GWD: rotating target detection based on Gaussian Wasserstein distance | ICML 2021

  This paper describes the main problems of rotating target detection in detail , The rotating regression target is defined as Gaussian distribution , Use Wasserstein Distance measures the distance between Gaussian distributions for training . at present , Conventional target detection also has many methods to transform regression into probability distribution function , This article has the same merits , Worth reading

The paper : Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss

• Address of thesis ：https://arxiv.org/abs/2101.11952
• Paper code ：https://github.com/yangxue0827/RotationDetection

Introduction

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  Targets with arbitrary orientation are everywhere in the detection data set , Target detection relative to horizontal , Rotating target detection is still in its infancy . at present , majority SOTA Research has focused on the rotation angle of the regression target , Solving the rotation angle brings new problems ：i) The index is inconsistent with the loss .ii) The regression interval of rotation angle is discontinuous . iii) Square problem . in fact , There is no good solution to the above problems , This will greatly affect the performance of the model , Especially when the angle is at the boundary of the range .

  In order to solve the above problems , The paper proposes that GWD Method , Firstly, a two-dimensional Gaussian distribution is used to model the rotating target , And then use Gaussian Wasserstein Distance(GWD) Instead of nondifferentiable rotation IoU, according to GWD Calculation loss value , This aligns model training with metrics .

  The main contributions of this paper are as follows ：

• Three main problems of rotating target detection are summarized .
• Use Gaussian Wasserstein Distance(GWD) Describe rotation bbox Distance between , Reuse GWD Calculate instead of IoU Lost loss, And it is differentiable .
• GWD-based Loss can solve the problem of discontinuous rotation angle range and square problem , And right bbox Is defined in a way that does not require .
• Test on multiple public datasets , The methods of the thesis have good performance .

Rotated Object Regression Detector Revisit

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Bounding Box Definition

  chart 2 Two rotations are shown bbox How to define ：OpenCV form $D{oc}$ And the long side form $D{le}$, The angle of the former is $h_{oc}$ And the abscissa $\theta\in[-90^{\circ},0^{\circ})$, The angle of the latter is the angle between the long side and the abscissa $\theta\in[-90^{\circ},90^{\circ})$, The two definitions can be transformed into each other ( Regardless of the center point )：

  The main difference between the two representations lies in the order of edges and the angle $(h,w,\theta)$, same bbox In different ways , You may need to swap the order of edges or the addition and subtraction of angles 90. In many studies nowadays , Combine the design of the model with bbox To avoid specific problems ： Such as $D{oc}$ Square problem can be avoided ,$D{le}$ The edge exchange problem can be avoided .

Inconsistency between Metric and Loss（ Inconsistency between indicators and losses ）

  IoU It is an important evaluation index in the detection field , But the regression loss function used in actual training ( Such as $l_n$-norms) There are often inconsistencies with the evaluation indicators , That is, a smaller loss value does not equal a higher performance . at present , Some measures have been taken to solve the inconsistency problem in the field of horizontal target detection , Such as DIoU and GIoU. In the field of rotating target detection , Due to the addition of angle regression , Make the problem of inconsistency more prominent , But there is still no good solution , The paper also lists some examples to compare IoU Loss and smooth L1 Loss ：

• Case 1: Relationship between angle difference and loss value , Curve geometry is monotonic , But only smooth L1 A curve is a convex curve , It can be optimized to the global optimal solution .

• Case 2: The relationship between the difference in aspect ratio and the loss value ,smooth-l1 The loss value is fixed ( Mainly from the angle difference ), and IoU The loss varies dramatically with the horizontal axis .

• Case 3: Influence of center point offset on loss value , The curves are monotonic , but smooth L1 The curve is not highly consistent with the difference .

  From the above analysis, we can see that , In the field of rotating target detection ,IoU Loss can better fill the difference between judgment criteria and regression loss . But it's a pity. , In the field of rotating target detection , Two rotations bbox Between the IoU Computation is nondifferentiable , Can't be used for training . So , This paper is based on Wasserstein distance Propose a differentiable loss to replace IoU Loss , By the way, it can also solve the discontinuous problem of rotation angle regression interval and the square problem .

Boundary Discontinuity and Square-Like Problem（ Rotation angle regression interval discontinuity and square problem ）

  The image above Case1-2 The problem of interval discontinuity of rotation angle regression is summarized , With OpenCV Formal Case 2 For example , about anchor$(0,0,70,10,-90^{\circ})$ as well as GT$(0,0,10,70,-25^{\circ})$, There are two methods of regression ：

• way1 Rotate counterclockwise for a small angle , The predicted result is $(0,0,70,10,-115^{\circ})$, But because of the periodicity of the angle (PoA) And edge order exchange (EoE), If you use smooth L1 Loss function , This result is related to GT Will produce a huge loss of value . in addition , This angle is also beyond the predetermined angle range .
• choice way2 You need to scale the width and height at the same time , Rotate clockwise by a large angle .

  The above problems usually occur in anchor and GT When the angle of is at the boundary of the angle range , When anchor and GT When the angle of is not at the boundary position ,way1 There will be no huge loss value . therefore , about smooth-L1, The optimal treatment of boundary angle and non boundary angle will be too consistent , This will also hinder the training of the model .

  The square problem mainly occurs in the detection method using the long side form , Because the square target has no absolute long side , The expression of the long side form to the square object itself is not unique . With Case3 For example , There is anchor$(0,0,45,44,0^{\circ})$ as well as GT$(0,0,45,43,-60^{\circ})$,way1 It can be rotated clockwise by a small angle to become the position and GT coincident $(0,0,45,43,30^{\circ})$. However, due to the large angle difference ,way1 There will be a higher regression loss . therefore , Need to look like way2 Then rotate it counterclockwise for a large angle . The main reason for the square problem is not mentioned above PoA and EoE, It is the inconsistency between the measurement standard and the loss calculation .

The Proposed Method

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  After the above analysis , The paper hopes that the regression loss function of the new rotating target detection method can satisfy the following points ：

• Requirement1: And IoU The metrics are highly consistent .
• Requirement2: It's very small , Allow direct learning .
• Requirement3: Smoother the boundary scene of the angle regression range .

Wasserstein Distance for Rotating Box

  At present, most IoU Loss can be considered as a function of distance , Based on this , This paper is based on Wasserstein distance A new regression loss function is proposed . First , Rotate bbox$\mathcal{B}(x,y,h,w,\theta)$ Turn into 2-D Gaussian distribution $\mathcal{N}(m,\sum)$：

  $R$ For the rotation matrix ,$S$ Is the diagonal vector of the eigenvalue . about $\mathbb{R}^n$ Any two probability measures on $\mu$ and $\upsilon$, Its Wasserstein distance $W$ It can be expressed as ：

  The formula 2 For all random vector combinations $(X,Y)\in\mathbb{R}^n\times\mathbb{R}^n,X\sim\mu,Y\sim\upsilon$ Calculate , Put in the Gaussian distribution $d:=W(\mathcal{N}(m_1,\sum_1);\mathcal{N}(m_2,\sum_2))$, Convert to get ：

  Special attention ：

  Consider the exchangeable case ( Horizontal target detection )$\sum_1\sum_2=\sum_2\sum_1$ Next , The formula 3 Convertible to ：

  $\parallel\parallel_F$ by Frobenius norm , there bbox They are all horizontal , The formula 5 Approximate to $l_2$-norm Loss , indicate Wasserstein Distance is consistent with the loss commonly used in horizontal detection tasks , Can be used to regress losses . The formula calculation here is more complicated , If you are interested, you can look at the references .

Gaussian Wasserstein Distance Regression Loss

  The paper adopts nonlinear transformation function $f$ take GWD It maps to $\frac{1}{\tau+f(d^2)}$, Get something similar to IoU Loss function ：

  The previous graph also describes the use of different nonlinear functions $f$ Loss function curve under , You can see the formula 6 Very close to IoU Loss curve , Can also measure non intersecting bbox. therefore , The formula 6 Obviously, it can satisfy Requirement1 and Requirement2, Let's start the analysis Requirement3, First give the formula 1 Characteristics of ：

  According to the characteristics 1 You know ,GWD The loss function is for OpenCV Form and long side form are equal , That is, the model does not need to fix a specific bbox Expression training . With Case2 Of Way1 For example ,GT$(0,0,70,10,65^{\circ})$ And forecasting $(0,0,70,10,-115^{\circ})$ Have the same mean $m$ And variance $\sum$,GWD The loss function does not output large loss values . And according to the characteristics 2 And characteristics 3,Case2 and Case3 Of way1 Similarly, it will not produce large loss value , therefore GWD The loss function also satisfies Requirement3.

  As a whole ,GWD The advantages of rotating target detection are as follows ：

• GWD bring bbox The different definitions of are equal , Ensure that the model can focus on improving the accuracy , There is no need to worry bbox Definition form of .
• GWD It's differentiable IoU Loss alternatives , It is highly consistent with the detection index . and ,GWD No intersection can be measured bbox Distance between , Be similar to GIoU and DIoU Characteristics of .
• GWD The problem of discontinuity and squareness in the regression interval of rotation angle is avoided , It reduces the learning difficulty of the model .

Overall Loss Function Design

  The paper will RetinaNet As a basic detector ,bbox Expressed as $(x,y,w,h,\theta)$, The experiment mainly uses OpenCV form , Regression goals are defined as ：

  Variable $x$,$x_a$,$x^{*}$ Distribution representative GT,anchor And forecast results , The final multitask loss function is ：

  $N$ by anchor Count ,$objn$ An indicator of the foreground or background ,$b_n$ For forecast bbox,$gt_n$ by GT,$t_n$ by GT The label of ,$p_n$ Label the forecast ,$\lambda_1=1$ and $\lambda_2=2$ Is a super parameter ,$L{cls}$ by focal loss.

Experiments

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  Compare other solutions to specific problems .

  stay DOTA Compare multiple models on a dataset , There are many other experiments in the paper , Those who are interested can go and have a look .

Conclusion

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  This paper describes the main problems of rotating target detection in detail , The rotating regression target is defined as Gaussian distribution , Use Wasserstein Distance measures the distance between Gaussian distributions for training . at present , Conventional target detection also has many methods to transform regression into probability distribution function , This article has the same merits , Worth reading .

Reference Content

• Wasserstein distance between two Gaussians - https://djalil.chafai.net/blog/2010/04/30/wasserstein-distance-between-two-gaussians/    undefined 

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