. Geometric cosmetics 4 35

36 Raster vector:

37 Summary: Geometric transformations Affine transformation 2D plane into 2D plane Vector Vector (co ordinate transformations: equiarea, similarity, affine, projective) Vector Raster (priority rules, allocation rules) Raster Vector (object definition) 37

38 Study materials: Theory Chang, 2006 Chapter 5.5: Data Conversion Chapter 7: Geometric transformations Practical: GRS practical manual, Wageningen UR Module 6: Transformations Part 2

39 Vector vector transformations 2 type Accepted Not-Accepted equi area similarity affine projective non-linear 39