【Wing Loss】《Wing Loss for Robust Facial Landmark Localisation with Convolutional Neural Networks》

CVPR-2018

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1 Background and Motivation

Key points of the face , Like the tip of the nose , Eye Center , For others such as face recognition / Facial recognition / 3D Face reconstruction and other face analysis tasks provide a wealth of geometric information

The development of deep learning has also greatly improved the face key point location task in unstructured face scenes

One crucial aspect of deep learning is to define a loss function leading to better-learnt representation from underlying data.

The author analyzes different loss Effect in face key point detection task , Put forward new losses wing loss

2 Related Work

• Different regressions are analyzed loss Advantages and disadvantages , Put forward wing loss For face key point location
• Put forward pose-based data balance
• Propose a new method of face key point detection Network structure

3 Advantages / Contributions

• Network Architectures
  Go straight back to
  Forecast thermodynamic diagram

• Dealing with Pose Variations
  multiview models
  use 3D face models
  multi-task learning（ Promote each other ）

• Cascaded Networks

4 Method

1） Loss function

The loss functions commonly used in regression tasks are as follows

L1 / L2 / smooth L1

L2 loss is sensitive to outliers

smooth L1 loss yes L1 and L2 The combination of , It's also a special case of the Huber loss

come from [ Face key point detection ] Wing loss Interpretation of the thesis

By analyzing AFLW On dataset NME（Normalised Mean Error） The cumulative distribution histogram of

loss functions analysed in the last section（L1 / L2 / Smooth L1） perform well for large errors（ That is, the roughly red framed area , Large error , But the corresponding samples are relatively few ）

more attention should be paid to small and medium range errors（ It's roughly a green framed area ,NME partial medium and small, There are many samples —— The curve is steep ）

The author further analyzes

Error is $x$ Under the circumstances

L1 The magnitude of the loss gradient is 1, Optimize step size （optimal step sizes） Then for $x$, The greater the error , The more optimization times
L2 The magnitude of the loss gradient is $x$, The optimization step is 1, The greater the error , The greater the gradient

In both cases the update towards the solution will be dominated by larger errors

That is to say ,it is hard to correct relatively small displacements

The author introduces ln$x$ loss To alleviate the above L1 / L2 loss The disadvantage of being too affected by large errors ,

ln$x$ Gradient magnitude $\frac{1}{x}$, The optimization step is $x^2$, Small error when , Big gradient Small steps , Big error when , Small gradient Large step size

For large error and small error scenarios , Both gradient and step size have a good equilibrium

Considering the large initial error of face key point location task , To speed up convergence , The author introduces L1 loss（L2 Yes outline sensitive ）, The overall design is as follows

$C=w-wln(1+|w|/\epsilon )$ Constant , Ensure the smoothness of the piecewise function

$\epsilon$ It should not be set too small , According to the gradient $-\frac{w}{\epsilon +x}$ It can be seen that ,$\epsilon$ After hours , In the face of small errors , There may be a gradient explosion

2）Pose-based data balancing

In order to solve extreme pose variations

Procrustes Analysis + PAC To analyze the shape distribution of faces in the dataset

Principle comes from 《Master Opencv… Reading notes 》 Non rigid face tracking II

The distribution of projection coefficient of the training samples is represented by a histogram with K bins give the result as follows

Abscissa face angle , Number of ordinate samples

Pose-based data balancing The strategy is to put bin Face samples corresponding to relatively few positions , Repeat sampling , Make it more balanced

3） Network structure

A focus on loss And sample strategy , The design of network structure is relatively simple

Pose-based data balancing Relieved out-of-plane head rotations problem

There are other factors that affect the final face key point location

in-plane head rotations and inaccurate bounding boxes output from a poor face detector etc.

So the author cascade For a moment

The first stage CNN6, Input 64x64x3, Output keys + Refined offset of face frame ？（refine the input image for the second network by removing the in-plane head rotation and correcting the bounding box, I can't see too much information ）
The first stage CNN7, Input 128x127x3, Output keys

5 Experiments

5.1 Datasets and Metrics

AFLW：19 A little bit ,AFLW protocol The evaluation index ——NME + Face frame width
300W：68 A little bit ,NME + inter-pupil distance

5.2 Experiments

1）loss
AFLW On dataset , Different loss Comparison

Explore the next wing loss in $w$ and $\epsilon$ Setting of super parameters

2）Pose-based data balancing Strategy

Even if CNN coordination L1 and L2 loss, Also super fierce , explain Pose-based data balancing The strategy is very effective

300W

3）Run time and network architectures

6 Conclusion（own） / Future work

• CNN6 What is the output of , Ha ha ha ！ I have to check the code

• wing loss, chart 4 Is the core source of inspiration
  

• Pose-based data balancing

• Angle definition ：
  
  The picture is from How to rotate the face in the image ？ | CVPR 2018

• in-plane / out-of-plane, Quote the following two answers

  It should be that stress or deformation occurs in a xoy In the plane , Call in-plane, Yes z The component force or displacement of the direction is called out-of-plane

  Deformation is relative to a plane , There are some deformations in this plane , Some deformations are out of plane deformations , That's the corresponding in-plane and out-of-plane

• Learn others' understanding