Automatic Skinning via Constrained Energy Optimization Alec Jacobson - PowerPoint PPT Presentation

Previous methods fail in one way or another � Euclidean ∆ 2 w j ∆ w j smooth ✓ - ✓ non-negative ✓ ✓ - shape-aware - ✓ ✓ local -/ ✓ - - monotonic - ✓ - arbitrary handles - ✓ ✓ [Shepard 1968, [Baran & Popovic 2007, [Botsch & Kobbelt 2004, Sibson 1980, Joshi et al. 2007] Sorkine et al. 2004, Schaefer et al. 2006] Finch et al. 2011] No free lunch? � Are some properties mutually exclusive? � 66 �

Previous methods fail in one way or another � Euclidean ∆ 2 w j ∆ w j smooth ✓ - ✓ non-negative ✓ ✓ - shape-aware - ✓ ✓ local -/ ✓ - - monotonic - ✓ - arbitrary handles - ✓ ✓ [Shepard 1968, [Baran & Popovic 2007, [Botsch & Kobbelt 2004, Sibson 1980, Joshi et al. 2007] Sorkine et al. 2004, Schaefer et al. 2006] Finch et al. 2011] No free lunch? � Are some properties mutually exclusive? � 67 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 [Botsch & Kobbelt 2004, Sorkine et al. 2004, Joshi & Carr 2008, Jacobson et al. 2010, Finch et al. 2011, Andrews et al. 2011] � 68 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles  1 v ∈ h j ,   w j ( v ) = 0 v ∈ h k  linear on cage facets  [Botsch & Kobbelt 2004, Sorkine et al. 2004, Joshi & Carr 2008, Jacobson et al. 2010, Finch et al. 2011, Andrews et al. 2011] � 69 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity 0 ≤ w j ≤ 1 , m X w j = 1 j =1 [Jacobson et al. 2011] � 70 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity 0 ≤ w j ≤ 1 , + locality m X w j = 1 j =1 [Jacobson et al. 2011] � 71 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity + locality k w k 1 = 1 [Rustamov 2011] � 72 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity m X + locality k w k 1 = 1 ! | w j | = 1 j =1 [Rustamov 2011] � 73 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity m m X X + locality k w k 1 = 1 ! | w j | = 1 ! w j = 1 , j =1 j =1 0  w j  1 [Rustamov 2011] � 74 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity + locality r w j · r u j > 0 + monotonicity [Weinkauf et al. 2011, Jacobson et al. 2012, Günther et al. 2014] � 75 �

Previous methods fail in one way or another � Euclidean ∆ w j = u ∆ 2 w j smooth ✓ - ✓ non-negative ✓ ✓ - shape-aware - ✓ ✓ local -/ ✓ - - monotonic - ✓ - arbitrary handles - ✓ ✓ [Shepard 1968, [Baran & Popovic 2007, [Botsch & Kobbelt 2004, Sibson 1980, Joshi et al. 2007] Sorkine et al. 2004, Schaefer et al. 2006] Finch et al. 2011] 76 �

Constrained optimization ensures satisfaction of all properties � m Z ( ∆ w j ) 2 dV X argmin + shape-aware w j ,j =1 ,...,m Ω + smoothness j =1 + arbitrary handles + non-negativity + locality r w j · r u j > 0 + monotonicity [Weinkauf et al. 2011, Jacobson et al. 2012, Günther Günther et al. 2014 et al. 2014] � 77 �

Weights retain nice properties in 3D � 78 �

Weights retain nice properties in 3D � 79 �

Variational formulation allows additional, problem-specific constraints � 80 �

Variational formulation allows additional, problem-specific constraints � 81 �

Energy encodes prior on deformation, � could swap smoothness for rigidity � Left, middle: smoothness energy � Right: [Kavan & Sorkine 2012] � 82 �

Energy encodes prior on deformation, � could swap smoothness for rigidity � Left, middle: smoothness energy � Right: [Kavan & Sorkine 2012] � 83 �

FEM struggles with meshes in the wild � 84 �

FEM struggles with meshes in the wild � [Jacobson et al. 2013] � 85 �

FEM struggles with meshes in the wild � [Jacobson et al. 2013] � [Dionne & de Lasa 2013] � 86 �

FEM struggles with meshes in the wild � [Jacobson et al. 2013] � [Bharaj et al. 2012] � [Dionne & de Lasa 2013] � 87 �

Recent research automates each step � choose construct compute transforms handles weights 88 �

Good weights are not enough � Rotation chosen ignorant of Rotation optimized � shape’s deformation � for best deformation � [Jacobson et al. 2011], cf. traditional IK � [Jacobson et al. 2011] � 89 �

Good weights are not enough � Rotation chosen ignorant of Rotation optimized � shape’s deformation � for best deformation � [Jacobson et al. 2011], cf. traditional IK � [Jacobson et al. 2011] � 90 �

Good weights are not enough � Rotation chosen ignorant of Rotation optimized � shape’s deformation � for best deformation � [Jacobson et al. 2011], cf. traditional IK � [Jacobson et al. 2011] � 91 �

Shape-aware IK finds best transformations � as measured by shape’s deformation � 92 �

Shape-aware IK finds best transformations � as measured by shape’s deformation � 93 �

Skinning is a coherent sub space of deformation � full space: #V x 3 DOFs � [traditional physics, modeling] � 94 �

Skinning is a coherent sub space of deformation � skinning space: #B x 12 DOFs � [Der et al. 2006, Huang et al. 2006, Au et al. 2007, Jacobson et al. 2012] �

Skinning is a coherent sub space of deformation � modal space: 50 linear modes � [Hildebrandt et al. 2011, Barbic et al. 2012] � 96 �

Skinning is a coherent sub space of deformation � inherits semantics from rig 97 �

Regularity and parsimony allows very fast � non-linear energy optimization at runtime � [Jacobson et al. 2012] � 98 �

Same idea applies for real-time � physically based dynamics � 99 � [Faure et al. 2011, Jacobson 2013, Liu et al. 2013, Bouaziz et al. 2014] �

Posing still requires more research � • Safe contacts, collisions in real time � • Leverage amassed data: semantics � • Better virtual and physical interfaces � 100 �