---
tags: Human Face
---
# FaceNet 人臉識別 (CVPR2015)
Paper : FaceNet: A Unified Embedding for Face Recognition and Clustering
> In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity.

## Contribution
1. 使用CNN提取Face Emedding, 並直接對Face Emedding做優化
2. 提出triplet loss

## Architecture

## Triplet loss
- The embedding is represented by $f(x)\in R^{d}$. It embeds an image $x$ into a $d$-dimensional Euclidean space, and $||f(x)||^2_{2}=1$.
- $x^{a}_i:$image of anchor, $x^{p}_i:$image of positive, $x^{n}_i:$image of negative
- objective: $$
||f(x^{a}_i)-f(x^{p}_i)||^2_{2}+m \leq ||f(x^{a}_i)-f(x^{n}_i)||^2_{2}
$$
- loss function:$$
\sum_{i}{||f(x^{a}_i)-f(x^{p}_i)||^2_{2}- ||f(x^{a}_i)-f(x^{n}_i)||^2_{2}+m}$$
- triplet selection:
- 目的：若窮舉所有的triplet，triplet的數量是非常大的。舉例來說，在一個1000個人的資料集，每人有100張圖片的情況下，triplet數量會有 $1000*100*99*100*999$ 個。
- Solution：
- 在每個mini-batch選擇anchor positive pair和anchor negative pair，並在每個mini-batch從資料集抽取40個人，並從每個人抽取40張圖片，再抽取非40人中的圖片200張，總共1800張圖片當作一個mini-batch。
- 在mini-batch中挑選所有的anchor positive pair，並選擇相對於每個anchor最為困難的anchor negative pair(離anchor embedding距離最遠的negative embedding)，triplet數量為 $40*40*39$ 個。
- 但因為一直使用最困難的anchor negative pair，會導致model收斂到local minimum， 所以在選擇anchor negative pair會多一個條件， 並稱為為semi hard。
$$
||f(x^{a}_i)-f(x^{p}_i)||^2_{2} \leq ||f(x^{a}_i)-f(x^{n}_i)||^2_{2}
$$
## Experiment
- Evaluation method (face verification task)
- All faces pairs $(i, j)$ of the same identity are denoted with $P_{same}$, whereas all pairs of different identities are denoted with $P_{diff}$.
- true accepts : $TA(d)=\{(i,j)\in P_{same}|D(x_{i}, x_{j})\lt d\}$
- false accepts : $FA(d)=\{(i,j)\in P_{diff}|D(x_{i}, x_{j})\lt d\}$
- validation rate : $VAL(d)=|TA(d)|/|P_{same}|$
- false accept rate : $FAR(d)=|FP(d)|/|P_{diff}|$
- $VAL@10^{-3}FAR$ : $VAL(d_{FAR})$ with $d_{FAR}=FAR^{-1}(10^{-3})$

- Network Architectures choose

| architecture | $VAL@10^{-3}FAR$ | FLOPS |
| ----------------------------- |:----------------:|:-----:|
| NN1 (Zeiler&Fergus 220×220) | 87.9% | 1.6B |
| NN2 (Inception 224×224) | 89.4% | 1.6B |
| NN3 (Inception 160×160) | 88.3% | 500M |
| NN4 (Inception 96×96) | 82.0% | 285M |
| NNS1 (mini Inception 165×165) | 82.4% | 220M |
| NNS2 (tiny Inception 140×116) | 51.9% | 20M |

- Image quality
- Embedding Dimensionality
- Trainin data amount

## Reference
code : [link](https://github.com/davidsandberg/facenet)
paper : [link](https://arxiv.org/pdf/1503.03832.pdf)