RAIDG Robust Estimation of Approximate Infinite Dimensional Gaussian
RAID-G : Robust Estimation of Approximate Infinite Dimensional Gaussian with Application to Material Recognition IEEE 2016 Conference on Computer Vision and Pattern Recognition Qilong Wang 1, Peihua Li 1, Wangmeng Zuo 2 and Lei Zhang 3 1 School of Information and Communications Engineering, Dalian University of Technology, China 2 School of Computer Science and Technology, Harbin Institute of Technology, China 3 Department of Computing, Hong Kong Polytechnic University, Hong Kong …… Motivation Scene COV or Gau. Retrieval Texture Fine-grained Tracking Material Recognition on Five Benchmarks Overview Ø One of extensions to Gaussian representations is infinite dimensional Gaussian descriptors. Methods FMD UIUC Material KTH-TIPS 2 b DTD Open Surfaces COV-CNN 80. 2 ± 1. 1 80. 5 ± 3. 6 76. 7 ± 2. 8 70. 1 ± 1. 2 55. 0 Ø Alternative extension to Gaussian representations is to enhance the original features – CNN features. Gau-CNN 81. 3 ± 1. 4 81. 7 ± 2. 9 77. 5 ± 2. 4 70. 5 ± 1. 5 55. 7 Ro. G-CNN 83. 6 ± 1. 6 84. 5 ± 1. 8 79. 5 ± 1. 5 73. 9 ± 1. 1 58. 9 RAID-G-CNN-Hel 84. 4 ± 1. 3 85. 7 ± 2. 1 80. 4 ± 1. 2 75. 8 ± 1. 4 60. 3 RAID-G-CNN-Chi 84. 9 ± 1. 4 86. 3 ± 2. 9 81. 3 ± 1. 6 76. 4 ± 1. 1 61. 1 FC 77. 4 ± 1. 8 75. 9 ± 2. 3 75. 4 ± 1. 5 62. 9 ± 0. 8 43. 4 FV-CNN 79. 8 ± 1. 8 80. 5 ± 2. 7 81. 8 ± 2. 5 72. 3 ± 1. 0 59. 5 FC + FV-CNN 82. 4 ± 1. 5 82. 6 ± 2. 1 81. 1 ± 2. 4 74. 7 ± 1. 0 60. 9 Challenges: 1. Computing infinite dimensional Gaussian. 2. Robust estimation of Gaussian with high dimension and small sample. RAID-G Ø Modeling images with RIAD-G in multiscale manner. Ø VGG-VD 16 without fine-tuning. Key Issues & Solutions Computing infinite dimensional Gaussian Comparison with Counterparts The idea is to map, through some kernel functions, the original features into some Reproducing Kernel Hilbert Space where we construct infinite dimensional Gaussian. Methods Harandi et al. [CVPR 14] v. N-MLE Gaussian Matching where S is sample covariance. How to compute distance between Gaussians efficiently and effectively ? Mapping manifold of Gaussian into the space of SPD matrices: where is von Neumann divergence between matrices. where RBF kernel (no explicit mapping) Log-HS [NIPS 14] Gaussian: Classical MLE Estimator Linear SVM? Zhou et al. [PAMI 06] Robust Estimation of Approximate Infinite Dimensional Gaussian We face covariance estimation with high dimension and small sample. It is well known that conventional Maximum Likelihood Estimation (MLE) is not robust to this problem. Kernels & Mapping F-Norm Metric on SPD matrices Ledoit-Wolf estimator ( Faraki et al. [ICASSP 15] Random Fourier transform Nystrom method for RBF kernel RIAD-G (Ours) Hellinger’s kernel 2 kernel �� No ) Yes v. N-MLE Yes Ø The feature mappings we introduced are very efficient and suit for very high dimensional features. Ø The v. N-MLE method can handle robust covariance estimation with high dimension and small sample. Ø Our RIAD-G can be fed into a linear SVM for scalable classification. Methods FMD UIUC Gau-CNN (LW) 81. 3 ± 1. 4 81. 7 ± 2. 9 Gau-CNN (Stein) 81. 9 ± 0. 7 82. 2 ± 1. 8 Gau-CNN (MMSE) 81. 2 ± 1. 2 80. 9 ± 1. 9 Gau-CNN (EL-SP) 81. 5 ± 1. 6 82. 0 ± 2. 3 Ro. G-CNN (v. N-MLE) 83. 6 ± 1. 6 84. 5 ± 1. 8 Gau-CNN-Chi (LW) 83. 1 ± 0. 9 81. 6 ± 4. 1 Gau-CNN-Chi (Stein) 83. 2 ± 0. 8 83. 6 ± 3. 0 Gau-CNN-Chi (MMSE) 83. 1 ± 0. 8 82. 0 ± 4. 3 Gau-CNN-Chi (EL-SP) 83. 2 ± 1. 1 82. 1 ± 3. 1 RAID-G-CNN-Chi (v. N-MLE) 84. 9 ± 1. 4 86. 3 ± 2. 9 Methods KTH-TIPS 2 b Methods FMD UIUC RAID-G-Hel (23 D Handcrafted features) 78. 8 ± 4. 8 RAID-G-CNN-r. Ft (1 x) 79. 7 ± 1. 6 80. 6 ± 2. 2 RAID-G-Chi (23 D Handcrafted features) 78. 2 ± 4. 7 RAID-G-CNN-r. Ft (3 x) 80. 6 ± 2. 3 81. 8 ± 2. 7 RAID-G-CNN-Hel 89. 0 ± 5. 4 RAID-G-CNN-Nystr�� m (1 x) 82. 2 ± 2. 2 83. 3 ± 3. 1 RAID-G-CNN-Chi 89. 3 ± 4. 5 RAID-G-CNN-Nystr�� m (3 x) 82. 8 ± 1. 9 84. 0 ± 2. 7 Log-E RBF (baseline) (23 D Handcrafted features) 74. 1 ± 7. 4 RAID-G-CNN-Hel 84. 4 ± 1. 3 85. 7 ± 2. 1 Harandi et al. [CVPR 14] (23 D Handcrafted features) 80. 1 ± 4. 6 RAID-G-CNN-Chi 84. 9 ± 1. 4 86. 3 ± 2. 9 Log-HS [NIPS 14] (23 D Handcrafted features) 81. 9 ± 3. 3 Fine-grained Classification & Scene Categorization RIAD-G Bird-CUB 200 -2011 82. 1 Indoor 67 82. 8 SUN 397 67. 1 Large Scale Image Retrieval in Web Store Ø Ø > 3 M gallery images 2 nd among 843 teams
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