---
tags: Human Face
---

# DeepID1 (CVPR2014)

## 特點
本篇重點為`\特徵提取/`
1. Data Augmentation
2. Feature extraction
3. Face verification
## Deep ConvNets

> `max-pooling layer3` + `conv layer 4`
> 最後需要160個神經元的輸出(DeepID)

## Feature extraction

1. 3個scale
2. 鼻頭，左右眼，左右嘴角為中心
3. 彩色圖加上灰度圖
4. 水平翻轉
$$
3scale\times10patch\times2type\times2flip=120
$$
> 水平翻轉和原圖，用同一個`Conv Net`
> 對齊是利用 facial point detection method proposed by Sun et al.
## Architecture again

## Face verification
Joint Bayesian technique for face verification based on the DeepID.
$$
x = \mu+\epsilon
$$
$\mu\sim N(0,S_\mu)$：the face identity.
$\epsilon\sim N(0,S_\epsilon)$：intra-personal variations.
and
\begin{align*}
\begin{bmatrix}
x_1 \\ x_2
\end{bmatrix}
\begin{bmatrix}
x_1^T & x_2^T
\end{bmatrix} &=
\begin{bmatrix}
\mu_1+\epsilon_1 \\ \mu_2+\epsilon_2
\end{bmatrix}
\begin{bmatrix}
(\mu_1+\epsilon_1)^T & (\mu_2+\epsilon_2)^T
\end{bmatrix} \\
&=\begin{bmatrix}
(\mu_1+\epsilon_1)(\mu_1+\epsilon_1)^T & (\mu_1+\epsilon_1)(\mu_2+\epsilon_2)^T \\
(\mu_2+\epsilon_2)(\mu_1+\epsilon_1)^T & (\mu_2+\epsilon_2)(\mu_2+\epsilon_2)^T
\end{bmatrix} \\
&= \begin{bmatrix}
\mu_1 \mu_1^T + \mu_1 \epsilon_1^T + \epsilon_1 \mu_1^T + \epsilon_1 \epsilon_1^T & \mu_1 \mu_2^T + \mu_1 \epsilon_2^T + \epsilon_1 \mu_2^T + \epsilon_1 \epsilon_2^T \\
\mu_2 \mu_1^T + \mu_2 \epsilon_1^T + \epsilon_2 \mu_1^T + \epsilon_2 \epsilon_1^T & \mu_2 \mu_2^T + \mu_2 \epsilon_2^T + \epsilon_2 \mu_2^T + \epsilon_2 \epsilon_2^T
\end{bmatrix}
\end{align*}
Hence, $P(x_1,x_2 \mid H_I)$ can be viewed as a joint probability of two pictures under intra-personal (same) variation hypothesis.
\begin{align*}
\Sigma_{I} =
\begin{bmatrix}
S_{\mu}+S_{\epsilon} & S_{\mu} \\
S_{\mu} & S_{\mu}+S_{\epsilon}
\end{bmatrix}
\end{align*}
On the other hand, both the identities and intra-person variations are independent Under $H_E$. Hence, the covariance matrix of the distribution $P (x_1, x_2 \mid H_E)$ is
\begin{align*}
\Sigma_{E} =
\begin{bmatrix}
S_{\mu}+S_{\epsilon} & 0 \\
0 & S_{\mu}+S_{\epsilon}
\end{bmatrix}
\end{align*}
With the above two conditional joint probabilities, the log likelihood ratio $r(x_1, x_2)$ can be obtained in a closed form after simple algebra operations:
$$
r(x_1, x_2) = \log \frac{P (x_1, x_2 \mid H_I)}{P (x_1, x_2 \mid H_E)}
$$

## 問題
昱睿
- 在第二篇中的 Figure2. ，他的網路架構是 `conv3 + conv4` 一起去做`fully-connected`，這有什麼特別的用意或好處嗎？還是就只是想要拿比較多 feature maps 去做`fully-connected`而已？
> This is critical to feature learning because after successive down-sampling along the cascade, the fourth convolutional layer contains too few neurons and becomes the bottleneck for information propagation.
Adding the bypassing connections between the third convolutional layer (referred to as the skipping layer) and the last hidden layer reduces the possible information loss in the fourth convolutional layer.

## 連結
[DeepID](http://mmlab.ie.cuhk.edu.hk/pdf/YiSun_CVPR14.pdf)