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Tutorial on Object Detection (Faster R-CNN)
- 1. Tutorial Faster R-CNN Object Detection: Localization & Classification Hwa Pyung Kim Department of Computational Science and Engineering, Yonsei University hpkim0512@yonsei.ac.kr
- 2. 𝑥 𝑦 𝑤 ℎ Bounding box regression (localization): Where? Object Detection: Classification + Regression A dog at (𝒙, 𝒚, 𝒘, 𝒉) + = 1 0 0 ⋮ Dog Cat ⋮ Person Classification (recognition): What? Objection Detection Feature map Encoding (conv&pool) Combining features 𝒙, 𝒚 w h Bounding box information • 𝒙, 𝒚 : top left corner position • w = width • h = height
- 3. Dog Cat Person ⋮ pool5 features[224,224,3] [7,7,512] Input image 224 224 7 = 224 32 32 = 25 5 = # of pooling 7 7 Vgg16 Networks Pooling CNN-based Object Detection: There are clues of dog (What) at local position (Where) in the convolution feature map Fully-connected layers Classification Regression 𝑥 𝑦 𝑤 ℎ 1 0 0 ⋮ These red boxes contains clues of “dog at the bounding box (𝑥, 𝑦, 𝑤, ℎ)”. ⋯ ⋯ Dog
- 4. Multiple Object Detection: Localize and Classify all objects appearing in the image How many objects are in there? • Classify these multiply overlapping objects • Identify their bounding boxes PASCAL VOC2007
- 5. Background Person Dining table Extract “region proposals” using selective search method. ConvNet Region based CNN (R-CNN) method CNN input (fixed size) Affine image warping: Compute fixed-size CNN input from each region proposal, regardless of the region’s shape Classifier & Regressor Classifier & Regressor Classifier & Regressor
- 6. Fast R-CNN feature map ConvNet Classifier & Regressor RoI pooling: Convert the features inside valid RoI into a small feature map with a fixed spatial
- 7. Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks feature map Region Proposal Network RoI pooling proposals ConvNet Classifier & Regressor What is Region Proposal Network?
- 8. Region Proposal Network (RPN) Region Proposal Network 380 480 11 = 360 32 , 15 = 480 32 32 = 25 5 = # of pooling 512 = # of filters 15 11 512 Conv feature map RPN RPN outputs a set of rectangular object proposals, each with an objectness score. How? Region proposals
- 9. Region Proposal Network Conv feature map 15 11 512 Region Proposals & Anchor Boxes 𝑠 𝑜𝑏𝑗 𝑠 𝑛𝑜𝑏𝑗 t𝑥 t𝑦 t𝑤 tℎ Fully- connected layers Input: each sliding window 3×3×512 For each sliding window (red cuboid) expressed by a vector 𝟑 × 𝟑 × 𝟓𝟏𝟐 , the proposal is parametrized relative to an anchor. 𝑝𝑥 = 𝑎𝑥 + 𝑎𝑤 ⋅ 𝑡𝑥 𝑝𝑦 = 𝑎𝑦 + 𝑎ℎ ⋅ 𝑡𝑦 𝑝𝑤 = 𝑎𝑤 ⋅ exp 𝑡𝑤 𝑝ℎ = 𝑎ℎ ⋅ exp 𝑡ℎ Output: • 4 coordinates: 𝑝𝑥 , 𝑝𝑦, 𝑝𝑤, 𝑝ℎ • 2 scores: 𝑠 𝑜𝑏𝑗 , 𝑠 𝑛𝑜𝑏𝑗 that estimate probability of object or not object for each proposal Anchor box information • 𝒂𝒙 , 𝒂𝒚 : center position • 𝒂𝒘 = width • 𝒂𝒉 = height Anchor box For example, 𝑎𝑤 = 𝑎ℎ = 128 • 𝑎𝑤 and 𝑎ℎ are fixed. • 𝑎𝑥 , 𝑎𝑦 is determined by the position of the red box
- 10. Region Proposals & Anchor Boxes ⋮ 𝑠1 𝑜𝑏𝑗 𝑠1 𝑛𝑜𝑏𝑗 t𝑥1 t𝑦1 t𝑤1 tℎ1Conv feature map 15 11 512 Fully- connected layers 3×3×512 • 𝑎𝑤𝑖 and 𝑎ℎ𝑖 are fixed. • 𝑎𝑥𝑖, 𝑎𝑦𝑖 is determined by the position of the red box 9 Anchor boxes = 3 ratios × 3 scales For example, 𝑎𝑤1 = 𝑎ℎ1 = 128, 𝑎𝑤2 = 𝑎ℎ2 = 2 × 128, 𝑎𝑤3 = 𝑎ℎ3 = 4 × 128, 𝑎𝑤4 = 2 × 𝑎ℎ4 = 128, ⋯ 𝑎𝑤7 = 1 2 × 𝑎ℎ7 = 128, ⋯ Output: For 𝑖 = 1, ⋯ , 9, • 4 coordinates: 𝑝𝑥𝑖, 𝑝𝑦𝑖, 𝑝𝑤𝑖, 𝑝ℎ𝑖 • 2 scores: 𝑠𝑖 𝑜𝑏𝑗 , 𝑠𝑖 𝑛𝑜𝑏𝑗 that estimate probability of object or not object for each proposal For each sliding window (red cuboid) expressed by a vector 𝟑 × 𝟑 × 𝟓𝟏𝟐 , the 9 proposals are parametrized relative to 9 anchors. Input: each sliding window Region Proposal Network 𝑠2 𝑜𝑏𝑗 𝑠2 𝑛𝑜𝑏𝑗 t𝑥2 t𝑦2 t𝑤2 tℎ2 𝑠9 𝑜𝑏𝑗 𝑠9 𝑛𝑜𝑏𝑗 t𝑥9 t𝑦9 t𝑤9 tℎ9 For 𝑖 = 1, ⋯ 9, 𝑝𝑥𝑖 = 𝑎𝑥𝑖 + 𝑎𝑤𝑖 ⋅ t𝑥𝑖 𝑝𝑦𝑖 = 𝑎𝑦𝑖 + 𝑎ℎ𝑖 ⋅ t𝑦𝑖 𝑝𝑤𝑖 = 𝑎𝑤𝑖 ⋅ exp t𝑤𝑖 𝑝ℎ𝑖 = 𝑎ℎ𝑖 ⋅ exp tℎ𝑖 Anchor box information • 𝒂𝒙𝒊, 𝒂𝒚𝒊 : center position • 𝒂𝒘𝒊 = width • 𝒂𝒉𝒊 = height
- 11. Region Proposal Network Fully- connected layers Conv feature map Anchor boxes 15 11 512 For 𝑖 = 1, ⋯ 9, 𝑝𝑥𝑖 = 𝑎𝑥𝑖 + 𝑎𝑤𝑖 ⋅ 𝑡𝑥𝑖 𝑝𝑦𝑖 = 𝑎𝑦𝑖 + 𝑎ℎ𝑖 ⋅ 𝑡𝑦𝑖 𝑝𝑤𝑖 = 𝑎𝑤𝑖 ⋅ exp 𝑡𝑤𝑖 𝑝ℎ𝑖 = 𝑎ℎ𝑖 ⋅ exp 𝑡ℎ𝑖 𝑝𝑖 = exp 𝑠𝑖 𝑜𝑏𝑗 exp 𝑠𝑖 𝑜𝑏𝑗 + exp 𝑠𝑖 𝑛𝑜𝑏𝑗 ⋮ 𝑝1 𝑝𝑥1 𝑝𝑦1 𝑝𝑤1 𝑝ℎ1 𝑝2 𝑝𝑥2 𝑝𝑦2 𝑝𝑤2 𝑝ℎ2 𝑝9 𝑝𝑥9 𝑝𝑦9 𝑝𝑤9 𝑝ℎ9 Extract 9 Proposals relative to 9 Anchors Proposals 3×3×512 ⋮ 𝑠1 𝑜𝑏𝑗 𝑠1 𝑛𝑜𝑏𝑗 t𝑥1 t𝑦1 t𝑤1 tℎ1 𝑠2 𝑜𝑏𝑗 𝑠2 𝑛𝑜𝑏𝑗 t𝑥2 t𝑦2 t𝑤2 tℎ2 𝑠9 𝑜𝑏𝑗 𝑠9 𝑛𝑜𝑏𝑗 t𝑥9 t𝑦9 t𝑤9 tℎ9
- 12. ⋮ ⋮ Total # of windows # of proposals per a window Total # of proposals: 11 × 15 × 9 = 1485 Conv feature map The proposals highly overlaps each other! Need to reduce redundancy. Generate Region Proposals 15 11 512 Total#ofwindows=11×15 Region Proposal Network
- 13. Reduce redundancy by Non-Maximum Suppression (NMS) 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 173p𝑟𝑜𝑝𝑜𝑠𝑎𝑙1 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1480𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙2 ⋯ 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1485 ⋯ ⋯ Most probable proposal Region Proposal Network Step 1. Take the most probable proposal from 1485 proposals Proposal information • 𝒑𝒙𝒊, 𝒑𝒚𝒊 : top left corner position • 𝒑𝒘𝒊 = width • 𝒑𝒉𝒊 = height • 𝒑𝒊 = objectness probability, 𝒑 𝟏 ≥ 𝒑 𝟐 ≥ 𝒑 𝟏𝟒𝟖𝟓 𝑝𝑥1, 𝑝𝑦1, 𝑝𝑤1, 𝑝ℎ1, 𝑝1 𝑝𝑥2, 𝑝𝑦2, 𝑝𝑤2, 𝑝ℎ2, 𝑝2 𝑝𝑥173, 𝑝𝑦173, 𝑝𝑤173, 𝑝ℎ173, 𝑝173 𝑝𝑥1480, 𝑝𝑦1480, 𝑝𝑤1480, 𝑝ℎ1480, 𝑝1480 𝑝𝑥1485, 𝑝𝑦1485, 𝑝𝑤1485, 𝑝ℎ1485, 𝑝1485
- 14. Region Proposal Network Step 2. Compute the 𝐼𝑜𝑈 between the most probable and the other proposals, and reduce proposals having 𝑰𝒐𝑼 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (0.7) Step 1. Take the most probable proposal from 1485 proposals Reduce redundancy by Non-Maximum Suppression (NMS) 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 173 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1480 0.83𝐼𝑂𝑈 = 0.71 ⋯ ⋯ 0.30 0 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1485 ⋯ 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 2
- 15. Region Proposal Network Step 1. Take the most probable proposal from 1485 proposals Reduce redundancy by Non-Maximum Suppression (NMS) 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 173 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1480 0.830.71 ⋯ ⋯ 0.30 0 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 1485 ⋯ 𝑝𝑟𝑜𝑝𝑜𝑠𝑎𝑙 2 Step 2. Compute the 𝐼𝑜𝑈 between the most probable and the other proposals, and reduce proposals having 𝑰𝒐𝑼 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (0.7) 𝐼𝑂𝑈 =
- 16. Most probable proposal 30 proposals having IoU>0.7 are discarded. Region Proposal Network Given the most probable proposal, the blue proposals have 𝑰𝒐𝑼 > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (0.7) Summary of step 1-2 in NMS. Step 3: Get the next most probable proposal among the rest 1485 − 30 proposals & repeat the previous process. Next most probable proposal 36 proposals having IoU>0.7 are discarded. Reduce redundancy by NMS
- 17. Region Proposal Network Before NMS After NMS 1,485 proposals 300 proposals Repeats the previous procedure until… Reduce redundancy by NMS
- 18. Summary of RPN Inputs: • Conv feature map Outputs: • Region proposals coordinates. • Probabilities representing how likely the image in that region proposal will be an object. Region Proposal Network
- 19. feature map Region Proposal Network RoI pooling proposals ConvNet Now we are ready to explain Classifier & Regressor. Classifier & Regressor Classifier & Regressor
- 20. RoI pooling layer Proposal 𝑝𝑥, 𝑝𝑦, 𝑝𝑤, 𝑝ℎ 𝑝𝑥′ , 𝑝𝑦′ , 𝑝𝑤′ , 𝑝ℎ′ 𝑝𝑥, 𝑝𝑦, 𝑝𝑤, 𝑝ℎ Classifier & Regressor Bilinear interpolation & Max pooling Input for Classifier & Regressor : fixed-size Conv feature map Bilinear interpolation & Max pooling Convert the features inside valid RoI into a small feature map with a fixed spatial extent. 𝑝𝑥′ = 𝑝𝑥 ⋅ 15 , 𝑝𝑦′ = 𝑝𝑦 ⋅ 11 , 𝑝𝑤′ = 𝑝𝑤 ⋅ 15 , 𝑝ℎ′ = 𝑝ℎ ⋅ 11 360 480 11 15 5 8 3 9 7 7 7 7 𝑝𝑥′ , 𝑝𝑦′ , 𝑝𝑤′ , 𝑝ℎ′
- 21. ⋯ 300 RoI pooled feature maps RoI pooling layer generates inputs for Classifier & Regressor Classifier & Regressor 7 7 512 7 7 512 7 7 512 7 7 512
- 22. ⋮ 𝑠0 𝑟𝑥0 𝑟𝑦0 𝑟𝑤0 𝑟ℎ0 𝑠15 𝑟𝑥15 𝑟𝑦15 𝑟𝑤15 𝑟ℎ15 𝑠20 𝑟𝑥20 𝑟𝑦20 𝑟𝑤20 𝑟ℎ20 𝑝0 = 0.0124 𝑝15 = 0.9797 𝑝20 = 0.0001 ⋮ RoI pooling Classification & Regression per each proposal 𝑥𝑖 = 𝑝𝑥 + 𝑝𝑤 ⋅ 𝑟𝑥𝑖 𝑦𝑖 = 𝑝𝑦 + 𝑝ℎ ⋅ 𝑟𝑦𝑖 𝑤𝑖 = 𝑝𝑤 ⋅ exp 𝑟𝑤𝑖 ℎ𝑖 = 𝑝ℎ ⋅ exp 𝑟ℎ𝑖 𝑝𝑖 = exp 𝑠𝑖 𝑗=0 20 exp 𝑠𝑗 Background Person TV monitor 𝑝𝑥, 𝑝𝑦, 𝑝𝑤, 𝑝ℎ Fully-connected layers ⋮ 𝑝0 𝑥0 𝑦0 𝑤0 ℎ0 𝑝15 𝑥15 𝑦15 𝑤15 ℎ15 𝑝20 𝑥20 𝑦20 𝑤20 ℎ20 ⋮ Proposal Classification & Bounding-box regression Each of the 21 classes gets its own refined bounding-box prediction and assign estimated probability. Classifier & Regressor 7 7 512 7×7×512 4096
- 23. Summary of Classification & Regression Regress & classify each class from proposals ⋮ Background Person TV monitor ⋮ ⋮ Reduce redundancy by NMS Dining table ⋮ None None Classifier & Regressor Discard bounding boxes (p < 0.6 or background) ⋮ ⋮ ⋮ Region Proposals
- 24. Summary of Classifier & Regressor Inputs: • Conv feature map • Region proposals Outputs: • Bounding boxes coordinate of objects in the image. • Classification of bounding boxes Classifier & Regressor
- 25. Training process for RPN Ground-truth proposals associated with anchors 𝐴𝑗 𝑘 Find the nearest bounding box from each anchors, 𝐵𝑖 𝑘 = argmax 𝐵∈ 𝐵(𝑘) 𝐼𝑜𝑈 𝐵, 𝐴𝑗 𝑘 • Ground-truth probability of objectness: 𝑝𝑗 (𝑘) ≔ 1, 𝑖𝑓 𝐼𝑜𝑈 𝐵𝑖 𝑘 , 𝐴𝑗 𝑘 > 0.7 0, 𝑖𝑓 𝐼𝑜𝑈 𝐵𝑖 𝑘 , 𝐴𝑗 𝑘 < 0.3 • Ground-truth proposal transformation: 𝑡𝑗 (𝑘) ≔ 𝑡𝑥𝑗 (𝑘) , 𝑡𝑦𝑗 (𝑘) , 𝑡𝑤𝑗 (𝑘) , 𝑡ℎ𝑗 (𝑘) where Δ 𝑥𝑗 (𝑘) = 𝑥𝑖 𝑘 − 𝑎𝑥𝑗 (𝑘) /𝑎𝑤𝑗 (𝑘) , Δ 𝑦𝑗 𝑘 = 𝑦𝑖 (𝑘) − 𝑎𝑦𝑗 (𝑘) /𝑎ℎ𝑗 (𝑘) , Δ 𝑤𝑗 = log 𝑤𝑖 𝑘 /𝑎𝑤𝑗 (𝑘) , Δℎ𝑗 𝑘 = log ℎ𝑖 𝑘 /𝑎ℎ𝑗 (𝑘) Predicted proposals • Predicted probability of objectness: 𝑝𝑗 𝑘 • Predicted proposal transformation: 𝑡𝑗 (𝑘) = 𝑡𝑥𝑗 𝑘 , 𝑡𝑦𝑗 𝑘 , t𝑤𝑗 𝑘 , tℎ𝑗 𝑘 where 𝑡𝑗 𝑘 , 𝑝𝑗 𝑘 𝑗=1 𝑁 𝑎𝑛𝑐 𝑘 = 𝑅𝑃𝑁 𝐶𝑁𝑁 𝑋 𝑘 ; 𝑊𝐶𝑁𝑁 ; 𝑊𝑅𝑃𝑁 , Anchor boxes 𝐴(𝑘) = 𝐴𝑗 𝑘 𝑗=1 𝑁 𝑎𝑛𝑐 (𝑘) where A𝑗 𝑘 = 𝑎𝑥𝑗 (𝑘) , 𝑎𝑦𝑗 (𝑘) , 𝑎𝑤𝑗 (𝑘) , 𝑎ℎ𝑗 (𝑘) Input • Image 𝑋 𝑘 Ground-truth • Bounding boxes 𝐵(𝑘) = 𝐵𝑖 𝑘 𝑖=1 𝑁 𝑜𝑏𝑗 (𝑘) where 𝐵𝑖 𝑘 = 𝑥𝑖 𝑘 , 𝑦𝑖 𝑘 , 𝑤𝑖 𝑘 , ℎ𝑖 𝑘 • Classes 𝐶(𝑘) = 𝐶𝑖 𝑘 𝑖=1 𝑁 𝑜𝑏𝑗 (𝑘) 𝐿 𝑅𝑃𝑁 𝑝𝑗 (𝑘) , 𝑡𝑗 (𝑘) , 𝑝𝑗 (𝑘) , 𝑡𝑗 (𝑘) ; 𝑊𝐶𝑁𝑁, 𝑊𝑅𝑃𝑁 = 1 2 𝑗=1 𝑁 𝑏𝑎𝑡𝑐ℎ 𝐻 𝑝𝑗 (𝑘) , 𝑝𝑗 𝑘 + 𝜆 𝑅𝑃𝑁 1 𝑁𝑎𝑛𝑐 (𝑘) 𝑗=1 𝑁 𝑏𝑎𝑡𝑐ℎ 𝑝𝑗 𝑘 𝑠𝑚𝑜𝑜𝑡ℎ 𝐿1 𝑡𝑗 𝑘 , 𝑡𝑗 𝑘 where 𝐻 is the cross−entropy function and 𝑠𝑚𝑜𝑜𝑡ℎ 𝐿1 𝑥 = 0.5𝑥2 , 𝑖𝑓 𝑥 < 1 𝑥 − 0.5, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.
- 26. Training process for Classifier & Regressor Input • Image 𝑋 𝑘 Ground-truth • Bounding boxes 𝐵(𝑘) = 𝐵𝑖 𝑘 𝑖=1 𝑁 𝑜𝑏𝑗 (𝑘) where 𝐵𝑖 𝑘 = 𝑥𝑖 𝑘 , 𝑦𝑖 𝑘 , 𝑤𝑖 𝑘 , ℎ𝑖 𝑘 • Classes 𝐶(𝑘) = 𝐶𝑖 𝑘 𝑖=1 𝑁 𝑜𝑏𝑗 (𝑘) c Ground-truth Classification & Regression associated with proposals 𝑃𝑗 (𝑘) Find the nearest bounding box from each proposals 𝐵𝑖 𝑘 = argmax 𝐵∈ 𝐵(𝑘) 𝐼𝑜𝑈 𝐵, 𝑃𝑗 𝑘 • Ground-truth Classification: 𝑐𝑗 (𝑘) ≔ 𝑐𝑗,0 (𝑘) , ⋯ , 𝑐𝑗,𝑁 𝑐𝑙𝑠 (𝑘) = 1,0, ⋯ , 0 , 𝑖𝑓 𝐼𝑜𝑈 𝐵𝑖 𝑘 , 𝑃𝑗 𝑘 < 0.5 0, ⋯ 0,1,0,⋯ , 0 , 𝑜𝑡ℎ𝑒𝑟𝑠 • Ground-truth Regression: 𝑟𝑗 (𝑘) ≔ 𝑟𝑥𝑗 (𝑘) , 𝑟𝑦𝑗 (𝑘) , 𝑟𝑤𝑗 (𝑘) , 𝑟ℎ𝑗 (𝑘) where 𝑟𝑥𝑗 (𝑘) = 𝑥𝑖 𝑘 − 𝑝𝑥 𝑗 (𝑘) /𝑝𝑤𝑗 (𝑘) , 𝑟𝑦𝑗 𝑘 = 𝑦𝑖 𝑘 − 𝑝𝑦𝑗 (𝑘) /𝑝ℎ 𝑗 (𝑘) , 𝑟𝑤𝑗 (𝑘) = log 𝑤𝑖 𝑘 /𝑝𝑤𝑗 (𝑘) , 𝑟ℎ𝑗 𝑘 = log ℎ𝑖 𝑘 /𝑝ℎ 𝑗 (𝑘) 𝐶𝑖 𝑘 + 1 𝑡ℎ 𝑐𝑜𝑚𝑝𝑜𝑒𝑛𝑒𝑡 Predicted Classification & Regression • Predicted Classification: 𝑐𝑗 𝑘 = 𝑐𝑗,0 𝑘 , ⋯ , 𝑐𝑗,𝑁 𝑐𝑙𝑠 𝑘 • Predicted Regression: 𝑟𝑗 (𝑘) = r𝑥𝑗 𝑘 , r𝑦𝑗 𝑘 , r𝑤𝑗 𝑘 , rℎ𝑗 𝑘 where 𝑟𝑗 𝑘 , 𝑐𝑗 𝑘 𝑗=1 𝑁 𝑎𝑛𝑐 𝑘 = 𝐶𝑅 𝐶𝑁𝑁 𝑋 𝑘 ; 𝑊𝐶𝑁𝑁 , 𝑃 𝑘 ; 𝑊𝐶𝑅 Region Proposals associated with anchors 𝐴𝑗 (𝑘) P(𝑘) ≔ 𝑃𝑗 𝑘 , 𝑝𝑗 𝑘 𝑗=1 𝑁 𝑎𝑛𝑐 𝑘 , 𝑃𝑗 𝑘 = 𝑝𝑥 𝑗 𝑘 , 𝑝𝑦𝑗 𝑘 , 𝑝𝑤𝑗 𝑘 , 𝑝ℎ 𝑗 𝑘 where 𝑝𝑥 𝑗 𝑘 = 𝑎𝑥𝑗 (𝑘) + 𝑎𝑤𝑗 (𝑘) 𝑡𝑥𝑗 (𝑘) , 𝑝𝑦𝑗 𝑘 = 𝑎𝑦𝑗 (𝑘) + 𝑎ℎ𝑗 (𝑘) 𝑡𝑦𝑗 (𝑘) 𝑝𝑤𝑗 𝑘 = 𝑎𝑤𝑗 𝑘 exp 𝑡𝑤𝑗 (𝑘) , 𝑝ℎ 𝑗 (𝑘) = 𝑎ℎ𝑗 (𝑘) exp 𝑡ℎ𝑗 (𝑘) 𝑃(𝑘) ← 𝑁𝑀𝑆(𝑃 𝑘 , 𝑁𝑝𝑟𝑜𝑝) 𝐿 𝐶𝑅 𝑟𝑗 (𝑘) , 𝑐𝑗 (𝑘) , 𝑟𝑗 (𝑘) , 𝑐𝑗 (𝑘) ; 𝑊𝐶𝑁𝑁, 𝑊𝐶𝑅 = 𝑗=1 𝑁 𝑝𝑟𝑜𝑝 𝐻 𝑐𝑗 𝑘 , 𝑐𝑗 𝑘 + 𝜆 𝐶𝑅 𝑗=1 𝑁 𝑝𝑟𝑜𝑝 1 − 𝑐𝑗,0 𝑘 𝑠𝑚𝑜𝑜𝑡ℎ 𝐿1 𝑟𝑗 𝑘 , 𝑟𝑗 𝑘 where 𝐻 is the cross−entropy function and 𝑠𝑚𝑜𝑜𝑡ℎ 𝐿1 𝑥 = 0.5𝑥2 , 𝑖𝑓 𝑥 < 1 𝑥 − 0.5, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒.
- 27. The History of object detection in deep learning Yolo Yolo v2 SSD RCNN Fast RCNN Faster RCNN Mask RCNN DSSD 2012.12 AlexNet 2014.9 VggNet & InceptionNet 15.12.10 ResNet 2013.11.11 2015.4.30 2015.5.14 15.6.8 15.12.2515.12.08 17.1.23 17.3.20
- 28. Application to Ultrasound-based Fetal biometry
- 29. References [Gitbooks] Object Localization and Detection https://leonardoaraujosantos.gitbooks.io/artificial-inteligence/object_localization_and_detection.html [ICCV2015 Tutorial] Convolutional Feature Maps https://courses.engr.illinois.edu/ece420/sp2017/iccv2015_tutorial_convolutional_feature_maps_kaiminghe.pdf [Infographic] The Modern History of Object Recognition https://github.com/Nikasa1889/HistoryObjectRecognition [Tensorflow Code] tf-Faster-RCNN https://github.com/kevinjliang/tf-Faster-RCNN [Medium] A Brief History of CNNs in Image Segmentation: From R-CNN to Mask R-CNN https://blog.athelas.com/a-brief-history-of-cnns-in-image-segmentation-from-r-cnn-to-mask-r-cnn-34ea83205de4 [pyimagesearch] Intersection over Union (IoU) for object detection https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/ [Stanford c231n] Lecture 11: Detection and Segmentation http://cs231n.stanford.edu/slides/2017/cs231n_2017_lecture11.pdf
- 30. Thank you E-mail: hpkim0512@yonsei.ac.kr/ Hompage: https://hpkim0512.blogspot.com