SCAPE: Shape Completion and Animation PEople Stanford University Dragomir Anguelov Praveen Srinivasan Daphne Koller Sebastian Thrun Jim Rodgers UC, Santa Cruz James Davis

Shape Completion

Animation PEople

Overview Training Data Set Black Box Human Pose/Shape Parameters Data Acquired Complete Meshes Non-Linear Optimization

Black Box Pose Deformation Model Non-rigid and rigid deformation Shape Deformation Model Variation across different individuals

Pose Deformation Model Non-Rigid Transform Q k Rigid Transform R L[k]

Mesh Reconstruction argminΣ k Σ j=2,3 || R i L[k] Q i k v’ jk – (y jk – y 1k ) || 2 y 1, …, y m Y1,k Y2,k Y3,k V2,k V3,k K-th Tri [Sumner et. al. 2004] Deformation Transfer for Triangle Meshes

Learning Parameter Q(R) argminΣ k Σ j=2,3 || R i k Q i k v’ kj – v i kj || 2 + {Q i 1 …Q i P } w s Σ k1, k2 adj I (L k1 = L k2 ) ||Q i k1 – Q i k2 || 2 Reconstruction_Cost argmin Reconstruction_Cost + {Q i 1 …Q i P } Smoothness_Cost =

Parameters of Pose Model Black Box Pose Deformation Model Human Parameters Pose Parameters Q

Shape Deformation Model Reconstruction argminΣ k Σ j=2,3 || R i k S i k Q i k (R)v’ kj – v i kj || 2 {Y 1 …Y m } V’k,2 V’k,3 V’k,2 V’k,3 SikSik

Learning Parameter S argminΣ k Σ j=2,3 || R i k S i k Q i k v’ kj – v i kj || 2 + {S i } w s Σ k1, k2 adj ||S i k1 – S i k2 || 2 Reconstruction_Cost argmin Reconstruction_Cost + {S i } Smoothness_Cost S i = φ U, μ ( β i ) = U β i + μ

Parameters of Shape Model Black Box Pose Deformation Model Shape Deformation Model Pose Parameters Q Shape Parameters U, μ Human Parameters Estimation of Human Model

E H [Y] = argminΣ k Σ j=2,3 || R k φ (β) Q k v’ jk – (y jk –y 1k ) || 2 y 1, …, y m Q-coefficient U-EigenVector, μ-mean Rotation β- mesh coefficient

Shape-Completion / Animation Training Data Set E H [Y] Q, U, μ R, β + E H [Y] + w z Σ L ||y L - z L || 2

Limitation Trained Model (Linear Regression Model) vs. particular pose/shape Susceptible to local-minimum(?) Skeleton Based