MIRU2020長尾賞受賞論文解説：Attention Branch Networkの展開
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CDLE勉強会#4 2020年8月19日
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MIRU2020長尾賞受賞論文解説：Attention Branch Networkの展開
- 1. 487-8501 1200 Tel 0568-51-8249 Fax 0568-51-9409 487-8501 1200 Tel 0568-51-9670 Fax 0568-51-1540 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 miya@vision.cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROB Chubu University Department of Robotics Science a College of Engineering Ayumi Miyako Machine Perception and Robotic 1200 Matsumoto-cho, Kasugai, A 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp 487-8501 1200 Tel 0568-51-8249 Fax 0568-51-9409 yuu@vision.cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Research Assistant Dr.Eng. Yuji Yamauchi Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-8249 Fax +81-568-51-9409 yuu@vision.cs.chubu.ac.jp 487-8501 1200 Tel 0568-51-9670 Fax 0568-51-1540 yamashita@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Computer Science College of Engineering Lecturer Dr.Eng. Takayoshi Yamashita Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9670 Fax +81-568-51-1540 yamashita@cs.chubu.ac.jp 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor Dr.Eng. Hironobu Fujiyoshi Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp
- 2. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 3. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 4. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 5. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR CONFIDENTIAL EXTENDED ABSTRACT. DO NOT DISTRIBUTE ANYWHERE. 23 Spatial Temporal Attention Graph 1,a) 1,b) 1,c) 1,d) Graph Convolutional Networks , . , , . , . , Spatial Temporal Attention Graph Convolutional Networks . Attention node , Attention edge . , , Mechanics-stream . Mechanics-stream , . , NTU-RGB+D NTU-RGB+D120 2 . 1. , . . , . , Graph Convolu- tional Networks (GCN) [1][2][3][4][5]. , GCN , . Spatial Temporal GCN (ST-GCN) [1] GCN . ST-GCN , , 1 a) siraki@mprg.cs.chubu.ac.jp b) hirakawa@mprg.cs.chubu.ac.jp c) takayoshi@isc.chubu.ac.jp d) fujiyoshi@isc.chubu.ac.jp . , [2][3]. , . , . , , . , Spatial Temporal Attention GCN (STA-GCN) . Attention edge , Attention node . Attention node Attention , . , Attention edge , . Attention node Attention edge , , Spatial temporal attention graph (Attention graph) . . [3][5]. . , . , . , , , , , , Mechanics-stream . 2. Spatial Temporal GCN (ST-GCN) [1] , GCN . ST-GCN , , 2 . ST-GCN , , . 1 Attention Branch Network: Learning of Attention Mechanism for Visual Explanation Hiroshi Fukui, Tsubasa Hirakawa, Takayoshi Yamashita, Hironobu Fujiyoshi Chubu University 1200 Matsumotocho, Kasugai, Aichi, Japan {fhiro@mprg.cs, hirakawa@mprg.cs, yamashita@isc, fujiyoshi@isc}.chubu.ac.jp Abstract Visual explanation enables humans to understand the de- cision making of deep convolutional neural network (CNN), but it is insufficient to contribute to improving CNN perfor- mance. In this paper, we focus on the attention map for vi- sual explanation, which represents a high response value as the attention location in image recognition. This attention region significantly improves the performance of CNN by introducing an attention mechanism that focuses on a spe- cific region in an image. In this work, we propose Attention Branch Network (ABN), which extends a response-based vi- sual explanation model by introducing a branch structure with an attention mechanism. ABN can be applicable to several image recognition tasks by introducing a branch for the attention mechanism and is trainable for visual expla- nation and image recognition in an end-to-end manner. We evaluate ABN on several image recognition tasks such as image classification, fine-grained recognition, and multiple facial attribute recognition. Experimental results indicate that ABN outperforms the baseline models on these image recognition tasks while generating an attention map for vi- sual explanation. Our code is available 1 . 1. Introduction Deep convolutional neural network (CNN) [1, 17] mod- els have been achieved the great performance on various image recognition tasks [25, 9, 7, 34, 8, 12, 18]. How- ever, despite CNN models performing well on such tasks, it is difficult to interpret the decision making of CNN in the inference process. To understand the decision mak- ing of CNN, methods of interpreting CNN have been pro- posed [39, 41, 26, 4, 24, 3, 22]. “Visual explanation” has been used to interpret the de- cision making of CNN by highlighting the attention loca- 1https://github.com/machine-perception-robotics -group/attention_branch_network Attention map Attention map … Great grey owl Ruffed grouse (a) Class Activation Mapping (b) Attention Branch Network wc GAP&fc. Attention branch Perception branch Label Label Lper(xi) Latt(xi) Feature extractor Input image Input image L(xi) Attention mechanism Featuremap Feature extractor Figure 1. Network structures of class activation mapping and pro- posed attention branch network. tion in a top-down manner during the inference process. Visual explanation can be categorized into gradient-based or response-based. Gradient-based visual explanation typ- ically use gradients with auxiliary data, such as noise [4] and class index [24, 3]. Although these methods can inter- pret the decision making of CNN without re-training and modifying the architecture, they require the backpropaga- tion process to obtain gradients. In contrast, response- based visual explanation can interpret the decision mak- ing of CNN during the inference process. Class activation mapping (CAM) [41], which is a representative response- based visual explanation, can obtain an attention map in each category using the response of the convolution layer. CAM replaces the convolution and global average pool- ing (GAP) [20] and obtains an attention map that include high response value positions representing the class, as shown in Fig. 1(a). However, CAM requires replacing the fully-connected layer with a convolution layer and GAP, thus, decreasing the performance of CNN. To avoid this problem, gradient-based methods are of- 010705
- 6. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 7. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 8. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 9. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 10. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 11. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 12. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR × Σ Lall(x) = Eatt(x) + Eper(x) Eper(x) Eatt(x)
- 13. 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 How Small Network Can Detect Pedestrian? Anonymous CVPR submission Paper ID **** Abstract 1. Introduction t log y + (1 − t) log (1 − y) (1) vc i = 1 M × N M m=1 N n=1 fc m,n(xi) (2) v1 i , v2 i , v3 i , vc i (3) g (xi) = g(xi) · 1 C C c=1 fc (xi) (4) f (xi, yi) (5) 2. Concolusion References 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR 000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 CVPR #**** CVPR 2017 Submission #****. CONFIDENTIAL How Small Network Can Anonymous CVPR Paper ID * Abstract 1. Introduction t log y + (1 − t) log (1 − y) (1) vc i = 1 M × N M m=1 N n=1 fc m,n(xi) (2) v1 i , v2 i , v3 i , vc i (3) g (xi) = g(xi) · 1 C C c=1 fc (xi) (4) f (xi, yi) (5) 2. Concolusion × 000 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 How Small Network Can Detect Pedestrian? Anonymous CVPR submission Paper ID **** Abstract 1. Introduction t log y + (1 − t) log (1 − y) (1) vc i = 1 M × N M m=1 N n=1 fc m,n(xi) (2) v1 i , v2 i , v3 i , vc i (3) g (xi) = g(xi) · 1 C C c=1 fc (xi) (4) f (xi, yi) (5) 2. Concolusion References Σ 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 1. Introduction t log y + (1 − t) log (1 − y) (1) vc i = 1 M × N M m=1 N n=1 fc m,n(xi) (2) v1 i , v2 i , v3 i , vc i (3) g (xi) = g(xi) · 1 C C c=1 fc (xi) (4) f (xi, yi) (5) 2. Concolusion References
- 14. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 15. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 16. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 17. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 18. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR × × ×
- 19. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 20. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 21. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 22. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 23. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR × Σ
- 24. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 25. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR Conv. Conv. GAP Res. Block 5 output Attention branch Perception branch Res. Attention Block Conv. Attention mapAttention map Feature extractor Label 𝐿 𝑚𝑎𝑝 𝐿𝑎𝑡𝑡(𝑥) 𝐿𝑝𝑒𝑟(𝑥) 𝐿 𝑚𝑎𝑝 = 𝛼 𝑥 − 𝑦 2 2 𝐿𝑎𝑙𝑙(𝑥) = 𝐿𝑎𝑡𝑡(𝑥) + 𝐿𝑝𝑒𝑟(𝑥) + 𝐿 𝑚𝑎𝑝
- 26. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 27. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 28. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 29. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 30. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR ❌
- 31. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 32. Policy Value Input Global Network Conv. Sigmoid Conv. ReLU Conv. ReLU Conv. FC. Conv. Maxpooling+ReLU Conv. Maxpooling+ReLU Conv. Maxpooling+ReLU Value branch Policy branch FC. Policy Value ConvLSTM GAP Feature extractor Mask-Attention Input Attention Mechanism ••• Policy Value Input worker n Environment Policy Value Input worker 1 Environment Policy Value Input worker 2 Environment Feature extractor Value branch Policy branch Mask-Attention 1: Mask A3C
- 33. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 34. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 35. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR
- 36. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR 0 Tt
- 37. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR Input Output Convolutions Full Connection A V = {v0, v1, . . . , vN }<latexit sha1_base64="ahF1XlmO+63oShDr5uLd56z8mV0=">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</latexit><latexit 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- 38. 487-8501 1200 Tel 0568-51-9096 Fax 0568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GROUP Chubu University Department of Robotics Science and Technology College of Engineering Professor MACHINE PERCEPTION AND ROBOTICS GR Chubu University Department of Robotics Science and Techn College of Engineering Professor Dr.Eng. Hironobu Fujiyosh Machine Perception and Robotics Group 1200 Matsumoto-cho, Kasugai, Aichi 487-8501 Japan Tel +81-568-51-9096 Fax +81-568-51-9409 hf@cs.chubu.ac.jp http://vision.cs.chubu.ac.jp MACHINE PERCEPTION AND ROBOTICS GR ˜A = A + I<latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit 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sha1_base64="8mDTFuyI8sljk3/zYyuzBgw/Je8=">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</latexit> ˜A = A + I<latexit 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sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">AAACgnicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQvIVsckpcWUZOakpCo41tqCeEBaG0x71sYLKBvoGYCBAibDEMpQZoCCgHyB5QwxDCkM+QzJDKUMuQypDHkMJUB2DkMiQzEQRjMYMhgwFADFYhmqgWJFQFYmWD6VoZaBC6i3FKgqFagiESiaDSTTgbxoqGgekA8ysxisOxloSw4QFwF1KjCoGlw1WGnw2eCEwWqDlwZ/cJpVDTYD5JZKIJ0E0ZtaEM/fJRH8naCuXCBdwpCB0IXXzSUMaQwWYLdmAt1eABYB+SIZor+savrnYKsg1Wo1g0UGr4HuX2hw0+Aw0Ad5ZV+SlwamBs1m4AJGgCF6cGMywoz0DA30DANNlB08oFHBwSDNoMSgAQxvcwYHBg+GAIZQoL3NDCsZNjFsZmJh0mIyZDKGKGVihOoRZkABTDYAxMqUJQ==</latexit> ˜A = A + I<latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit> ˜A = A + I<latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit><latexit sha1_base64="TomtJlApWF/mxlr+rHF9E8Br6dU=">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</latexit>