Fast and Deep Deformation Approximations STEPHEN W BAILEY

Fast and Deep Deformation Approximations STEPHEN W. BAILEY, University of California, Berkeley DAVE OTTE, Dream. Works Animation PAUL DILORENZO, Dream. Works Animation JAMES F. O’BRIEN, University of California, Berkeley

Introduction Real-time character rigs often lack a high level of detail Film-quality rig might be able to run at interactive rates only on a high-end machine

Related work Linear blend skinning / skeleton subspace deformation [Magnenat-Thalmann et al. 1988] Skin slide, muscle bulges, cloth wrinkles are hard to simulate pose space deformations [Lewis et al. 2000; Sloan et al. 2001]

Related Work (cont. ) Two-Layer Sparse Compression of Dense-Weight Blend Skinning [Le and Deng 2013]

System Overview Deformation computation is the bottleneck

Rig function : r(p) V = r ( p ) S = [X 1, t 1, X 2, t 2, X 3, t 3, …, Xm, tm] Rig function = skeletal motion system + deformation system Skeleton motion system : rig parameter skeleton Defromation system : skeleton vertex positions S = m(p) V = d(S) r( p ) = (d。m)(p)

Deformation Approximation

Nonlinear Deformation

Implementation Using Feed-forward neural network Two fully connected hidden layers and a dense output layer Input : bone transformation matrices and the translation vectors Hidden layers : tanh nonlinearity Output layer : dense linear layer Each bone contribute 12 inputs Use Adam optimization method to train the models

Implementation (cont. ) input layer Hidden layer 12 neurons 512 neurons Hidden layer output layer 512 neurons V*3 neurons

Data Generation The choice of training data is important for the rig approximator’s accuracy

Result 10, 000 ~ 20, 000 example poses was sufficient to train accurate approximation models for each rig

Result (cont. ) More dynamic motions more error

Comparison Compared with linear blend skinning (LBS) and rotational regression (RR, [Wang et (RR, al. 2007] )

Comparison (cont. )

Comparison (cont. )

Model speed Use only CPU to evaluate the networks Running the model on GPU is slower model having large in/outputs than size of the hidden layers in the network (most of the time spent on transferring data) Training time : 2 -3 hours

Limitations and Potential Application Unable to lean the deformations not associated with bones Can not handle dynamics or non-deterministic behavior Deformation of character’s face Combined with motion capture skeleton