The KFIoU Loss for Rotated Object Detection
Authors: Xue Yang
Yue Zhou
Gefan Zhang
Jirui Yang
Wentao Wang
Junchi Yan
XIAOPENG ZHANG
Qi Tian
Venue: ICLR 2023 poster (2023)
Keywords: Rotation Detection
SkewIoU loss
Kalman Filter

Abstract: Differing from the well-developed horizontal object detection area whereby the computing-friendly IoU based loss is readily adopted and well fits with the detection metrics, rotation detectors often involve a more complicated loss based on SkewIoU which is unfriendly to gradient-based training. In this paper, we propose an effective approximate SkewIoU loss based on Gaussian modeling and Gaussian product, which mainly consists of two items. The first term is a scale-insensitive center point loss, which is used to quickly narrow the distance between the center points of the two bounding boxes. In the distance-independent second term, the product of the Gaussian distributions is adopted to inherently mimic the mechanism of SkewIoU by its definition, and show its alignment with the SkewIoU loss at trend-level within a certain distance (i.e. within 9 pixels). This is in contrast to recent Gaussian modeling based rotation detectors e.g. GWD loss and KLD loss that involve a human-specified distribution distance metric which require additional hyperparameter tuning that vary across datasets and detectors. The resulting new loss called KFIoU loss is easier to implement and works better compared with exact SkewIoU loss, thanks to its full differentiability and ability to handle the non-overlapping cases. We further extend our technique to the 3-D case which also suffers from the same issues as 2-D. Extensive results on various datasets with different base detectors show the effectiveness of our approach. 

Published as a conference paper at ICLR 2023
THE KFIOU LOSS FOR ROTATED OBJECT DETECTION
Xue Yang', Yue Zhou', Gefan ? Jirui Yang', Wentao Wang', Junchi Yan Xiaopeng Zhang Qi Tian'
Moo Key Lab of Artificial Intelligence, Shanghai Jiao Tong University
#COWAROBOT Co. Ltd. Unniversity of Chinese Academy of Sciences 'Huawei Cloud (rangxue-2019-sjpe
wwt117, yan yanjuuchh }es jes.ueuuu on
(thangxiacpeng122 Jittor Code: https://github: wttp://ttt///t//////o//
hwll@hhawweicccmm com
PyTorch Code: https://githnn com/ open-mmlabammntttaae
TenscrFlow Code: https: htrps://gtie thub. hww.:/aannnueel3///oocacclleeeee http///tttttiooeeettttt.
ABSTRACT
Differing from the well-developed horizontal object detection area whereby the caaputing-frienddl IoU based loss is readily adopted and well fits with the de- tection metrics, rotation detectors often involve more complicated loss based on SkewloU which unfriendly gradient-based training. In this paper, we propose effective approximate SkewloU loss based on Gaussian modeling and Gaussian product, which mainly consists of two items. The first term a scale-insensitive center point loss, which is used to quickly narrow the distance between the center points of the two bounding boxes. the distance-independent second term, the product of the Gaussian distributions is adopted to inherently mimic the mech- anism of SkewloU by its definition, and show its alignment with the SkewloU loss at trend-level within certain distance (i.e. within 9 pixels). This is in con- trast to recent Gaussian modeling based rotation detectors e.g. GWD loss and KLDD loss that involve human-specified distribution distance metric which re- quire additional hyperparameter tuning that vary across datasets and detectors. The resulting new loss called KFIoU loss is easier implement and works better compared with exact SkewloU loss, thanks to its full differentiability and ability handle the con-ovealap cases. We further extend our technique to the 3-D case which also suffers from the same issues as 2-D. Extensive results on various datasets with different base detectors show the effectiveness our approach.
INTRODUCTION
Rotated object detection is a relatively emerging but challenging area, due to the difficulties of locating the arbitrary-oriented objects and separating them effectively from the background, such as aerial images (Yang et al., 2018a; Ding et al., 2019; Yang et al., 2018b), scene text (Jiang al., 2017; Zhou et al., 2017). Though considerable progresses have been recently made, for practical settings, there still exist challenges for rotating objects with large aspect ratio, dense distribution.
The Skew Intersection over Union (SkewloU) between large aspect ratio objects is sensitive to the deviations of the object positions. This causes the negative impact of the inconsistency be- tween metric (dominated by SkewloU) and regression loss (e.g. 4n-norms), which is common in horizontal detection, and is further amplified in rotation detection. The red and orange arrows in Fig. 1 show the inconsistency between SkewloU and Smooth LI Loss. Specifically, when the angle deviation is fixed (red arrow), SkewloU will decrease sharply as the aspect ratio increases, while the Smooth L1 loss is unchanged (mainly from the angle difference). Similarly, when SkewloU does not change (orange arrow), Smooth I.1 loss increases as the angle deviation increases.
"Correspondence author is Junchi Yan who is also affiliated with Shanghai AI Laboratory. The work was partly done when the first author Xue Yang intern at Huawei Cloud. The work was also in part supported by NSFC (62222607), Shanghai Municipal Science and Technology Major Project (2211S22)220002,,,

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Published as a conference paper at ICLR 2023
Solution for inconsistency between the metric and regression loss has been extensively dis- cussed in horizontal detection by using IoU loss and related variants, such as GloU loss (Rezatofighi al., 2019) and DIoU loss (Zheng et al., 2020b). However, the applications of these solutions to rotation detection are blocked be- cause the analytical solution of the SkewloU cal- culation process' is not easy to be provided due to the complexity of intersection between two ro- tated boxes (Zhou et al., 2019). Especially, there exist some custom operations (intersection of two edges and sorting the vertexes etc.) whose deriva- tive functions have not been implemented in the existing deep learning frameworks (Abadi et al., 2016; Paszke et al., 2017; Hu et al., 2020). Be- sides, the calculation of SkewloU is not differen- tiable when there are more than eight intersection points between two bounding boxes, i.e. two boundary boxes are completely coincident, or one edge is coincident, which will lead to the failure to obtain very accurate prediction results. Thus. developing an -syplee-mm and fully differ- entiable approximate SkewloU loss is meaningful and several works (Chen et al., 2020; Zheng et al., 2020a; Yang et al., 2021e;d) have been proposed.
ShewtoU
SawdeJ contart
o2e e
-appect Ratro-15
Appocct Ratlo-d27
-Appuct -Appcc Ratioo1
Figure 1: For rotation detection (Yang et al,, 2021b), there is a notable inconsistency between the final detection metric i.c. mAP (largely de- pending on SkewloU) and regression-basee -based loss e.g. the popular Smooth LI. See Fig. 3(a) and Fig. 3(b) for more specific comparison.
This paper aims to find an easy-to-implement and better-performing alternative. We design an al- ternative to SkewloU loss based on Gaussian product, named KFIoU loss", which can be easily implemented by the existing operations of the deep learning framework without the need for ad- ditional acceleration (e.g. C++CUUDA). Specifically, we convert the rotated bounding box into Gaussian distribution, which can avoid the well-known boundary discontinuity and square-like problems (Yang et al., 2021c) in rotation detection. Then we use a center point loss to narrow the distance between the center of the two Gaussian distributions, follow by calculating the overlap area under the new position through the product of the Gaussian distributions. By calculating the error variance and comparing the final performance of different methods, we find trend-level alignment with the SkewloU loss is critical for solving the inconsistency between metric and loss, and further improving the performance. Furthermore, compared to best-tuned Gaussian distance metric based methods, our proposed method achieves more competitive performance without hyperparameter tuning. The highlights are as follows:
1) For rotation detection, instead of exactly computing the SkewloU loss which is tedious and unfriendly to differentiable learning, we propose our easy-to-implemen approximate loss, named KFloU loss, which works better since it is fully differentiable and able to handle the non-overlapping cases. It follows the protocol of Gaussian modeling for objects, yet innovatively uses Gaussian prod- uct to mimic SkewloU's computing mechanism within looser distance.
2) Compared to Gaussian-based losses (GWD loss, KL.D loss) that try to approximate SkewloU loss by specifying a distance which need extra hyperparameters tuning and metric selection that vary across datasets and detectors, our mechanism level simulation to SkewloU is more interpretable and natural, and free from hyperparameter tuning.
3) We also show that KFIoU loss achieves the better trend-level alignment with SkewloU loss within certain distance than GWD loss and KLD loss, where the trend deviation is measured by our devised error variance. The effectiveness of such a trend-level alignment strategy is verified by comparing KFloU loss with ideal SkewloU loss. On extensive benchmarks (aerial images, scene texts, face), our approach also outperforms other best-tuned SOTA alternatives.
4) We further extend the Gaussian modeling and KFIoU loss from 2-D 3-D rotation detection, with notable improvement compared with baselines. To our best knowledge, this is the first 3- D rotation detector based on Gaussian modeling which also verifies its effectiveness, which is in
See an open-source version with thousands of lines of code for implementing the loss at https // git siu. com/ hee///pennnee mm1 almmm/v//////////mmm/////m// /mc//////////// ppt///ll1111111 118844, while our new loss only costs tens of lines of code. we term our loss as KFloU as the product of Gaussian is an important step in Kalman filtering.
2

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Published as a conference paper at ICLR 2023
contrast to (Yang al., 2021c;d; 2022) focusing 2-D rotation detection. The source code is available at TensoFlow (Abadi et al., 2016)- AlphaRotate (Yang et al., 2021c), PyTorch (Paszke et al., 2017)-based MMRotate (Zhou et al., 2022) and Jittor (Hu et al., 2020)-22000ae 2220-bbaedd JDet.
RELATED WORK
Rotated Object Detection. Rotated object detection is an emerging direction, which attempts to extend classical horizontal detectors (Girshick, 2015; Ren et al., 2015; Lin et al., 201 7a;b) to the rotation case by adopting the rotated bounding boxes. Aerial images and scene text popular application scenarios of rotation detector. For aerial images, objects are often arbitrary-oricnted and dense-distributed with large aspect ratios. To this end, ICN (Azimi al., 2018), ROI-Transformer (Ding et al., 2019), SCRDet (Yang et al., 2019), Mask OBB (Wang et al., 2019), Gliding Vertex (Xu al., 2020), ReDet (Han et al., 2021b) are two-stage mainstreamed approaches whose pipeline is inherited from Faster RCNN (Ren et al., 2015), while DRN (Pan et al., 2020), DAL (Ming et al., 2021b), Det (Yang et al., 2021b), RSDet (Qian al., 1a;b) and S A-Net (Han al., 2021a) are based on single-stage methods for faster detection speed. For scene text detection, RRPN (Ma et al., 2018) employs rotated RPN to generate rotated proposals and further perform rotated bounding box regression. TexiBoxes++ (Liao et al., 2018a) adopts vertex regression SSD (Liu et al., 2016). RRD (Liao et al., 2018b) improves TextBoxes++ by decoupling classification and bounding box regression iiaation-invariatt and rotation sensitive features, respectively. The regression loss of the above algorithms is rarely SkewloU loss due to the complexity of implementing SkewloU.
Variants of loU-based Loss. The inconsistency between metric and regression loss is common is- sue for both horizontal detection and rotation detection. Solution for this inconsistency has been ex- tensively discussed in horizontal detection by using IoU related loss. For instance, Unitbox (Yu al., 2016) proposes an IoU loss which regresses the four bounds of a predicted box as a whole unit. More works (Rezatofighi al., 2019; Zheng et al., 2020b) extend the idea of Unitbox by introducing GloU (Rezatofighi et al., 2019) and DIoU (Zheng et al., 2020b) for bounding box regression. However, their applications rotation detection blocked due the hard-to- toidd--tm-lleeentt SkewloU. Recently, some approximate methods for SoU loss have been proposed. Box/Polygon based: SCRDet (Yang al., 2019) propose IoU-Smooth I.1, which partly circumvents the need SkewloU loss with gradient backpropagation by combining loU and Smooth I.1 loss. To tackle the uncertainty of convex caused by rotation, the work (Zheng et al., 2020a) proposes a projection operation to estimate the intersection area for both 2-D/3-D object detection. PolarMask (Xie et al., 2020) proposes Polar IoU loss that can largely ease the optimization and considerably improve the accuracy. CFA (Guo et al., 2021) proposes convex hull based CloU loss for optimization of point based detectors. Pixel based: PloU (Chen et al., 2020) calculates the SkewloU directly by accumulating the contribution of interior overlapping pixels. Gaussian based: GWD (Yang al., 2021c) and KLD (Yang al., 2021d) simulate SkewloU by Gaussian distance measurement.
3
This section presents the preliminary according to (Yang et al., 2021c), for how to convert an arbitrary-oriented 2-D/3-D bounding box Gaussian distribution Gp,, E).
RAR P = (a. v. (=))
where R. represents the rotation matrix, and A represents the diagonal matrix of eigenvalues.
Take 3-D object (xa y, z, w. h, f) as an example:
cos 0 sin
u
0
0
R
sin
cos
A
0
h2
0
(2)
0
0
0
[2
is worth noting that the recent works GWD loss (Yang et al., 2021c) and KLD loss (Yang et al., 2021d) also belong to the Gaussian modeling based. Compared with our work, their difference is that they use the nonlinear transformation distribution distance to approximate SkewloU loss. In this process, additional hyperparameters introduced, Since Gaussian modeling has the natural
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Published as a conference paper at ICLR 2023
Table 1: Comparison of the properties and performance of different regression losses. Base model is RetinaNet. BC and HP denote Boundary Continuity and Hyperparameter. indicates that the first term of KLD is taken as the center point loss, i.c. Lo( 12, E1).
Loss
Representation
Implement
BC
Consistency
HP
EVart
DOTA-vL0
DOTA-vI.
DOTA-12.0
Boox
casy
x
(T))
plain Skewloll
bbax
hand
58.27
59.01
45.87
GWD
Gaussian
(..))
0.019041297
68.93
60.03
46.65
KLD
Gaussian
casy
(T.f)
KFloU (ours)
Goussian
casy
x
0.002348355
70.64
62.71
48.04
KFloU"
Gaussian
eacy
0.002264243
71.60
63.75
48.94
B0.X, 8)
M(e.2)
Melou
Nulu
M
My Kn)
N,
== RAR
(1,9)"
R
A
(cose
1//4
-Sins
0
Kelli Ra)
Σ 400000 (07o)
an 3) My (it (,
K H.
KPNN
Anriy (aa) Aeroy Ca) (
Acroy
Aeria (2)
Lay Rg) - 1 KFfol!
(4) Convest the basasding bus to
(6) Namnow lhe easte distanne by warke
(v) Clz, the Chumssia distriuation of the: overlapping area by Gaussian product
(d) Invest Classiaa diat butiion to bibua lu colculate approsimate Skrafou and less
Goussian distribution
point loss
SkewloUJ loss approximation process in two-dimensional space based Gaussian prod- uct. Compared with GWD loss (Yang et al., 2021c) and KLD loss (Yang et al., 2021d), our approach follows the calculation process of SkewloU without introducing additional hyperparameters. We be- lieve such a design is more mathematically rigorous and more in line with SkewloU loss.
Figure 2:
advantages of being immune to boundary discontinuity and square-like problems, in this paper, we will take another perspective approximate the SkewloU loss better train the detector without any extra hyperparameter, which can be more in line with SkewloU calculation. Tab. shows the comparison of properties between different losses. It should be noted that the results presented in our experiments of GWD loss and KLD loss are obtained by best-tuned hyperparameters in DOTA, but not optimal in others.
PROPOSED METHOD
In this section, present main approach. Fig. 2 shows the approximate process of SkewloU loss in two-dimensional space based on Gaussian product. Briefly, we first convert the bounding box Gaussian distribution discussed in Sec. 3, and move the center points of the two Gaussian distributions to make them close. Then, the distribution function of the overlapping area is obtained by Gaussian product. Finally, the obtained distribution function is inverted into a rotated bounding box to calculate the overlapping area and the SkewloU and loss.
4.1 SKEWIOU BASED ON GAUSSIAN PRODUCT
First of all, we can easily calculate the volume of the corresponding rotating box based on its co- variance (VxEE)) when obtain new Gaussian distribution:
V=(E) = 2" 'II
III eig(E) 2"
2"
Σ
(3)
where n denotes the number of dimensions.
To obtain the final SkewloU, calculating the area of overlap is critical. For two Gaussian distri- butions, Nxx (x Σ1) and N2 Σz), we use the product of the Gaussian distributions to get the distribution function of the overlapping area:
aN Σ) = -Ne(11 Nx)as(pa Ex)
(4)
Note here is written by:
NN (Ma, Ei Ex)
(5)
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Published as a conference paper at ICLR 2023
18
Approxómate Skowrou Loss 82
3.
1.4
12
0.8
08
20
63
Angle difference
Aspeect
1-iou
-t-smooth
1-lou
SkewloU
-- Iif
1 1-1/--gtt
11 Lgwed ULd
LMfoouee
(a) Angle difference case.
(b) Aspect ratio case.
(c) Regardless of the case.
Figure 3: Behavior comparison of different losses in different cases. (a) depicts the relation between angle difference and loss functions. (b) shows the changes of the five loss under different aspect ratio condition. (c) gives seatter plot between approximate losses and SkewloU loss, 1,000 examples regardless of the case by randomly generating box pairs with the close centers (within 5 pixels).
where μ = + K( - -1). = - KE and K is the Kalman gain, K = E
(Σ, E2) -
We observe that E is only related the covariance (E, and Σ2) of the given two Gaussian dis- tributions, which means that no matter how the two Gaussian distributions move, as long as the covariance is fixed, the area calculated by Eq. 3 will not change (distance-indepenndnn)) This is obviously not in line with intuition: the overlapping area should be reduced when the two Gaussian distributions are far away. The main reason is (N Σ) is not a standard Gaussian distribution (probability sum is not 1), we cannot directly use Σ to calculate the area of the current overlap by Eq. without considering a. Eq. shows that a related the distance between the center points (11 (22) of the two Gaussian distributions. Based the above findings, we can first use a center point loss Le to narrow the distance between the center of the two Gaussian distributions. In this way, can be approximated as a constant, and the introduction of the Le also allows the entire loss to continue to optimize the detector in non-overlapping cases. Then, calculate the overlap area under the new position by Eq. 3. According to Fig. 2. overlap area is calculated as follows:
V8, )
KFIoU=
(6)
VE, (Ei) + Vs, Σg)
Vs3 (E)
where B,, B2 and B3 refer to the three different bounding boxes shown in the right part of Fig. 2. In the appendix, we prove that the upper bounds of KFloU in n-dimensional space 2 For 2-D/3-D detection, the upper bounds are 1/ and 7/2-1 respectively when n 2 and n 3. We can easily stretch the range of KFIoU to [0, 1] by linear transformation according to the upper bound, and then compare it with IoU for consistency.
-
Fig. 3(a)-3(b) show the curves of five loss forms for two bounding boxes with the same center in different cases. Note that we have expanded KFIoU by 3 times so that its value range is [0, 1] like SkewloU. Fig. 3(a) depicts the relation between angle difference and loss functions. Though they all bear monotonicity. obviously the Smooth L1 loss curve more distinctive. Fig. 3(b) shows the changes of the five loss under different aspect ratio conditions. It can be seen that the Smooth L1 loss of the two bounding boxes are constant (mainly from the angle difference), but other losses will change drastically can maintain the best trend-level alignment with the SkewloU loss within pixels devariation. This conclusion still holds at pixels, which is already quite distance, especially for acrial image.
the aspect ratio varies. Regardless of the case in Fig. 3(c), KFIoU loss
To further explore the behavior of different approximate SkewloU losses, we design the metrics of error mean (EMean) and error variance (EVar) as follows:
1 N
1 N
EMean
[SkelloUptao SkewloUapp),
EVar
(SkewloU.ap - EMean)*
where EVar measures the trend-level consistency between the designed loss and the SkewloU loss.
Tab. calculates the EVar of different losses in Fig. 3(c). In general, EVar fiom < &EVar < EVar, Lyed < EVar,, In our analysis, this is probably due to the fundamental inconsistency between
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Published as a conference paper at ICLR 2023
the distribution distance used in GWD/KLD and the definition of similarity in SkewloU. More- over, for GWD such inconsistency is more pronouced, because it has no scale invariance under the same IoU, and case with a larger scale will get larger loss value, it greatly magnify its trend inconsistency with SkewloU loss. The results in Tab. also verifies our analysis. In contrast, the calculation process of KFIoU loss is essentially the calculation of the overlap rate, so it does not require hyperparameters and can maintain a high trend-level consistency with SkewloU loss.
Combined with the corresponding performance on three datasets, smaller EVars tend to have better performance in a general level. When EVar is small enough, which implies sufficient consistency, the performance difference of different methods (e.g. KLD loss and KFIoU loss) is close. Therefore, we come to the conclusion that the key to maintaining the consistency between metric and regres- sion loss lies in the trend-level consistency between approximate and exact SkewloU loss rather than value-level consistency. The reason why the ceuussian-based losses (e.g. KFIoU loss, KLD loss, GWD loss) outperform the plain SkewloU loss is due to the advanced parameter optimization mechanism, effective measurement for non-overlapping cases, and complete derivation. However, the introduction of hyperparameters makes KLD loss and GWD loss less stable than KFIoU loss in terms of Evar and performance. Compared with GWD and KLD, which use the distribution dis- tance to approximate SkewloU, KFIoU is physically more reasonable (in line with the calculation process of SkewloU) and simpler, well as empirically more effective than best-tuned GWD and KLD. In addition, KFIoU implementation is much simpler than plain SkewloU and can be easily implemented by the existing operations of the deep learning framework.
4.2 THE PROPOSED KFIOU LOss
We take 2-D object detection as the main example for notation brevity, though our experiments further cover the 3-D case. We use the one-stage detector RetinaNet (Lin et al., 2017b) as the baseline. Rotated rectangle is represented by five parameters (x, y, w, h, 0). First, we shall clarify that the network has not changed the output of the original regression branch, that is, it is not directly predicting the parameters of the Gaussian distribution. The whole training process of detector is summarized as follows: i) predict offset (t", ty typ. tg): ii) decode prediction box; iii) convert prediction box and target ground-truth into Gaussian distribution; iv) calculate Lg and L of two Gaussian distributions. Therefore, the inference time remains unchanged. The regression equation of (x, y, w. h)) is as follows:
tg = (x xa)/wa Wai fy =y Vlayyaaahha tw = (oo((w//w))) //wa), where x, y, w, denote the box's center coordinates, width and height, respectively. I, Fa. x= are for ground-truth box, anchor box, and predicted box (likewise for y, w. h).
tn = =lo(hhhh/
(8)
= (z x.)/wa. wa to --ly'-ua//h =
t7 log(hh//
For the regression of 6, we use two forms as the baselines:
i) Direct regression, marked Reg. (A0). The model directly predicts the angle offset tō:
to (0 - 0.) =/180, fp = (0" 100-0,1 0a) . 7/180
(9)
ii) Indirect regression, marked Reg." (sin cos 0). The model predicts two vectors (t and foos g) to match the two targets from the ground truth (fsin and f 0):
fun = sin (0 x/ x/180), teos = cos (0- 1...//// 7/180), tine = sin (8" π 180), ti = cos (0* π -/180)
(10)
To ensure that 4im 2
1 is satisfied, we will perform the following normalization processing:
t
t
ti
tcem
(11)
+ 122
The multi-task loss is:
Liotat A
Npos
Leeg (S((o)).(((t))
A
Σ
N
Lots (en, bn)
(12)
where N and Npns indicates the number of all anchors and that of positive anchors. b, denotes the n-th predicted bounding box, gln, is the n-th target ground-truth. g(-) is Gaussian transfer function.

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Published as a conference paper at ICLR 2023
Table 2: Ablation study on various 2-D datasets with different base detectors. 'R', 'F' and 'G' indicate random rotation, flipping, and graying. indicates that the first term of KLD is taken as the center point loss, i.c. Lo p2; E1). Base detector RetinaNet.
Dataset
Data Aug.
Reg, Loss
Hmean/APso
Hmean/APao 74.74
Hmean/APss 48.42
Hmean/APa:
Hmean/APiia
HRSC2016
R+F+G
Smooth L1
84.28
12.56
47.76
KFloL
(+0.3)
82.23 (+7.49)
58.32 (+9,90)
18.34 (+5.78
51.29 (+3.53)
Smooth 1.1
70.98
62.42
36.73
12.56
37.89
MSRA-TDSO0
R+F
KFloU
76.30 (+5.32)
(+7.42)
47.58 (+10.85)
19.21 (+665)
44.96 (+7.07)
ICDAR2015
Smooth L.T
69.78
64.15
36.97
8.71
37.73
KFloU
(46.12)
69.28 (45.13)
40.03 (+3.66)
9.18 (40.47)
41.17 (43.44)
Smooth LI
95.92
87,50
55.81
12.67
52.77
FDDB
KFloU
97.25 (+1.3))
94.89 (+7.39)
77.38 (+21.57)
25.62 (+12.93)
63.25 (+10.48)
Smooth L.
65.00
57.84
33.68
11.39
35.16
DOTA-vI.0
KFloU:
67.68 (+2.68)
62.18 (44.34)
37.30 (+3.62)
14.21 (+2.82)
38.51 (43.35)
KFloU
68.23 (43.23)
63.23 (45.39)
38.34 (+4.66)
13.72 (+2.33)
38.80 (43.64)
in represents the label of the n-th object, Pn is the n-th probability distribution of classes calculated
by sigmoid function. λ1. X2 control the trade-off and are set to {0.01, 1}. The classification loss Leie is set as the focal loss (Lin et al., 2017b). The regression loss is set by Lreg Le + Lxf- where
La Σ2)
KFlo
(13)
See more ablation experiments on the functional form of (E,, En) in the Appendix. For center point loss Le, this paper provides two different forms:
1) The loss adopted in Faster RCNN (Lin et al., 2017a) (default): Lo(t, t") = Eie(a.)) (n(t,, ti).
2) The first term of KLD (Yang et al., 2021d) (advanced), which has an advanced center point optimization mechanism: Le (c(11 M2, Σ1) In ((12 111) E (M2 M1) +1).
5
EXPERIMENTS
5.1 DATASETS AND IMPLEMENTATION DETAILS
Aerial image dataset: DOTA (Xia et al., 2018) one of the largest datasets for oriented object detection in aerial images with three released versions: DOTA-v1.0, DOTA-v1.5 and DOTA-v2.0. DOTA-v1.0 contains 15 common categories, 2,806 images and 188,282 instances. DOTA-v1.5 uses the same images as DOTA-v1.0, but extremely small instances (less than 10 pixels) are also an- notated. Moreover, a new category, containing 402,089 instances in total is added in this version. While DOTA-v2.0 contains 18 common categories. 11,268 images and 1,793,658 instances. We divide the images into 600 x 600 subimages with an overlap 150 pixels and scale to 800 x 800. HRSC2016 (Liu et al., 2017) contains images from two scenarios with ships on and close inshore. The training, validation and test set include 436, 181 and 444 images.
Scene text dataset: ICDAR2015 (Karatzas et al., 2015) includes 1,000 training images and 500 testing images. MSRA-TDS00 (Yao et al., 2012) has 300 training images and 200 testing images. They are popular for oriented scene text detection and spotting.
Face dataset: FDDB (Jain & Learned-Miller, 2010) is a dataset designed for unconstrained face detection, in which faces have a wide variability of face scales, poses, and appearance. This dataset contains annotations for 5,171 faces in a set of 2,845 images. We manually use 70% as the training set and the rest as the validation set.
We use AlphaRotate (Yang et al., 2021e) for main implementation and experiment, where many advanced detectors are integrated. Experiments are performed on a server with GeForce RTX 3090 Ti and 24G memory. Experiments are initialized by ResNet50 (He et al., 2016) by default unless otherwise specified. We perform experiments on two aerial benchmarks, two scene text benchmarks and one face benchmark to verify the generality of our techniques. Weight decay and momentum are set 0.0001 and 0.9, respectively. We employ Momentummptimizer over 4 GPUs with total of images per mini-batch (1 image per GPU). All the used datasets are trained by 20 epochs, and learn- ing rate is reduced tenfold at 12 epochs and 16 epochs, respectively. The initial learning rate is 1e-3. The number of image iterations per epoch for DOTA-v1.0, DOTA-v1.5. DOTA-v2.0, HRSC2016, ICDAR2015, MSRA-TDSON and FDDB are 54k. 64k, 80k, 10k. 10k. 5k and 4k respectively, and doubled if data augmentation (e.g. random graying and rotation) or multi-scale training are enabled.
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Published as a conference paper at ICLR 2023
Table 3: Results on KITTI val split 3D detection and BEV Detection.
Method
mAP
3D Detection Mod.
mAP
BEV Detection Mod.
PointPillars
64.28
78.90
50.96
62.99
70.10
88.08
55.51
66.69
+GWD
65,50
78.57
55.19
62.74
71.48
88.30
58.49
67.66
+KLD
66.19
80.36
52.94
65.27
71.18
88.11
57.26
68.19
+KFloU
66.71
80.19
54.94
65.00
72.08
89.90
57.81
68.55
KITTI (Geiger et al., 2012) contains 7,481 training and 7,518 testing samples for 3-D object detec- tion. The training samples are generally divided into the train split (3,712 samples) and the val split (3,769 samples). The evaluation is classified into Easy. Moderate or Hard according to the object size, occlusion and truncation. All results are evaluated by the mean average precision with a rotated IoU threshold 0.7 for cars and 0.5 for pedestrian and cyclists. To evaluate the model's performance on KITTI val split, we train our model on the train set and report the results on the val set.
We use PointPillar (Lang et al., 2019) implemented in MMDetection3D (Contributors, 2020) as the baseline, and the training schedule inherited from SECOND (Yan al., 2018); ADAM optimizer with a cosine-shaper cyclic learning rate scheduler that spans 160 epochs. The learning rate starts from le-4 and reaches 1e-3 at the 60th epoch, and then goes down gradually to le-7 finally. In the development phase, the experiments are conducted with a single model for 3-class joint detection.
5.2 ABLATION STUDY AND FURTHER COMPARISON
Ablation study on different center point losses. Tab. 1 compares the two different center point losses proposed in Sec. 4.2 three versions of DOTA datasets. Even with the most commonly used L)), KFloU loss achieves competitive performance, significantly better than GWD loss and comparable to KLD loss. For fairer comparison, after adopting the same center point loss term as KLD loss (e 142 Σ1), the performance of KFloU loss is further improved, which is better than KLD loss thanks better center point optimization mechanism.
Ablation study on various 2-D datasets with different detectors. Tab. 2 compares Smooth LI loss and KFIoU loss by indicators with different ToU thresholds. For HRSC2016 con- taining large number of ships with large aspect ratios, KFIoU loss has 9.90% improvement over Smooth LI on AP7s- For the scene text datasets MSRA-TD500 and ICDAR2015, KFloU achieves 7.07% and 3.44% improvements on Hmean reach- ing 44.96% and 41.17% % respectively. The same conclusion can be reached on FDDB and DOTA-v1.0 datasets.
Table 4: Accuracy (%) comparison on DOTA. The bold red and blue indicate the top two performances. Doc and Die denotes OpenCV Definition (0 E [-900.09] and Long Edge Definition (0 E [-90", 90%) of RBox. 'H' and 'R' denote the horizontal and rotating anchors, respec- tively. indicates that the first term of KL. taken the center point loss, i.c. (e 12, E1).
Box DOTA-110
DOTA-v15
DOTA-120
RetimaNet (Reg)) (201/b)
D.
65.73
53.77
41.6
RetimaNet-11 -e (Reg.) (20176)
De
64.17
56.10
43.06
RetinaNee H (Keg. (Xeg.") (20077)
D
65.78
57.17
43.92
RetinaNet-K (Reg.) (2017))
Dec
67.25
56.50
42.01
PluU
Dw
Joti-Smooth (2019)
D.
66.99
59.16
Modulazed Loss (2021
D..
66.05
57.75
45.17
Modulased Loss (2021a)
Quad.
67.20
61.12
46.71
RJL (3021a)
Qual.
66.06
58.91
45.35
(2020)
D.
67.38
53.55
43.34
Ablation study of KFIoU loss on 3- detection. We generalize the KFloU loss from 2-D to 3-D, with results in Tab. 3. involves 3-D detection and BEV detection on KITTI val split, and significant performance improvements are also achieved. On the moderate level of 3-D detection and BEV detection, KFloU loss improves PointPillars by 2.43% and 1.98% respectively.
DCL (BCL) (2021a)
D.,
plain SkewleUJ (2019)
D.
68.27
59.01
45.87
GWD (202
D..
68.93
60.03
46.65
KLD (2021d)
D..
71.28
62.50
47.69
KFou (Ouns)
Dec
70.64
62.71
48.04
KFioU' (Ous)
D
63.75
Comparison with peer methods. Methods in Tab. 4 are based on the same baseline RetinaNet, and initialized by ResNet50 (He et al., 2016) without using data augmentation and multi-scale train- ing/testing. They are trained/tested under the same environment and hyperparameters. These meth- ods are all published solutions to the boundary discontinuity in rotation detection.
First, we conduct ablation experiments on anchor form, rotated bounding box definition form, and angle regression form based on RetinaNet. Rotating anchors provides accurate prior, which makes
8

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Published as a conference paper at ICLR 2023
Table 5: AP of different objects DOTA-vI. .0. Red and blue: top two performances.
Method
Barkhhoe
180
18R
1,1
50
10C
51
SWF
8AA
IIC
Plot (ibai)
DEA-11
51133
15:70
75.15
61.00
58 111
9016
70:40
08.10
(1)
01.00
55100
Singlsstag
Of Ee--NNr (20200
BE:04
00.31
62.14
47.33
61.21
71.32
74.08
78.62
90.76
52.23
81.36
68.95
60.17
53.21
56.95
61.03
71.04
DAL (1101))
R-401
68.61
19
m/
66.27
70:17
63.89
76.10
78.55
90.84
99.05
78.41
58.71
63:00
69.3
09.23
71.97
69.65
71:22
DRN (200m)
8:104
59.71
52.34
47.22
64.10
76.22
74.43
55.84
50.57
56.18
64.29
57.65
61.93
69.30
09.63
58.45
73.23
DCL, (2002ia)
B-152
50.15
73.57
98.15
90.89
56.64
67.97
67:35
76.05
07.05
14.05
(2021c)
K-152
77.53
68.45
73.47
67:77
12.57
76.30
KFlAl
je"Der (30318)
B-152
59.00
67.77
68.11
06-77
83.27
50.31
65.67
62.18
67.55
72.67
76-47
(3021)
R-152
$9.08
56.37
$0.96
57.17
52.34
69:94
15.53
76.67
Welonodaay
76.10
S"A-Nor (2001
IPDDs (2021-)
R:152
64.99
84.53
50.21
67.77
74.92
50
De KLD (2001d)
R-152
15.13
16.38
67. 51
19.00
67.31
73.57
71.35
79.34
05.08
M0663
R DeD KFFaU (Cunn)
Swas-T
$0.50
54.26
99.90
81.05
81.74
85.45
58.77
50.85
67.03
62.79
70.68
74.31
78.17
$1.67
72.37
50.90
R'De-KFFal KFFaU (Ours)
R-152
$5.89
55.14
00.05
81.13
81.78
85.71
58.27
$0.67
67.12
67.91
69.77
73.70
79.25
$1.31
74,56
$1,03
Tost-Inasx
63.44
73:22
73.88
$3.90
41.01
SCRRaa (3019)
B-101
$9.98
50.65
53.00
69.36
68.16
60.32
72.41
50.85
K7.94
36
65.02
66.68
66.25
56.24
65.21
12.61
Twe-stage
Gliding Venex (2025)
CSL (2000)
R-152
K-191
50.25
19.64
15.00
55.53
$4.64
$2.25
77.34
73.31
73.01
76.44
73.14
73.51
56.92
77.62
90.74
50.84
86.15
7901
96.11
86.69
63.50
59.55
68.04
70.91
73.83
72.04
71.10
70.30
57.32
68.03
75.02
76.17
RSiber-ll (200110
R-150
59:91
14.05
53.71
74.35
71.53
78.31
72
91
67.39
53
65.64
05.17 17
15.35
19:74
61:31
70.34
SCRDese (2013)
R-101
55:44
73.09
77.54
71.11
36.05
69.52
65.90
73.74
71.29
76.81
(2021 1gg
Oriented (2021)
Bol-Toae XPPnl
37744
14.41
07.21
80.10
35.07
15.65
9090
15.16
7530
7155
75.95
75.07
the model show strong performance in large aspect ratio objects (e.g. SV, LV, SH). However, the large number of anchors makes it time-consuming Therefore, we use horizontal anchors by default to balance accuracy and speed. In terms of definition, experiments show that OpenCV definition (Woc) (Yang et al., 2019) is slightly better than Long Edge definition (Dic) (Ma et al., 2018) on the three versions of DOTA. Angle direct regression (Reg.) always suffers from the boundary disconti- nuity problem as widely studied recently (Yang & Yan, 2020). In contrast, angle indirect regression (Reg".) is a simpler way to avoid above issues and brings performance boost according to Tab. 4.
PloU calculates the SkewloU by accumulating the contribution of interior overlapping pixels but the effect not significant. loU-Smooth 1.1 partly circumvents the need for SkewloU loss with gradient backpropagation by combining IoU and Smooth LI loss. Although IoU-Smooth L1 has achieved an improvement of 226%/...9%%/....... 15% on DOTA-v 1.0/v 155/2..0, the gradient is still dominated by Smooth L1 but still worse than plain SkewloU loss. Modulated Loss and RIL implement ordered and disordered quadrilateral detection respectively, and the more accurate representation makes them both have considerable performance improvement. In particular, Modulated Loss achieves the third highest performance on DOTA-v1 .5/22.0. CSL and DCL convert the angle prediction from regression to classification, cleverly eliminating the boundary discontinuity problem caused by the angle periodicity. GWD loss, KLD loss and KFIoU loss are three different regression losses based on Gaussian distribution. The results presented in our experiments of GWD loss and KLD loss are obtained by best-tuned hyperparameters. In contrast, KFloU loss is free from hyperparameter tuning and has more stable performance increase due to a more consistent calculation process with SkewloU loss the center point gets closer.
5.3 COMPARISON WITH THE SFATE-OF-THE-AM
Tab. 5 compares recent detectors on DOTA-v1.0, .0, as categorized by single- refine-, and two-stage based methods. Since different methods use different image resolution, network structure, training strategies and various tricks, we cannot make absolutely fair comparisons. In terms of overall perfor- mance, our method has achieved the best performance far, at around 77.35 //1.003 103..%%%%
6 CONCLUSION
We have presented a trend-level consistent approximate to the ideal but gradient-training unfriendly SkewloU loss for rotation detection, and we call it KFIoU loss as the product of the Gaussian distributions is adopted to directly mimic the computing mechanism of SkewloU loss by definition. This design differs from the distribution distance based losses including GWD loss and KLD loss which in our analysis have fundamental difficulty in achieving trend-level alignment with SkewloU loss without tuning hyperparameters. Moreover, KFloU is easier to implement and works better than plain SkewloU due to the effective measurement for non-overlapping cases and complete derivation. Experimental results various 2D and 3D datasets show the effectiveness of our approach.

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Published as a conference paper at ICLR 2023
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Yue Zhou, Xue Yang. Gefan Zhang, Jiabao Wang, Yanyi Liu, Liping Hou, Xue Jiang, Xingzhao Liu, Junchi Yan, Chengqi Lyu, Wenwei Zhang, and Kai Chen. Mmrotate: rotated object de- tection benchmark using pytorch. In Proceedings of the 30th ACM International Conference Mullimedia, pp. 7331-7334, 2022.
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A
PROOF OF KFIOU UPPER BOUND
For an n-dimensional Gaussian distribution, its volume is:
V ==2" 1 2.. 1-/
(14)
For Exy, we have
Exyl =|=1 - E1(E1 + E2)
-
=|Σ, [Σ] + Σn) -EE
(15)
E Σ
Σ Σn
According to Minkowski's inequality:
E + Σ3/
E1 +++1 -|E/|
(16)
Simultaneous mean inequalities:
Σ
Σg
32
2
Σ
2
1
(17)
Thus:
Σ
Σ
Σg
2
(18)
Σ
Σ
Σn
2
and
E1
E1
Σ1
3
Σ2
Eayl
Σ
Eg
2
(19)
Σ
|
Exyl+
2
Combine the mean inequalities again:
Σ
E2
Σ 1/2 +
E21
Expl
(20)
22
25+1
According to Eq. 14, we have
V1 + 1/2
Vas S
(21)
24+1
Therefore, the upper bound of KFloU is
Vks
KFIoU
(22)
Vi 1/2
Vas
2 +1+1
When n = 2 and n = 3, the upper bounds are & and
V32-1 respectively.
B SUPPLEMENTARY EXPERIMENT
Ablation study of three forms of KFTOU loss on two detectors. We use two different detectors and three different KFIoU based loss functions to verify its effectiveness, as shown Tab. 6. RetinaNet- based detector will have a large number of Now-SkewloU prediction bounding box in the early stage of training, and will produce very large loss after the log function, which weakens the improvement of the model. Compared with the linear function, the derivative of the exp-based function will pay more attention to the training difficult samples, so it has a higher performance, at 70.64% %. In contrast, Rd Det-based detector can generate high-quality prediction box at the beginning of training by adding refinement stages, so will not suffer the same troubles as RetinaNet. Due to the same mechanism of focusing difficult samples, log and exp-basee functions are both better than linear functions, and the best performance is achieved on the log-basee based function, about 72.28 %. We also expand KFloU by 3 times to make its range truly consistent with the loU loss, at [0, 1). However, this
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Table 6: Ablation study of different KFIoU loss forms with different detectors DOTA-v1.0.
Method
Smooth LI
In(KFIoU
1- KFIoU
el-KHtel -1
el-3kFlot -1
In(3KFIoU
RetinaNer
65.73
69.80 (+4.07)
70.19 (+4.46)
70.64 (+4.91)
(9.6419339
De
70.66
72.28 (+1.62)
71.09 (+0,43)
71.58 (+0.92)
71.77 (+1.1)
Table 7: Ablation study of training strategies and tricks. Rotate and MS indicate rotation au augmenta- tion and multi-scale training and testing.
RetinaNei
R-00
R:30
12c
20.10)
57.11
$0.06
41:12
41.35
00.01
70.44
72.20
10710
62.49
35251
15.15
24.86
111b
10.91
7961
79.23
7331
38.54
56.40
51.00
61.87
53321
67.15
45.33
25.33
64:35
SPA-Na
E-0
10-10
29:11
19:65
18.11
35
00.91
3111
06.10
00.71
18:88
11.35
K:0
10707
11:11
11.30
17
19300
57.56
59090
3705
15.20
00.75
75.0
71.71
10.18
8:50
1he
09.00
02.00
13.40
71
78:15
77:43
37.07
90.50
30.05
85 17
63.11
63.69
74.30
71 11
11:35
T6.17
Swis-T
00..0
13:34
76.95
78.06
38.00
90.90
09
77.87
53.99
TT:18
8,50
24c
09.12
34.54
68.73
78
79.65
85.79
95.45
50.50
$7.03
55 25
69.15
70,25
79,88
81.56
10.35
80.22
Swas1
12c
09..4
14.41
02.22
$2.51
50.10
$5.07
85
10,90
81.32
25.58
72.50
71.95
78.90
74.15
75.27
60.93
X--00
20110
11:31
11:03
15777
01.0
31877
33:1
0136
63.0
16:1
8:50
12:
89.00
53.40
$5.91
$1.00
59.14
63.24
85
50.50
84.61
95.33
65
11.50
75.90
77.66
63.56
18.59
Swas-T
12-
89.41
13.06
$6.92
50.45
$4.34
85
10.91
15.99
87.64
07.00
71.88
75.34
73.63
72.11
19:35
R.101
07.55
71.60
78.31
19.83
S
12:
99.34
53.75
59.77
50.5
84:03
98.0
90.84
86.85
$7.03
71.1
71.17
76.90
7742
11.55
10:55
Swas
24c
80.50
14.36
$9.90
81.00
$1.74
35.45
85.77
90.55
8100
87.79
70.66
14.31
79.17
81.07
12.37
$0.90
Table 8: Results on KITTI val split 3D detection and BEV Detection.
mAP
Car
3D Detection
Ped.
3D Detection
Cyc.
3D Detection
Method
Mod.
Easy
Mod.
Hard
Easy
Mod.
Hard
Easy
Mod.
Hard
PointPillars
64.28
88.26
78.90
76.06
57.10
50.96
46.38
83,77
62.99
59.65
+GWD
65.50
87.38
78.57
75.87
61.69
55.19
50.04
81.61
62.74
59.18
+KLD
66.19
89.55
80.36
76.02
59.95
52.94
48.22
85.61
65.27
61.45
+KFIoU
66.71
89.56
80.19
77.16
60.97
54.94
50.75
84.96
65.00
61.00
mAP
Car
BEV Detection
Ped.
BEV Detection
Cyc.
BEV Detection
Method
Mod.
Easy
Mod.
Hard
Easy
Mod.
Hard
Easy
Mod.
Hard
PointPillars
70.10
93.81
88.08
86.80
61.49
55.51
51.13
87,20
66.69
63.02
+GWD
71.48
92.02
88.30
85.72
64.67
58.49
53.45
86.92
67,66
63,37
*KLD
71.18
93.33
88.11
85 .4.44
64.46
57.26
52.53
$7.40
68.19
64.47
+KFloU
72.08
92.15
89.90
85.66
63.45
57.81
53.07
87.52
68.55
64.56
consistency do not bring any additional gains, so the following experiments are all use the KFloU before non-expansion.
Ablation study of training strategies and tricks. We reimplement KFIoU based on the more powerful benchmark, MMRotate (Zhou et al., 2022). We a single GeForce RTX 3090 Ti with a total batch size of 2 for training. For ResNet (He et al., 2016), SGD optimizer is adopted with an initial learning rate of 0.0025. The momentum and weight decay are 0.9 and 0.0001, respectively. For Swin Transformer (Liu et al., 20 AdamW (Kingma & Ba, 2014; Loshchilov & Hutter, 2018) optimizer is adopted with an initial learning rate of 0.0001. The weight decay is 0.05. In addition, we adopt learning rate warmup for 500 iterations, and the learning rate is divided by 10 at each decay step. Tab. performs ablation experiments on four detectors: RetinaNet (Lin al., 2017b), S A-Net (Han et al., 2021a), Ret (Yang et al., 2021b), and Rol Transformer (Ding et al., 2019). The experimental results prove that KFIoU can stably enhance the performance of the detector. In order to further improve the performance of the model DOTA, we verified many commonly used training strategies and tricks, including backbone, training schedule, data augmentation and multi- scale training and testing, shown in Tab. 7.
Ablation study of KFIoU loss on 3-D case. More detailed results in KITTI are shown in Tab. 8.
Ablation study more datasets. The performance of different loss functions is compared in Tab. 9 on ICDAR2015, UCAS-AOD, SSDD (Li et al., 2017) and HRSID (Wei et al., 2020b) datasets, and KFloU is still the best.
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Table 9: Results datasets, the base detector is RetinaNet.
UCAS-AOD
SSDD
HRSID
Loss
ICDAR2015
Car
Plane
mAPs0 50
Inshore
Inshore
Smooth Li
69.78
92.62
96.30
94.56
68.47
51.41
GWD
74.29
94.03
96.86
95,44
77.71
51.11
KLD
75.32
94.34
97.94
96.14
76.84
52.80
KFIoU
75.90
94.51
98.41
96.46
77.89
53.45
Figure 4: Visual comparison between Smooth L1 loss-based (left), GWD-based (middle) and the KFloU-based (right) detectors on DOTA (2-D) and KITTI (3-D). For 3-D object detection, red and blue box denotes ground-truth and predict bounding box, respectively.
C VISUALIZATION
Fig. ad Fig. show the visual comparison of three different loss functions on the different kinds of datasets. Compared with Smooth LI Loss, KFIoU loss is significantly better.
D TREND CONSISTENCY SIMULATION
Fig. 6(a) and Fig. 6(b) show the impact of center deviation and object scale on the trend consistency of each loss function. Note that each data in the figure is calculated from the average of 1,000 random aspect ratio and rotation angle examples. Two conclusions can be drawn: i) the smaller the center deviation, the better trend consistency of the KFloU loss; ii) KLD loss and KFIoU loss are insensitive to scale changes.
E LIMITATION
Note that the Gaussian modeling has limitation that it cannot be directly applied to quadrilat- cral/polygon detection (Ming et al., 202 Xu et al., 2020) which is also an important task in aerial images, scene text, etc. In addition, the Gaussian distribution of the square like object is close to the isotropic circle, which is not suitable the object heading detection.
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Figure 5: Visual comparison between Smooth L1 loss-based (left), GWD-based (middle) and the KFloU-based (right) detectors on FDDB.
-10-2
Ervr Variance
Loss
Variance
0.15
L1 Loss
GWD loss
0.1
GWD loss
KLD loss
KI.D loss
KFloU loss
KFlloU loss
0
2
4
6
8
10
Maximum Center Point Shifting
Maximum Object Scale
(b)
Figure 6: (a) Impact of center deviation on the trend consistency of each loss function. (b) Impact of object scale the trend consistency of each loss function under pixels center deviations.
17


Reviews:
[{"review_id": "tmnlSFt2qao", "reviewer": "Reviewer_2M4a", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "Training deep models to correctly detect and outline rotated objects is difficult due to the nature of the metric of reference (SkewIoU). The authors propose KFIoU, an easily computable and differentiable loss that relies on transforming bounding boxes into Gaussians and estimating the overlap between the Gaussians analytically. Experiments demonstrate both that the derived proxy loss follows SkewIoU trends fairly well, and leads to strong performance on both 2D and 3D benchmarks.\n", "summary_of_the_review": "KFIoU is an interesting and easy to implement proxy for SkewIoU that follows easy to understand principles. Experimental results show the loss outperforms much of its competition and even sets a new state of the art on the DOTA dataset. As such, I recommend acceptance for this paper.", "strength_and_weaknesses": "Strengths:\n- KFIoU is an easy to compute and differentiate loss with well principled motivation.\n- KFIoU is hyper-parameter free and fairly simple to implement.\n- The paper is mostly well-written with clear illustrations (notably Fig. 2) that sum up the problem and solution.\n- Experimental results seem to validate the efficiency of the method with regards to previous approaches on both 2D and 3D detection tasks.\n\nWeaknesses:\n- No indication of uncertainty or context is given on the results. What is the standard deviation? How many runs were performed for each result? Are the baseline results reported or reproduced? If reported, are the settings comparable?\n- The center loss is simply added as a correction term. This seems to work well, but it does not really reflect the product of Gaussian at the center of the paper. Have the authors tried using the distance between centers as a multiplicative factor on the KFIoU?\n- This is more of an issue of semantics, but I am unconvinced by the paper’s positioning around Kalman filtering. At its core, KFIoU computes the overlap between two Gaussians through a product of the pdfs which is well known to also be a Gaussian pdf up to a scale factor. While this procedure is indeed very important in Kalman filtering to reconcile observations and predictions, it is just a small part of the entire process. As such, I feel like the paper’s reliance on Kalman filtering detracts from its actual key points.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "os-uPD3z3B", "reviewer": "Reviewer_Q8Fo", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The authors proposed a new loss, called KFIoU, for the detection of rotated objects. Based on Kalman filters and Gaussian modeling, this loss aims at approximating the SkewIoU loss, which is unfriendly to differentiable learning. Formulated this way, the SkewIoU loss does not rely on any additional hyperparameter, contrary to its counterparts. Moreover, experiments show that the proposed loss is nearer to the SkewIoU loss than the other approximator counterparts of the literature in terms of error variance.", "summary_of_the_review": "The KFIoU loss proposed by the authors seems interesting compared to other SkewIoU estimators, while not relying on additional hyperparameters. While the approach reaches SOTA results on the DOTA dataset, some choices are questionable regarding the other comparisons, making it difficult to compare with the state of the art on the other 2D datasets.", "strength_and_weaknesses": "Strength: \n\nContrary to other SkewIoU loss approximations in the literature (GWD/KLD), the proposed KFIoU loss does not involve any new hyperparameter. \n \nThe proposed KFIoU loss enabled the authors to reach competitive/SOTA results on the DOTA dataset. The ablation study show that the FKIoU loss achieves better results than the smooth L1 loss on three detection tasks (aerial, scene text, and face).\nThe results on the 3D detection seem also promising.\n \nWeaknesses: \n \nSome results do not seem fair compared to SOTA.\nTable 1 shows that GWD and KLD reach better results than the smooth L1 loss on the DOTA datasets. However, in the ablation study of table 2, where the approach is evaluated on the other 2D datasets, the proposed loss is only compared with the smooth L1 loss. Why not comparing with GWD and KLD ?\nIn Table 5, when comparing the 2-stage approaches, the backbone used is different from all the other works, preventing the fair comparison. One can ask if the improvement is due to the loss, or to the backbone.\n\nBe careful with the proofreading, some errors complicate the reading (e.g. logical connectors in the beginning of the abstract).\n\nThe limitation mentioned in the appendix should be highlighted in a dedicated section, before the conclusion, for example.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "VXYFMP1_ub", "reviewer": "Reviewer_jv8Z", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In this paper, the authors introduce a KFIoU loss for rotated object detection.\nThe general idea of KFIoU loss is to approximate the SkewIoU based on Gaussian Modeling and Kalman filter. \nParticularly, a bounding box is firstly represented as a Gaussian distribution form.\nThen (1) a scale-insensitive center point loss to measure the distance between the centers of Gaussians and (2) a Kalman-based term to measure the overlapping between Gaussian distributions are adopted.\nFinally, these measurements are converted back to bounding box form for approximating the SkewIoU.\nThe proposed approach is validated on several detection benchmarks in both 2D and 3D cases to illustrate its advantages.", "summary_of_the_review": "Although many building blocks of the proposed approach already exist in previous works.\nAll modifications and contributions have been discusses. \nAblation study and comparison are comprehensive.\nExperiments have shown the advantages of the proposed approaches.\n", "strength_and_weaknesses": "STRENGTH\n- The adoptation of Kalman filter formulation to compute the overlapping in rotated objects is interesting.\n- The contributions and roles of each building block are analyzed and discussed. \n- Ablation study and comparison are comprehensive.\n- Experiments on both 2D/3D data have shown the advantages of the proposed approach.\n\nWEAKNESS\nIn Table 2, only L1 smooth is used as baseline.\nWhile the proposed approach give comparable/marginal results with KLD, more comparison with KLD in ablation study is recommended.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "QM_jsj9PQw", "reviewer": "Reviewer_2Kss", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The submitted article proposes a practical solution to the rotated object detection problem. To locate arbitrarily oriented objects in images, detectors often rely on the calculation of the SkewIoU. However, its closed-form calculation cannot always be provided and its implementation in popular deep learning framework is limited due to the missing implementation of custom functions. In this context, the authors propose a fully-differentiable approximation of the SkewIoU based on Kalman filter, called KFIoU. Extensive experiments show its practical effectiveness, both in 2-D and 3-D object detection problems.", "summary_of_the_review": "The paper, although not introducing a new approach to rotated object detection, solves the practical problem of implementation of the SkeweIoU by introducing the KLIoU. Effectiveness of the proposed term is validated by extensive experiments. Although the novelty is limited, the work has a practical impact. ", "strength_and_weaknesses": "The paper provides an efficient and practical implementation of a loss function for rotated object detection. Such a loss, called KFIoU, does not require any additional hyperparameters and can be easily implemented with fully differentiable functions in existing deep learning frameworks. However, limitations of other implementations are not sufficiently discussed. The authors could insist further on such limitations in order to highlights the advantages brought by the proposed KFIoU. \n\nSome parts can also be rephrased and typos are to be corrected. \nIn the abstract:\n\"modeing\" -> modeling\n\"which is used to quickly get the center points between bounding boxes closer to assist the second term\" -> it is not clear what you mean by that, especially I don't get what \"closer\" refers to.\nIn section 1:\n\"Rotated object detection is an relatively emerging\" -> is a relative ...\n\"The highlights are as follows\" -> the following\n2nd point: the first phrase is redundant and refers to highlight number 1.\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "F4OXnVfh2P", "reviewer": "Reviewer_cEDF", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This article presents a new loss (KFIoU) approximating the Skew Intersection over Union Loss (SkewIoU) for the rotated object detection problem. This loss is composed of a scale-insensitive center point loss, and a second distance-insensitive term using Gaussian modeling\nand Kalman filtering. Compared to other Gaussian modeling based losses like the GWD and KLD losses, this loss is hyperparameter free, and is the first one used in a 3D environment. It is also the closest to the SkewIoU loss, and produce state-of-the-art results.", "summary_of_the_review": "This article presents a possibly interesting evolution of Gaussian-based SkewIoU approximating losses. KFIoU does not need hyperparameters and has some encouraging experimental results.\nHowever, the method clearly lacks motivation, either theoretically or emperically, to support its lack of novelty compared to previous losses. Furthermore, the paper is often unclear, lacks critical comparisons with KLD and GWD, and with unsubstantiated claims (over SkewIoU \"unfriendliness\" for example).\nFor these reasons, I am leaning toward rejection.", "strength_and_weaknesses": "Strengths: The method proposed is in the logical continuation of Gaussian modeling based losses. Its main advantage is a seemingly closer approximation of the SkewIoU dynamics, while being hyperparameter free.\n\nWeaknesses: The method presented is really similar to the KLD loss, and present only very marginal improvements on DOTA (when using its center loss), and present no comparison with KLD for the other datasets of Table 2 and 3. \nThe choice of using Kalman Filter (over the previous Gaussian modeling based losses) to create this new loss is never truly motivated. It is not justified why this method should result in a more physically reasonable loss, or one that is theoretically closer to the true SkewIoU value (other than using a similar formula than IoU). The experiments justifying the \"alignment\" between the losses are not really convincing either (see below).", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster