---
tags: 生物辨識
---
# Cross-Domain Similarity Learning for Face Recognition in Unseen Domains
In this paper, we introduce a novel crossdomain metric learning loss, which we dub Cross-Domain Triplet (CDT) loss, to improve face recognition in unseen domains.
## Contribution
We introduce an effective `Cross-Domain Triplet` loss function which utilizes explicit `similarity metrics` existing in one domain, to learn compact clusters of identities from another domain.


裡面說他這神秘的方法是借鏡
`Distribution consistency based covariance metric networks for few-shot learning (AAAI19)`

The CovaMNet is designed to exploit both the covariance representation and covariance metric based on the distribution consistency for the few-shot classification tasks.

1. As supported by theoretical insights and experimental evaluations, our CDT loss aligns distributions of two domains in a discriminative manner.
2. By leveraging a meta-framework, our network parameters are further enforced to learn generalized features under domain shift.

## Proposed Method
$f_r(\cdot , \theta_r)$: representation-learning network
$f_e(\cdot , \theta_e)$: embedding network
$f_c(\cdot , \theta_c)$: classifier network

Mahalanobis distances
$$
d_{\Sigma}=\sqrt{(x-y)^T\Sigma(x-y)}
$$
where $\Sigma$ is a positive semidefinite matrix

### Cross-Domain Triplet loss
Define $R^+=f_r(a)-f_r(p)$
$$
\Sigma^+=\frac{1}{N-1}\sum^N_{i=1}(r^+_i-\mu^+)(r^+_i-\mu^+)^T
$$
Define $R^-=f_r(a)-f_r(n)$
$$
\Sigma^-=\frac{1}{N-1}\sum^N_{i=1}(r^-_i-\mu^-)(r^-_i-\mu^-)^T
$$
$l_{cdt}(^{i}\mathbb{T}, ^{j}\mathbb{T}; \theta_r)=$
$$
\frac{1}{B}\sum^{B}_{b=1}\left[\frac{1}{HW}\sum^H_{h=1}\sum^W_{w=1}d^2_{^j\Sigma^+}\left([f_r(^ia_b)]_{h,w}, [f_r(^ip_b)]_{h, w}\right)-\\
\frac{1}{HW}\sum^H_{h=1}\sum^W_{w=1}d^2_{^j\Sigma^-}\left([f_r(^ia_b)]_{h,w}, [f_r(^in_b)]_{h, w}\right)+\tau\right]_+
$$


## 連結
[1. PAPER](https://arxiv.org/pdf/2103.07503.pdf)
[2. 唯一的中文詳解](https://www.cnblogs.com/wanghui-garcia/p/14659459.html)