[table]capposition=above Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand Gesture Recognition Mostefa Ben naceur, Luc Brun, Olivier Lezoray Normandie Univ, ENSICAEN, CNRS, UNICAEN, GREYC, Caen France Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 1 / 8 

Context (a) 22 hand joints (graph) (b) Transforming hand joints into structured data (2D grid) where each joint has 3 dim (x, y, z) Input Xt = 20 16 12 8 4 19 15 11 7 3 18 14 10 6 2 17 13 9 5 1 (c) 2D grid with 3 dim is the input to our proposed model where each node of the 2D grid has at most 9 neighbors including itself Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 2 / 8 

Our proposed model: Deep SPDNe for offline 3D hand gesture recognition (1/2) 2DConv : Xt k = j∈Ni Wk,i Xt k−1,j Gmap : Xsb s,j = Σsb s,j + µsb s,j (µsb s,j )T µsb s,j (µsb s,j )T 1 (1) Reig : X1,sb s,j,k = Uk−1 max(ϵI, Vk−1 )UT k−1 LogEig : X2,sb s,j = Uk−1 log(Vk−1 )UT k−1 (2) Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 3 / 8 

Our proposed model: Deep SPDNe for offline 3D hand gesture recognition (2/2) VecMat : xsb s,j = fv (X2,sb s,j ) = [X2,sb s,j (1, 1), √ 2X2,sb s,j (1, 2) , ..., √ 2X2,sb s,j (1, dc out ), X2,sb s,j (2, 2), √ 2X2,sb s,j (2, 3) , ..., X2,sb s,j (dc out , dc out )]T (3) BiMap : X = fb (X1, ..., XN ; W1, ..., WN ) = N i=1 Wi Xi W T i (4) Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 4 / 8 

Our proposed model: Deep SPDNet and TDN pipeline for online 3D hand gesture recognition Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 5 / 8 

Experiments: Performance of Deep SPDNet and TDN pipeline to detect and recognize the sequences of clips Method Color Depth Pose Accuracy(%) HON4D [1] ✗ ✓ ✗ 70.61 Lie Group [2] ✗ ✗ ✓ 82.69 HBRNN [3] ✗ ✗ ✓ 77.40 JOULE-all [4] ✓ ✓ ✓ 78.78 Two stream-all [5] ✓ ✗ ✗ 75.30 Novel View [6] ✗ ✓ ✗ 69.21 LSTM [7] ✗ ✗ ✓ 80.14 Gram Matrix [8] ✗ ✗ ✓ 85.39 T Forests [9] ✗ ✗ ✓ 80.69 M Learning [10] ✗ ✗ ✓ 84.35 G Manifolds [11] ✗ ✗ ✓ 77.57 ST-TS-HGR-NET [12] ✗ ✗ ✓ 93.22 Two-stream NN [13] ✗ ✗ ✓ 90.26 Deep SPDNet ✗ ✗ ✓ 90.96 10 C/S 20 C/S 40 C/S 80 C/S 160 C/S 91.71(±0.65) 90.44(±1.4) 89.78(±1.5) 89.34(±1.56) 89.09(±1.51) 88.99(±0.92) 87.61(±1.57) 86.36(±2.23) 85.37(±2.59) 84.72(±2.66) 85.27(±0.88) 83.24(±2.15) 81.43(±3.14) 79.76(±4.05) 78.14(±4.90) Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 6 / 8 

Conclusion a novel Deep SPD model for skeleton-based offline 3D hand gesture recognition integrate symmetric positive definite (SPD) matrices in our deep learning model for learning statistical and discriminative hand gesture representations a stream of 10-frame clips is sufficient to solve the issue of online 3D hand gesture recognition using our proposed pipeline of Deep SPD and TDN networks Mostefa Ben naceur, Luc Brun, Olivier Lezoray () Lightweight Deep Symmetric Positive Definite Manifold Network for Real-Time 3D Hand G 7 / 8 

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