Weakly-Supervised Discovery of Geometry-Aware Representation for 3D Human Pose Estimation CVPR 2019

Weakly-Supervised Discovery of Geometry-Aware Representation for 3D Human Pose Estimation CVPR 2019

gold:

learn a geometry-aware 3D representation G\mathcal{G}G for the human pose

discover the geometry relation between paired images (Iti,Itj)( I^i_t,I^j_t)(Iti​,Itj​)
which are acquired from synchronized and calibrated cameras

  • i,ji,ji,j:different view point
  • ttt:acquiring time acquiring

main components

  • image skeleton mapping
  • skeleton-based view synthesis
  • representation consistency constraint

image-skeleton mapping

input raw image pair (Iti,Itj)( I^i_t,I^j_t)(Iti​,Itj​) with size of W×HW\times HW×H

  • i,ji,ji,j:different view point ,(synchronized and calibrated cameras i,ji,ji,j)

Cti,CtjC^i_t,C^j_tCti​,Ctj​:KKK keypoint heatmaps from a pre-trained 2D human pose eastimator

We follow previous works [45, 20, 18] to train the 2D estimator on MPII dataset.

constructed 8 pixels width 2D skeleton maps from heatmaps

binary skeleton maps pair (Sti,Stj)( S^i_t,S^j_t)(Sti​,Stj​),St(){0,1}(K1)×W×HS_t^{(\cdot)}\in\{0,1\}^{(K-1)\times W \times H}St(⋅)​∈{0,1}(K−1)×W×H

Geometry representation via view synthesis

training set T={(Sti,Stj,Rij)}\mathcal T = \{(S^i_t,S^j_t,R_{i\to j})\}T={(Sti​,Stj​,Ri→j​)}

  • pairs of two views of projection of same 3D skeleton (Sti,Stj)(S^i_t,S^j_t)(Sti​,Stj​)
  • relative rotation matrix RijR_{i\to j}Ri→j​ from coordinate system of camera iii to jjj

Straightforward way for learning representation in unsupervised/weakly-supervised manner is to utilize auto-encoding mechanism reconstrcting input image.

  • no geometry structure information
  • nor provides more useful information for 3D pose estimation than 2D coordinates

novel ‘skeleton-based view synthesis’ generate image under a new viewpoint.
Given an image under the known viewpoint as input

source domain : (input image) Si={Sti}i=1V\mathcal S^i = \{S^i_t\}^V_{i=1}Si={Sti​}i=1V​

  • VVV :amount of viewpoints

target domain :generate image Sj={Stj}i=1V\mathcal S^j = \{S^j_t\}^V_{i=1}Sj={Stj​}i=1V​

  • j̸=ij \not=ij̸​=i

encoder ϕ:SiG\phi:\mathcal S^i \to \mathcal Gϕ:Si→G

  • source skeleton StiSiS^i_t \to \mathcal S^iSti​→Si into a latent space GiGG_i\in \mathcal GGi​∈G

decoder ψ:Rij×GSi\psi:\mathcal R_{i\to j} \times \mathcal G \to \mathcal S_iψ:Ri→j​×G→Si​

  • ratation matrix RijR_{ i \to j }Ri→j​
  • GiG_iGi​ as the set of mmm discrete points on 3η\etaη-dimensional space
    in practice: G=[g1,g2,...gM]T,gm=(xm,ym,zm)G = [g_1,g_2,...g_M]^T,g_m = (x_m,y_m,z_m)G=[g1​,g2​,...gM​]T,gm​=(xm​,ym​,zm​)

L2(ϕψ,θ)=1NTψ(Rij×ϕ(Sti))StjL_{\ell2}(\phi \cdot\psi,\theta)=\frac{1}{N^T}\sum\lVert\psi(R_{i\to j}\times\phi(S^i_t))-S^j_t\rVertLℓ2​(ϕ⋅ψ,θ)=NT1​∑∥ψ(Ri→j​×ϕ(Sti​))−Stj​∥

Representation consistency constraint

image skeleton mapping + view synthesis (previous two steps)lead to unrealistic generation on target pose when there are large self occlusions in source view

Since there is no explicit constraint on latent space to facilitate G\mathcal GG to be semantic

We assume there exists an inverse mapping (one-to-one) between source domain and target domain, on the condition of the known relative rotation matrix. We could find:

a encoder μ:SjG\mu:\mathcal S^j \to \mathcal Gμ:Sj→G

  • maps target skeleton StjS^j_tStj​ to latent space G~jG\tilde G_j \in \mathcal GG~j​∈G

a decoder ν:Rji×GSti\nu:R_{j\to i}\times G \to S^i_tν:Rj→i​×G→Sti​

  • maps representation G~j\tilde G_jG~j​ back to source skeleton StiS^i_tSti​
  • G~i\tilde G_iG~i​ and GiG_iGi​ should be the same shared representation on G\mathcal GG with different rotation-related coefficients ------namely representation consistency

lrc=m=1Mf×GiG~i2l_{rc}=\sum_{m=1}^M\lVert f \times G_i -\tilde G_i \rVert^2lrc​=m=1∑M​∥f×Gi​−G~i​∥2

  • f=Rijf = R_{i \to j}f=Ri→j​ rotation-related transformation that map GiG_iGi​ to G~j\tilde G_jG~j​
  • a bidirectional encoderdecoder framework
    • generator(ϕ,ψ)generator(\phi,\psi)generator(ϕ,ψ),GijG_{ij}Gij​:rotated GiG_iGi​
    • generator(μ,ν)generator(\mu,\nu)generator(μ,ν)

      Weakly-Supervised Discovery of Geometry-Aware Representation for 3D Human Pose Estimation CVPR 2019

total loss of the bidirectional model
Weakly-Supervised Discovery of Geometry-Aware Representation for 3D Human Pose Estimation CVPR 2019

where θ and ζ denotes the parameters of two encode-decoder networks, respectively.

3D human pose estimation by learnt representation

given: monocular image III
goal : b={(xp,yp,zp)}p=1P\bold b = \{(x^p,y^p,z^p)\}^P_{p=1}b={(xp,yp,zp)}p=1P​,P body joints,bB\bold b \in \mathcal Bb∈B

function F:IB\mathcal F:\mathcal I \to \mathcal BF:I→B to learn the pose regression

2 fully connect layer

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