论文笔记2.2：PFLD（Practical Facial Landmark Detector）算法详解

2.Methodology

Against the aforementioned challenges, effective mea

sures need to be taken. In this section, we fifirst focus on the

design of loss function, which simultaneously takes care of

Challenges #1, #2, and #3. Then, we detail our architecture.

The whole deep network consists of a backbone subnet for

predicting landmark coordinates, which specififically consid

ers Challenge #4, as well as an auxiliary one for estimating

geometric information.

为了应对以上提到的种种挑战，需要采取高效的方法。在这一部分，我们首先关注损失函数的 设计 ，同时兼顾挑战 #1 #2 #3，然后我们详述我们的结构的一些细节。整个深度学习网络由用来预测关键点坐标的主干网络组成，也同时特地考虑到了挑战#4，用来辅助计算几何信息。

2.1 损失函数

The quality of training greatly depends on the design

of loss function, especially when the scale of training data

is not suffificiently large. For penalizing errors between

ground-truth landmarks X := [x1, ..., xN ] ∈ R2×N

and

predicted ones Y := [y1, ..., yN ] ∈ R2×N , the simplest

losses arguably go to `2 and `1 losses. However, equally

measuring the differences of landmark pairs is not so wise,

without considering geometric/structural information. For

instance, given a pair of xi

and yi

with their deviation

di := xi -

yi in the image space, if two projections (poses

with respect to a camera) are applied from 3D real face to

2D image, the intrinsic distances on the real face could be

signifificantly different. Hence, integrating geometric infor

mation into penalization is helpful to mitigating this issue.

For face images, the global geometric status - 3D pose -

is suffificient to determine the manner of projection. For

mally, let X denote the concerned location of 2D land

marks, which is a projection of 3D face landmarks, i.e.

U ∈ R4×N , each column of which corresponds to a 3D

location [ui , vi , zi, 1]T . By assuming a weak perspective

model as [14], a 2 ×
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