Skinning Mesh Animations

Transcription

1 Doug L. James, Christopher D. Twigg Carnegie Mellon University presented by Johannes Schmid 1

2 Outline Introduction & Motivation Overview & Details Results Discussion 2

3 Introduction Mesh sequence: 3

4 General setting Animation simplification Direct data reduction (PCA,...) Skeleton subspace deformation (SSD) 4

5 General setting Traditional skeleton: Hierarchy Joints Angles This paper s approach: No hierarchy Only transformations 5

6 Premises Mesh sequence: P = (p 1, p 2,..., p S ) t = 1..S: time p t : All vertices at step t Rest (or reference) pose: 6

7 Goal Linear Blend Skinning: vertex weights bone transforms vertex-bone influences We are looking for, and 7

8 Overview Identify near-rigid structures Estimate bone transforms Estimate vertex weights Progressive skin corrections 8

9 Overview Identify near-rigid structures Estimate bone transforms Estimate vertex weights Progressive skin corrections 9

10 Identify structures Triangle rotation sequence: Polar Decomposition: F = RW Rotation Stretch 10

11 Identify structures b Mean shift clustering over z j 11

12 Identify structures Triangles withinε of found modes/bones are core triangles Strongly associated with bone Make up near-rigid structure Total fraction of core triangles determines quality 12

13 Identify structures 13

14 Overview Identify near-rigid structures Estimate bone transforms Estimate vertex weights Progressive skin corrections 14

15 Estimate bone transforms Rigid bones Rotation and translation Take average rotation of core triangles Arithmetic mean of triangle rotation mat. Find translational part by fitting to the core triangle centroids 15

16 Estimate bone transforms Flexing bones Bones can stretch and shear (not bend) Rigid bones: rotation/translation pair (R,v) Flexing bones: (F,v) with F = RW LS fit to match motion of core triangle 16

17 Overview Identify near-rigid structures Estimate bone transforms Estimate vertex weights Progressive skin corrections 17

18 Estimate mesh skin Remember: Find : Find β bone transforms ( ) which individually lead to the best possible result 18

19 Estimate mesh skin Find vertex weights : Match transformed vertices to mesh sequence Weights must sum up to 1 19

20 Estimate mesh skin 20

21 Estimate mesh skin Weight over-fitting Negative weights lead to unstable skins Use nonnegative least squares (NNLS) to obtain strictly positive weights 21

22 Almost there... 22

23 Overview Identify near-rigid structures Estimate bone transforms Estimate vertex weights Progressive skin corrections 23

24 Progressive skin corrections As described in Kry, Paul G. et al. 2002: EigenSkin Transform errors back to rest pose Perform data reduction (PCA, SVD) Add result to rest pose 24

25 Results Benefits of skinned meshes: Animation compression 25

26 Results Benefits of skinned meshes: Hardware acceleration 26

27 Results Benefits of skinned meshes: Rest pose editing 27

28 Results Benefits of skinned meshes: Fast collision detection 28

29 Results Problems: Highly deformable models 29

30 Results Benefits of skinned meshes: Animation compression Hardware acceleration Rest pose editing Collision detection Problems: Highly deformable models Computation of skin: Order of Minutes 30

31 Opinions & Discussion 31