1. Cartographic Applications
Morphing,
and
Warping
Blending
Cartographic Applications

2. Definition
Morphing is a special technique that creates a smooth, controlled transformation of one image into another.

3. Transforming Shape

4. Warping vs Morphing Warping Single object
Specification of original and deformed states
Morphing
Two objects
Specification of initial and final states

5. Warping and Morphing Warping Morphing • Source object
• No target object
Morphing
• Target object

6. Warping versus Morphing Warping Morphing

7. Specification of Transformations
Global Transformations
Affine Maps
Projective Maps
Non-Linear Maps

8. Specification Definitions Correspondence Specification
association between two regions
defines original and final states
Specification
set of correspondences

11. Warping x Morphing Warping Morphing (metamorphosis) Single object
Specification of original and deformed states
Morphing (metamorphosis)
Two objects
Specification of initial and final states

12. Types of Specification
Parametric
Partition-based
Feature-based
Automatic or semi-automatic

13. Parametric Specification

14. Specification by Partition
Regions cover the entire object
Regular x Irregular partitions
Same topology: original and final sets

15. Partition Examples

16. Specification by Features
Regions do not cover the object
Dimension of features £ object dimension
Examples: points, vectors, planes, boxes,...

17. Feature (Vector) Examples

18. Transforming Attributes
Texture, Color

19. Linear Blending A and B objects in a vector space
c(t) = (1 - t) A + t B
c(0) = A, c(1) = B
Functions (attributes)
Subsets of space (shape)
Also Bilinear, Trilinear and Affine Blending

20. Shape Warp + Attribute Blending

21. Linear Color Interpolation (cross dissolve)

22. Some Guidelines for a good morphing
Feature preservation
Smoothness preservation
Avoid linearities
use adaptive methods

23. Avoid leakage
Select and warp foreground only

24. Example of Morphing and Attribute Transformation form Fantamorph

25. Geometry Deformation
Change of Coordinate Systems

26. Animation
Emphasis
Stretch
Squash
Distortion plus Motion

27. Animation
Keyframes
Tweens
Motion
Shape

28. The World according to Aaron “Garp” Arthur

29. Types of Warps

30. Warping Techniques Barycentric mapping Field-based mapping
Radial basis functions - RBF
Free-form deformation - FFD
Multi-pass spline mesh
Physically-based warping

31. Parametric (global) warping
Examples
aspect
translation
rotation
perspective
affine
cylindrical

32. Rotation
xT = xs (cos(q)) + ys (sin(q))
yT = ys (cos(q)) - xs (sin(q))

33. Scale Change xT = mxs yT = nys
Scaling coefficient m usually is the same as n

34. Translation
xs = xs + Dx
ys = ys + Dy

35. Bilinear Coordinate Transformation

36. Bilinear Coordinate Transformation
Transformation Equations are:
xT = axs + bys + cxsys + d
yT = exs + fys + gxsys + h
Which are solved simultaneously
From a minimum of 4 points whose
Coordinates are known in both systems.

37. Forward warping Send each pixel f(x,y) to its corresponding location
(x’,y’) = T(x,y) in the second image
if pixel lands “between” two pixels distribute color among neighboring pixels (x’,y’), known as “splatting”
Origin
Target
T(x,y) y y’ x x’
f(x,y)
g(x’,y’)

38. Inverse Warping
Get each pixel g(x’,y’) from its corresponding location
(x,y) = T-1(x’,y’) in the first image
if pixel comes from “between” two pixels, Interpolate color value from neighbors
nearest neighbor, bilinear, Gaussian, bicubic
Inverse warping usually better because it eliminates holes, but it is not always possible.
Origin
Target
T-1(x,y) y y’ x x x’
f(x,y)
g(x’,y’)

39. Applications Genesis in the graphic arts, movies
Yet, Morphing is not just a special effect:
Lens distortion correction
Graphical objects modeling
Motion capture data interpolation
Accelerated Rendering

40. Applications Mapping “significance” Area = the relative
significance of states based on electoral college votes

41. Applications: Interpolation of Animation
Example: Glacial Metamorphosis
Considerations:
Frame time resolution
Speed of motion
Realistic shapes

42. Georegister Maps: Example Rubber Sheeting in ArcGIS
For two raster maps in separate layers in ArcGIS. Look up procedure in Help under “georeferencing.”
Work with tools in georeferencing menu bar
httpChina Historical GIS: georeferencing

43. Applications: Photorectification
Example: Leica Photogrammetry Suite
Corrects for camera, camera angle, and relief distortions.

44. Applications: Showing Change
Not just areal change, but also warping of a surface to show change in mapped parameters, such as population density or temperature.

45. Terragen: Mount St. Helens Morph
Is this morph realistic?

46. Software used in different types of morphing
Image morphing software
Morpheous Photo Morpher
Winmorph
Abrosoft Fantatmorph
Terrain imaging software
Terragen
Bryrce
Other software capable of morphing
Autodesk Map 3D
Esri Arcview
Flash

47. Landscapes done in Bryce
‘Canyon Walls’ by Burpee ‘Hidden Valley‘ by Andy Simmons

48. Landscape created in terragen
By: Giancarolo