Face verification techniques: how to speed up dataset creation
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This document discusses triplet loss and embedding networks for image similarity. It proposes training an embedding network to map similar images closer together and dissimilar images farther apart in the embedded space. The network is trained using triplet loss, which minimizes the distance between an anchor and positive image (from the same class) while maximizing the distance between the anchor and a negative image (from a different class). Hard negative mining is used to select negative examples that violate the margin criterion. The network and loss function are differentiated to calculate gradients and update weights to learn embeddings that better satisfy the similarity and dissimilarity criteria.
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Face verification techniques: how to speed up dataset creation
- 15. • • • • •
- 16. • Complete freedom to chose 𝐺 𝑤 𝑋 (vgg, resnet, ecc) • 𝐸 𝑤(𝑋1, 𝑋2) = | 𝐺 𝑤 𝑋1 − 𝐺 𝑤 𝑋2 | • 𝐸 𝑤(𝑋1, 𝑋2) = 𝐸 𝑤(𝑋2, 𝑋1) • Objective: given a family of functions 𝐺 𝑤 𝑋 parameterized by 𝑊 and the similarity metric 𝐸 𝑤 𝑋1, 𝑋2 . The objective is to minimize 𝐸 𝑤 when 𝑋1 𝑎𝑛𝑑 𝑋2 are from the same category and maximize 𝐸 𝑤 when 𝑋1 𝑎𝑛𝑑 𝑋2 belong to different category.
- 17. • 𝐸 𝑤(𝑋1, 𝑋2) = | 𝐺 𝑤 𝑋1 − 𝐺 𝑤 𝑋2 | • 𝐸 𝑤 𝑔 𝑋1 𝑎𝑛𝑑 𝑋2 𝐸 𝑤 𝑖 • ∃𝑚 > 0, 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝐸 𝑤 𝑔 + 𝑚 < 𝐸 𝑤 𝑖 •
- 18. • • 𝐿 𝑋1, 𝑋2 = 1 − 𝑌 1 2 𝐸 𝑤 2 + 𝑌 1 2 {max(0, 𝑚 − 𝐸 𝑤)}2 𝐿 𝑋1, 𝑋2 = 1 2 {max(0, 𝑚 − 𝐸 𝑤)}2 𝑖𝑓 𝑋1, 𝑋2 𝑛𝑜𝑡 𝑏𝑒𝑙𝑜𝑛𝑔 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦 1 2 𝐸 𝑤 2 𝑖𝑓 𝑋1, 𝑋2 𝑏𝑒𝑙𝑜𝑛𝑔 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑐𝑎𝑡𝑒𝑔𝑜𝑟𝑦
- 19. • • • • •
- 20. ||𝑓 𝑥 ||2 = 1 𝑋 𝑎 𝑋 𝑝 𝑋 𝑛
- 21. • 𝑥 𝑎 𝑥 𝑝 𝑥 𝑛 • 𝑥 ℝ 𝑑 a p n a p n TRAINING
- 22. • 𝑇, ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑝 ||2 2 + 𝛼 < ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑛 ||2 2 • σ𝒊 𝑵 [ ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑝 ||2 2 − ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑛 ||2 2 + 𝛼]+ • 𝛼 𝛼 𝛼 𝑓 𝑥𝑖 𝑎 𝑓 𝑥𝑖 𝑛 𝑓 𝑥𝑖 𝑝
- 24. {𝑥𝑖 𝑎 , 𝑥𝑖 𝑝 , 𝑥𝑖 𝑛 }𝑖 {𝑓(𝑥𝑖 𝑎 ), 𝑓(𝑥𝑖 𝑝 ) 𝑓 (𝑥𝑖 𝑛 )}𝑖 𝐿′ = 𝜕𝐿 𝜕𝑓(𝑥 𝑖 𝑎) = 2 𝑓(𝑥𝑖 𝑛 − 𝑓(𝑥𝑖 𝑝 )) 𝑖𝑓 ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑝 ||2 2 − ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑛 ||2 2 + 𝛼 > 0 𝜕𝐿 𝜕𝑓(𝑥 𝑖 𝑝 ) = 2 𝑓(𝑥𝑖 𝑝 − 𝑓(𝑥𝑖 𝑎 )) 𝑖𝑓 ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑝 ||2 2 − ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑛 ||2 2 + 𝛼 > 0 𝜕𝐿 𝜕𝑓(𝑥 𝑖 𝑛) = 2 𝑓(𝑥𝑖 𝑎 − 𝑓(𝑥𝑖 𝑛 )) 𝑖𝑓 ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑝 ||2 2 − ||𝑓 𝑥𝑖 𝑎 − 𝑓 𝑥𝑖 𝑛 ||2 2 + 𝛼 > 0
- 25. {𝐹𝑛 𝑖, 𝑊𝑛 𝑖} 𝑛 𝑖 𝜕𝐿 𝜕𝐹𝑛 𝑖 𝜕𝐿 𝜕𝐹𝑛 𝑖 × 𝜕𝐹𝑛 𝑖 𝜕𝐹𝑛−1 𝑖 … Triplet Loss 𝐿𝑎𝑦𝑒𝑟𝑛 𝐿𝑎𝑦𝑒𝑟𝑛−1 𝑊𝑛 𝑖 = 𝑊𝑛 𝑖 − μ 𝜕𝐿 𝜕𝐹𝑛 𝑖 × 𝜕𝐹𝑛 𝑖 𝜕𝑊𝑛 𝑖 = 𝑊𝑛 𝑖 − μ 𝜕𝐿 𝜕𝐹(𝑋 𝑎) 𝑛 𝑖 × 𝜕𝐹(𝑋 𝑎) 𝑛 𝑖 𝜕𝑊𝑛 𝑖 + 𝜕𝐿 𝜕𝐹(𝑋 𝑝) 𝑛 𝑖 × 𝜕𝐹(𝑋 𝑝) 𝑛 𝑖 𝜕𝑊𝑛 𝑖 + 𝜕𝐿 𝜕𝐹(𝑋 𝑛) 𝑛 𝑖 × 𝜕𝐹(𝑋 𝑛) 𝑛 𝑖 𝜕𝑊𝑛 𝑖