1. 3D Morphing

2. 3D preobrazba polž-žaba
Demo

3. Področja uporabe Scientific Visualization Education Entertainment
Computer Animation
gives the animator the ability to “fill” an animation between key-framed objects

4. Kako izvedemo preobrazbo
To interpolate object shapes
To interpolate object attributes including color, textures, and normal fields

5. Dobra preobrazba Natural Need user control
Keep as much as possible of the two shapes during the transformation
They are subjective aesthetic criteria
Need user control
intuitive
not too heavy
can be adapted to user’s knowledge

6. The problem of blending two surfaces, even polyhedral ones, is not simple.
In order to blend two polyhedral models, most techniques require establishing a full correspondence between their structures
However, a correspondence alone does not guarantee a smooth transition from the source model to the designated model, and the vertices’ paths have to avoid troublesome situations such as self-intersections.

7. Klasifikacija metod Boundary representations-based approaches
Volume-base approaches

8. 3D preobrazba What is 3D morphing ? Why 3D morphing ?
A 3D model of the object is transformed from one shape into another.
Why 3D morphing ?
Morphs are independent of viewing and lighting parameters.
View-dependent effects possible e.g., shadows, highlights, camera can be animated during the morph.
Traditional 2D morphs are inherently “flat” looking.
Features of a Good 3D morphing algorithm
Conceptually Simple
Minimal topological restrictions.
Easy to use user-control

9. 3D preobrazba krave v tigra
3D morphing between a cow and a tiger. Note that the camera roams during the animation and the model casts a shadow that evolves according to the shape of the 3D model. Such view-dependent effects are impossible with image-space metamorphosis.

10. Mehka animacija objektov
Import the tricks from traditional animation into computer animation
Give characters a pseudopersonality
Stretch and squeeze is used to highlight dynamic action such as deceleration due to collisions
shape distortion

11. Razlika med mehko animacijo objektov in modeliranjem
It blurs the traditional distinction between modeling and animating
a different model is created for each frame
animate the data that represents the model

12. 3D preobrazba
Given two objects, metamorphosis involves producing a sequence of intermediate objects that gradually evolve from one object to the other.

13. Naivna 3D preobrazba

14. Problem korespondence

15. Problem korespondence v 1 dimenziji

16. Problem korespondence v 3 dimenzijah

17. Preobrazba na osnovi poligonov

18. 3D model Polygons (triangles) Other parameters (normals, textures)
vertices

19. Princip 3D preobrazbe

20. 3d preobrazba slon žirafa 1

21. 3d preobrazba slon-žirafa 2

22. Omejitve preobrazbe, temelječe na poligonih

23. B-rep Based 3D morphing
Polyhedral Morphing Using Feature-Based Surface Decomposition
A. Gregory, A. State, M. C. Lin, D. Manocha, and M. A. Livingston. Interactive surface decomposition for polyhedral morphing. The Visual Computer (1999) 15:

24. Postopek 3D preobrazbe Two Input Polyhedra User Specify Correspondence
Compute merged
polyhedron
Edit trajectories
Interpolate
trajectories
Morphing sequence

25. Arhitektura sistema

26. Specificiranje korespondence

27. Kaj mora narediti uporabnik
The users only need to specify a few corresponding pairs of features on the two polyhedra.
They can then specify the trajectories along which these features travel during the morph using Bezier curves, as shown below

28. Skupna povezljivost

29. Prevleka (Overlay)

30. Preslikava na kroglo

31. Predelava mreže z delitvijo

32. Primerjava metod

33. Računanje korespondence
Feature-Nets decompose input polyhedra into morphing patches
For each corresponding Morphing Patch pair:
map both onto a 2D polygon
merge the vertex-edge graphs
reconstruct the facets

34. Računanje korespondence
A (Igloo)
B (House)

35. Računanje korespondence
Patch A
Patch B
Extremal Vertices

36. Preslikava
Patch A
Patch B

37. Zlivanje (Merging)
Patch A
Patch B

38. Rekonstrukcija

39. Končana korespondenca

40. Specifikacija trajektorij preobrazbe

41. Interpolacija krivulj

42. Omejitve interpolacije
Reeves, William T.
“Inbetweening for Computer Animation Utilizing Moving Point Constraints”
SIGGRAPH 81, pp

44. Volume-base Approaches
D. Cohen-Or, D. Levin, A. Solomovoci. Three-dimensional distance field metamorphosis. ACM Trans. Graphics 17: , 1998

45. Tehnike The objects are expressed as level sets of distance functions
Two steps:
Warp: deform the 3D space in order to make the two objects to be morphed coincide as much as possible
Interpolation: linear interpolate distance fields deformed by the warp

46. Interakcija
The user interface allows to select feature (or anchor) points in each voxelized object space and map the anchor points of the source object to the anchor points of the target object

47. Given two or more objects of general topology, intermediate objects are constructed by a distance field metamorphosis.
In the presented method the interpolation of the distance field is guided by a warp function controlled by a set of corresponding anchor points. Some rules for defining a smooth least-distorting warp function are given.
To reduce the distortion of the intermediate shapes, the warp function is decomposed into a rigid rotational part and an elastic part.

48. The distance field interpolation method is modified so that the interpolation is done in correlation with the warp function. The method provides the animator with a technique that can be used to create a set of models forming a smooth transition between pairs of a given sequence of keyframe models.
The advantage of the approach is that it is capable of morphing between objects having a different topological genus where no correspondence between the geometric primitives of the models needs to be established. The desired correspondence is defined by an animator in terms of a relatively small number of anchor
points.

49. 3D Shape Interpolation (1)

50. Animating Shape Change
Per-vertex animation curves
beginning and end known
Simply change parameters with time
Twist angle
Scaling constant
Seed vertex position
All standard rules apply
Curve smoothness, motion controls, etc.

51. 3D Shape Interpolation Approaches
Matching topology
Star shaped polyhedra
Star shaped with respect to an axis
General map to sphere
Merging topologies)
Recursive subdivision)

52. Matching Topology  same meshes with same vertex-edge topology

53. Matching Topology  different meshes with same vertex-edge topology
N = 5k vertices
N = 5k vertices
N = 5k vertices
N = 5k vertices

54. Matching Topology
N = 5k vertices
N = 5k vertices 5 7 2 5 7 2

55. Matching Topology Vertex Normal Material (diffuse, specular)
Texture (u,v) 5 7 2 5 7 2

56. Used in Free From Deformation (FFD)
Matching Topology
Used in Free From Deformation (FFD)
Sequential FFD

57. Matching Topology
Hierarchical FFD

58. Matching Topology
FFD and Animation

59. Matching Topology
FFD and Articulated Joints

60. Light Field Morphing A general framework for image-based 3D morphing
Enables morphing between image-based objects
3D morphing without modeling
Suitable for objects with complex surface properties (e.g., fur, subsurface scattering, hypertexture)
Light field morphing is a general framework for image-based 3D morphing. With light field morphing we can perform 3D morphing without modeling. So a main advantage of our technique is that we can easily work with objects that are difficult to model with traditional techniques. For example, light field morphing makes it very easy to morph objects with complex surface properties such as fur, subsurface scattering, and hypertexture.

61. Morphing = Correspondence
Image morphing
= 2D pixel correspondence
Geometry-based 3D morphing
= 3D vertex correspondence
Light field morphing
= 4D ray correspondence

62. Contributions A UI for specifying features in 4D ray space
Ray-space warping
Handling visibility changes due to object shape change
Our work is based on ray correspondence and we make two main contributions. First, we developed an intuitive UI for specifying features in the abstract 4D ray space. Second, we propose ray-space warping technique for handling visibility change due to object shape change. This is a new type of visibility change that has not being addressed in either IBR community or morphing community.

63. Pregled
UI Component
LF0
LF1
Specifying
features
LF0 with
features
LF1 with
Light field
warping
Warped
LF1
LF0
Morphed LF
Blending
Here’s an overview of light field morphing. The first step in light field morphing is to specify features in both input light fields. Then we warp both light fields for feature alignment. Finally, the warped light fields are blended to produce the light field morph. Now let’s first examine the feature specification step.

64. Specifying Features Feature points 3D points on object surface
Specified by manual correspondence guided by epipolar geometry
In a few minutes I will show you a video of feature specification. To get you prepared for that, I’ll explain the feature elements we used. First, the simplest feature elements are feature points, which are 3D points on the object surface. The user specifies a feature point by doing manual correspondence in two light field views and system guides the user using the eipolar geometry. After the user specifies a feature point in the first light field view and goes to the second view for correspondence, he will see an epipolar line in the second view. To completely specify p, he only has to search the feature point on the epipolar line.

65. Specifying Features Feature lines Feature polygons
Non-planar, but relatively flat & w/o self-occlusion
Necessary only in areas with visibility changes
A feature line is simply a line connecting two feature points. A feature polygon is specified by selecting a set of points in counter-clockwise order. Feature polygons are usually non-planar but relatively flat, as you can see here. We will break a feature polygon if it is not sufficiently flat and causes self occlusion. One thing I want to emphasize here is that feature polygons are only necessary in areas of visibility change caused object shape change.

66. Specifying Features No 3D reconstruction from feature polygons
Background pixel (ray)
Pixels (rays) with no visibility changes
Morphing controlled by background edges
Background edges are key-framed
In addition to 3D feature elements, we also need 2D feature elements. To see why this is the case, let’s look at the picture on the right. Here we rendered feature polygons opaque below each object. You can see that the feature polygons are rather sparse and do not form a 3D reconstruction. The pixels not covered by any feature polygons are called background pixels and they have no visibility changes. For these pixels, light field morphing is a 2D image morphing. To control the behaviors of the background pixels, we introduce 2D feature elements called background edges. The background edges are specified in a few key views and interpolated to all other views. The key views for this example are shown as yellow dots here in the view space.

67. Overview ... ... Morphing Component
LF0
LF1
Specifying
features
LF0 with
features
LF1 with
Light field
warping
Warped
LF1
LF0
Morphed LF
Blending
Feature polygon 2
Feature polygon n
...
Feature polygon 1
Ray bundle 1
Ray bundle 2
Ray bundle n
...
Computing
visibility
map
Ray space
warping
Now let’s examine the light field warping step. From the feature polygons, we can compute the global visibility map of the light field. The global visibility map decomposes the light field into a set of ray bundles plus the background rays. To warp the light field, we simply warp all the ray bundles using ray-space warping and process the remaining background pixels using image warping.
LF with
features
Warped LF

68. Global Visibility Map
GVM describes the visibility of feature polygons in each view
Key to visibility processing
GVM = A light field of false colors, associating each ray with a feature polygon
The global visibility map describes the visibility of the feature polygons in each view and this information is the key to visibility processing. A GVM is a light field of false colors, indicating the feature polygon visible along each ray. Here on the bottom row we show two views of the GVM. The corresponding views of the light field are on the top.

69. Computing GVM
Rendering a set of non-planar but relatively flat polygons
No self-occlusions
Two-pass OpenGL rendering with stencil buffer
Trade off: planar vs non-planar feature polygons
We compute the GVM by render the feature polygons using OpenGL. An interesting twist here is that the feature polygons are non-planar. So they cannot be rendered in the usual way. Assuming the feature polygons have no self-occlusion, we can render them in two passes using the stencil buffer. This is a stand trick and you can find it in a good OpenGL book.
If you’re not comfortable with non-planar polygons, you can force the feature polygons to be flat by only allowing the user to specify triangles. But then the user has to specify many more feature polygons. In practice, we find that non-planar feature polygons work much better.