Delving into Cascaded Instability: A Lipschitz Continuity View on Image Restoration and Object Detection Synergy
Authors: Qing Zhao
Weijian Deng
Pengxu Wei
ZiYi Dong
Hannan Lu
Xiangyang Ji
Liang Lin
Venue: NeurIPS 2025 poster ()
Keywords: Object Detection under Adverse Conditions; Image Restoration; Lipschitz Continuity
Primary area: deep_learning

Abstract: To improve detection robustness in adverse conditions (e.g., haze and low light), image restoration is commonly applied as a pre-processing step to enhance image quality for the detector. However, the functional mismatch between restoration and detection networks can introduce instability and hinder effective integration---an issue that remains underexplored. We revisit this limitation through the lens of Lipschitz continuity, analyzing the functional differences between restoration and detection networks in both the input space and the parameter space. Our analysis shows that restoration networks perform smooth, continuous transformations, while object detectors operate with discontinuous decision boundaries, making them highly sensitive to minor perturbations. This mismatch introduces instability in traditional cascade frameworks, where even imperceptible noise from restoration is amplified during detection, disrupting gradient flow and hindering optimization. To address this, we propose Lipschitz-regularized object detection (LROD), a simple yet effective framework that integrates image restoration directly into the detector’s feature learning, harmonizing the Lipschitz continuity of both tasks during training. We implement this framework as Lipschitz-regularized YOLO (LR-YOLO), extending seamlessly to existing YOLO detectors. Extensive experiments on haze and low-light benchmarks demonstrate that LR-YOLO consistently improves detection stability, optimization smoothness, and overall accuracy.

Delving into Cascaded Instability: A Lipschitz Continuity View on Image Restoration and Object Detection Synergy
Qing Zhao'
Weijian Deng²
Pengxu Wei
Ziyi Dong'
Hanman Lu
Xiangyang Ji Lin Liang!
Sun Yat-sen University
PAustralian National University
Harbin Institute of Technology *Tsinghua University 'Peng Cheng Laboratory
1zhaoq78, dongzy6 Email2.sysu.cdu.. dengwj16 ammil..mmalmomm cripx3@mailssysu.cdu.. luhannan @ hit edu.cn, xyji pajj@tsinnhua.edu.com linliang iece.org
Abstract
To improve detection robustness adverse conditions (e.g., haze and low light), image restoration is commonly applied pre-processing step enhance image quality for the detector. However, the functional mismatch between restoration and detection networks issue that remains underexplored. We revisit this limitation through the lens Lipschitz continuity, analyzing the functional differences between restoration and detection networks in both the input space and the parameter space. Our analy- sis shows that restoration networks perform smooth, continuous transformations, while object detectors operate with discontinuous decision boundaries, making them highly sensitive to minor perturbations. This mismatch introduces instability in traditional cascade frameworks, where even imperceptible noise from restoration is amplified during detection, disrupting gradient flow and hindering optimiza- tion. To address this, we propose Lipschiz-reegularized object detection (LROD), simple yet effective framework that integrates image restoration directly into the detector's 's feature learning, harmonizing the Lipschitz continuity of both tasks during training. We implement this framework as Lipschitz-regulartie (LR-YOLO), extending seamlessly to existing YOLO detectors. Extensive experi- ments on haze and low-light benchmarks demonstrate that AR-YOLO consistently improves detection stability, optimization smoothness, and overall accuracy.
introduce instability and hinder effective integration-
YOLO
Introduction
Adverse imaging conditions introduce challenges for object detection by causing various image degradations, including reduced contrast, blurred edges, and obscured object boundaries. A typical way to alleviate this issue is to employ image restoration as a pre-procsssing step, aiming to improve image quality before detection [ 2 B. However, its effectiveness is limited by the functional mismatch between restoration and detection networks. This inconsistency can introduce instability, where imperceptible noise introduced during restoration amplified during detection, leading to unreliable predictions 4 5 Moreover, the underlying differences between these tasks remain underexplored, hindering opportunities for better integration and enhanced robustness. To bridge this gap, understanding their functional behaviors is crucial for achieving effective synergy. To this end, we analyze the conventional Image destoration++Obee Detection cascade framework through the lens of Lipschitz continuity, focusing on two aspects: the input space and the parameter space.
Corresponding Author.
Code available:
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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(a) Image Restoration
(b) Object Detection
(c) Cascade
(d) Ours
Figure 1: Visualization of network functional behaviors under input perturbations. (a) Image Restoration networks exhibit smooth, continuous mappings. where input changes lead gradual adjustments. (b) Object Detection networks display sharp discontinuities due to abrupt decision boundaries in classification and bounding box regression.
(c) Cascade frameworks (Image Restoration + Object Detection) magnify instability, resulting in fragmented and non-smooth behavior. (d) Our method integrates low-Lipschitz image restoration into the feature learning of high-Lipschitz object detection, promoting smoother transitions and enhanced stability.
From the input space perspective, we leverage the concept of Lipschitz continuity, which characterizes the sensitivity of model's output to imput perturbations (6. Networks with lower Lipschitz constants exhibit smoother, more predictable changes, while higher constants indicate heightened sensitivity and instability. By computing the Jacobian norm 7 with respect to haze density variations, we observe that the Lipschitz constant of the object detection network is nearly an order of magnitude larger than that of the restoration network, highlighting its substantially lower smoothness. This disparity highlights the differences in their functional behaviors. Restoration networks exhibit smooth, continuous mappings, where small input perturbations result in gradual and predictable adjustments to the restored image. This smoothness stems from pixel-wise processing that consistently enhances local regions and propagates changes smoothly across the image. In contrast, object detection networks are inherently discontinuous, characterized by sharp decision boundaries in classification and bounding box regression. Even minor pixel-level changes can cause abrupt shifts class predictions or bounding box coordinates, reflecting non-smooth, step-like transitions in the output. This sharp contrast behavior contributes to instability when the two networks are cascaded. To further illustrate this disparity, visualize the functional behaviors in Figure (a) and (b), where the smooth transitions of restoration sharply contrast with the abrupt shifts observed in detection. This inconsistency introduces instability when the two networks cascaded: imperceptible noise introduced during restoration can be amplified during detection, resulting in overall non-smooth behavior in the cascade framework, shown in Figure 1 (c).
To further understand the instability observed conventional Image CiatorattoonOhbeee Detection cascade framework, extend our analysis to the parameter space of the networks, where Lipschitz continuity characterizes the sensitivity of a model's 's output to changes in its parameters. Our findings reveal that image restoration networks maintain relatively low Lipschitz constants, resulting in smooth and stable optimization trajectories during training. In contrast, object detection networks exhibit substantially higher Lipschitz constants, leading sharp gradient transitions and erratic convergence paths. This imbalance disrupts gradient flow, introduces mutual interference, and destabilizes joint optimization, further compounding the instability of traditional cascade frameworks.
Given the importance of network stability adverse conditions, a key challenge lies in harmonizing image restoration and object detection to address the inherent differences in Lipschitz continuity. To address this, we propose Lipschitz-regullaizze object detection (LROD), a simple yet effective framework that integrates image restoration directly into the detector's feature learning. Unlike conventional cascades, LROD harmonizes the Lipschitz continuity of both tasks during training, smoothing out perturbations before they propagate through the detector's discontinuous layers. This coupling mitigates noise amplification, enhancing stability in challenging environments. Furthermore, LROD introduces a parameter- -pacce regularization term to stabilize gradient flows, ensuring smoother optimization dynamics and improved robustness under varying degradation intensities.
We implement LROD into existing YOLO detectors, taking advantage of their real-time performance, resource efficiency, and suitability for edge deployment. This integration yields an efficient model, called Lipschitz-rogullarize YOLO (LR-YOLO YOLO), which can be scamlessly applied to YOLO series

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detectors (e.g., YOLOvI0 [8] and YOLOv8 19). As shown in Figure (d), our object detection achieves a smoother Lipschitz continuity compared to the cascade framework. Extensive experiments on image dehazing and low-light enhancement benchmarks demonstrate that IR-YOLOO improves detection stability and robustness compared to traditional cascade frameworks. In summary, our contributions are as follows:
Lipschitz Continuity Analysis:
we perform a detailed analysis of Lipschitz continuity in both the input space and the parameter space of image restoration and object detection networks. Our analysis uncovers critical mismatch in smoothness between these tasks, which potentially introduces instability and impedes effective integration. To our knowledge, this is the early work to provide a detailed Lipschitz continuity analysis aimed at understanding the instability challenges in cascade- based detection pipelines.
Dasschitz-Regulaiizee Framework: motivated by our analysis, we propose a simple and effective object detection framework that integrates image restoration directly into the detector's feature learning, harmonizing the Lipschitz continuity of both tasks during training. This design enhances smoothness and mitigates the instability inherent in traditional cascade-based methods.
Related Work
Object Detection Under Adverse Conditions. Existing research primarily focuses on cascade frameworks, where image restoration techniques such as image dehazing [00 low-light enhance- and all-in-one restoration [14] are used as pre-processing steps to improve image quality and enhance human trust in detection results compared to domain adaptation approaches [15).
ment [2 13
ReForDe 2 uses adversarial training to generate detection detection-friendly labels for fine-tuning restoration networks. SR4IR [16] introduces a training framework where image restoration is constrained by object detection, and detection training utilizes restoration outputs Image-adaptive techniques [ integrate differentiable image processing filters into the detection pipeline. FeatEnHancer [17] applies hierarchical feature enhancement to improve detection performance. Despite these advancements, the functional mismatch between restoration and detection networks is underexplored. Our work reports that the large disparity in Lipschitz continuity between the two tasks exacerbates non-smoothness when they cascaded, leading to instability under varying degradation intensities. To address this, we propose a hipschitz-regularre network, facilitating better harmonization between these two tasks.
framework that enhances the Lipschitz continuity of the detection
Lipschitz Continuity Analysis. Lipschitz continuity is useful in analyzing the stability and robust- ness of deep neural networks [18 19 20 Models with lower Lipschitz constants tend to exhibit better generalization performance, especially under adversarial conditions (11. This has motivated further research regularization techniques that constrain the Lipschitz constant to enhance model robust- ness. For instance, SN-GAN [2 controls the Lipschitz constant by restricting the spectral norm of network parameters, while other Lipschitz-based regularization techniques have been proposed to improve model stability (23]. Several studies have extended these ideas to network design [24), highlighting the critical role of Lipschitz continuity in controlling the smoothness and stability of neural networks. In our work, we analyze object detection stability under adverse conditions from both the input and parameter spaces using Lipschitz continuity as the lens of investigation. We demonstrate that the disparity in Lipschitz continuity between image restoration and object detection networks is primary source of non-smoothness and instability in cascade frameworks.
3 Lipschitz Continuity Perspective
3.1 Input Space Analysis: Model Stability in Adverse Conditions
Object detection in adverse conditions, such as haze or low light, is highly sensitive to variations in degradation intensity, including changes in haze density and luminance fluctuations. Traditional Image iitoorattoon>bbeer Detection cascade framework struggles with such variations, leading to (a), unstable detection results. As shown in Figure (a), even when partially mitigated by restoration, minor perturbations still cause significant shifts in detector features, exposing the framework's instability. To understand this, we analyze the problem through the lens of Lipschitz continuity, which quantifies model's 's sensitivity to input changes. Our findings reveal that the Lipschitz constant of
3

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Cascade
Ours
Image Restoration
Object Detection
Detectie
Jacobian Norm
Cascade
Our
Jacobian Norm
108
Coscale
Rss
20
(a) Distribution Detector Features Under Minor Variations
1.0
(b) Box-Plot Distribution Per-Sample Jacobian
Figure 2: Impact of haze density variations on feature stability and Lipschitz continuity. (a) Distribution of the detector backbone's 's features between two haze inputs x and + A under minor haze density variations A Pascal VOC [26] with synthetic haze. In the cascade framework. nearly half the features shift under slight haze density variations, while our Lipschitz-regularized object detection remains stable. (b) Box-plot distribution of Jacobian norms || V (ox))l each sample æ between image restoration and object detection task on Pascal VOC (26) with synthetic
haze. The Lipschitz constant of the object detection network is nearly an order of magnitude larger than that of the restoration network. This large disparity in Lipschitz continuity between the two tasks exacerbates the non-smoothness in the cascade framework. Our method constrains the Lipschitz constant of object detection to harmonize these two tasks better. ConvIR 11 and YOLOv8 9 are taken restoration and detection methods, respectively.
the detection network is nearly an order of magnitude larger than that of the restoration network, amplifying noise and disrupting stability under adverse conditions.
We begin by recalling the definition of Lipschitz continuity: A network f(; RD + R defined on some domain dJm(J) )) C IR with parameters 0, is called C-Lipschitz continuous if there exists real constant C >> 0 such that Van, 222 E dom(s) =I) 0) - [[a;2; 0)Ip S C/I simplicity, will compute the 2-norm, denoted || |]. throughout the rest of the paper, which can be easily generalized to other norms. Using Theorem 1 in (25). we know that for a differentiable, C- Lipschitz continuous network f(; 0) IR + R2 the Lipschitz constant of f(: 0) can be expressed as (f 0)) sup (f) | a (x; 0) suP=ędomi,)) V/ 0) where vaf( 0) is Jacobian of f w.r.t. input æ and || ||. denotes the dual norm (The dual norm of the 2-norm is itself).
22 ||p For
To quantitatively assess the Lipschitz constant of the image restoration and object detection network, we compute the above Jacobian norm for each sample x in the Pascal VOC dataset [26), considering variations haze density. As shown in Figure 2 (b), we observe that the Jacobian norm of the image restoration network ranges from 1 to 3.5 per sample, while the Jacobian norm of the object detection network nearly an order of magnitude larger than that of the image restoration network. This indicates that object detection has higher Lipschitz constant compared to image restoration. Therefore, the large disparity Lipschitz continuity between the two tasks leads to an unstable framework when they are directly cascaded. Specifically, even slight variations will inevitably be amplified by the restoration network since its Jacobian norm per sample exceeds 1, and further destabilized by the high-Lipschitz constant of the detection network with the cascade framework.
Remark 1. Image restoration networks exhibit smooth and continuous mappings, while object detection networks are more non-smooth from the perspective of Lipschitz continuity. This large disparity in Lipschitz continuity between the two tasks exacerbates the non non-smothhness when they are directly cascaded, leading to instability under variations degradation intensities.
3.2 Parameter Space Analysis: Training Stability
The disparity in Lipschitz continuity between restoration and detection networks extends beyond the input space, impacting their training stability. To understand this, we analyze the parameter space of the networks to capture how gradient updates influence model stability during optimization. Our analysis shows that restoration networks, with lower Lipschitz constants, maintain smooth optimization trajectories, while detection networks, with substantially higher Lipschitz constants, experience sharp gradient transitions and unstable convergence. This imbalance disrupts gradient flow, contributing to training instability in cascade-based designs.

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Cascade
Ours
Cascade 2i5
Image Restoration
Image Restoratiin ietorration
Object Detection
Object Deteectrr
(a) Landscape
(b) Optimization Trajectory
Figure Parameter-space smoothness and optimization stability comparison between the cascade framework and our Lipschitz-regularizz object detection. (a) Loss landscapes of restoration and detection tasks: restoration networks demonstrate smooth trajectories, while detection networks encounter sharp gradient transitions, indicating instability. (b) The cascade framework amplifies this imbalance, leading inefficient convergence and oscillatory optimization paths. (c) Our method introduces Lipschitz regularization to smooth the parameter space of object detection, enhancing stability and harmonizing with restoration. ConvIR I and YOLOv8 [9] are used as representative restoration and detection methods, respectively.
We extend the Lipschitz continuity analysis the parameter space: A network f fax; 0) defined on some parameter space & is called Lipschitz continuous in the parameter space there exists (f(((x;)) 0 such that 101, 0g O I=f 01) f(x 02)ll I Ce(f(z; 0) - 02ll. Due to the symmetry between and 0, an analogous result holds when the two variables are interchanged: The Lipschitz constant the parameter space of f f(;; f), defined on the parameter space O can be expressed Co (a;; f)) supøce o 0)], where Vof 0) represents the gradient of network parameters in the parameter space.
Given that the network trained using the gradient descent optimization algorithm, expressed as 0 0 Vo fa; ( 0) (n denotes the learning rate), the Lipschitz constant the parameter space is crucial for ensuring training stability. This is because the Lipschitz constant in the parameter space acts upper bound for the gradients of the network parameters during training.
The Lipschitz continuity in parameter space reflects the sensitivity of the model's output to variations in its parameters. To illustrate this, visualize the loss landscape by perturbing parameters along two directions, revealing their impact on optimization smoothness and stability. Specifically, we use the visualization method in (27 let 0 represent the fixed model parameters, select normalized direction vectors 5 and in the parameter space, and plot the function f(a, 3) = L( + as + B7) on the surface, where C is the loss function, and and are the coordinates the surface.
As shown in Figure 3 (a), the loss landscape of the image restoration network exhibits a smooth loss function, while the loss landscape of the object detection network is notably rough. This reflects differences in their Lipschitz constants parameter space: restoration networks tend to have lower Lipschitz constants, giving smoother gradients, while detection networks exhibit higher Lipschitz constants, showing sharper transitions, and increased sensitivity to parameter changes. Figure (b) further illustrates the optimization trajectories, where restoration follows stable paths, while detection experiences frequent shifts, indicating instability. This imbalance disrupts gradient flow during joint training, resulting in unstable convergence and reduced optimization efficiency.
Remark 2. Image restoration networks with lower Lipschitz constants exhibit smooth optimization trajectories, while object detection networks with higher Lipschitz constants experience sharp gradient transitions and unstable convergence. This imbalance in the parameter space between these two tasks results in training instability and reduced optimization efficiency in cascade-basee designs.
5

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Lipschit-Regguarized Object Detection
The analysis in Section reveals the disparities in Lipschitz continuity between restoration and detection networks, manifesting in both the input space and the parameter space. Driven by this, we propose lipschitz-regullrizzed object detection (LROD), simple and effective framework that harmonizes restoration and detection through targeted Lipschitz regularization. Specifically, LCOD introduces two core mechanisms: Lipschitz, regularization via low- low-Lipschitz restoration to constrain the Lipschitz constant of object detection in the input space, and 2) Lipschitz regularization via parameter- space smoothing constrain the Lipschitz constant in the parameter space.
4.1 Lipschitz Regularization via Low-Lipschitz Restoration
Lipschitz continuity analysis in input space (Section 3.1 shows that image restoration networks exhibit smooth, continuous mappings, while object detection networks more non-smooth. By leveraging the low-Lipschitz properties of the restoration task, we integrate restoration learning into the detector backbone's 's feature learning, constraining the Lipschitz constant of the object detection task in the input space. This better harmonizes the detection task with the low-Lipschitz restoration.
Remark 3 (Lipschitz Regularization via Low-Lipschitz Restoration). Let: fe, fo, fo, denote the object detection model, where for (:;66) is the backbone network parameterized by tb. and fer (:: Ba) is the detection head parameterized by 0a. Similarly, let: 99,.0. fe, fo, represent the image restoration model, where [o.(:;,) the restoration head parameterized by fy. sharing the same backbone fo.- Given weighted combination of the detection loss and the restoration loss:
C(0b, 0a 0r) Efee(ferce X Lres (90,,99))))) X>0
Let Lip(Jo,) == supx f1 (2=) be the Lipschitz constant of J'e defined by jacobian norm. If:
1. fres is Lipschitz continuous and ||V o, Fres (90,,00 Ill I G for G < [o, o, faet (f) There exists a training sample x and y > O such that: (Vo.ll (x*) Vo, Cres (90,,0.)) 2 7s
then under continuous time gradient descent 6, (*+1) + 0g μ Vo, [(O,, 0d. 0x) (fr denotes the learning rate), the evolution of the Lipschitz constant satisfiex:
d [Lip(Sa]]] S -
where E(t) = -Veelll (x=))l, Vo, Caer (fe,,e)) is the unconstrained change induced by the detection loss and 7 is the regularization via the restoration task.
This suggests that integrating the image restoration task directly into the detector's 's feature learning by sharing the detector's backbone helps suppress the model's sensitivity imput perturbations during training, effectively acting as a Lipschitz regularization, The detailed proof is in Appendix A
Specifically, we extract low-level features from the first three stages of the detector backbone, which preserve essential spatial and textural information for image restoration. These features are then passed through a restoration-specifie head obtain the restored images. By leveraging the inherently smoother Lipschitz continuity of the image restoration task, this restoration loss implicitly regularizes the feature representations used for object detection during training, thereby constraining the Lipschitz constant of the detection network in the input space. As shown in Figure 2 (a) and (b), our Lipschitz- regularized object detection exhibits smoother Lipschitz continuity compared both the original object detection and the cascade framework, with lower Lipschitz constants and more stable detector features under varying degradation intensities.
4.2 Lipschitz Regularization via Parameter-Space Smoothing
Lipschitz continuity analysis in parameter space (Section 3.2) shows that tow-Lipschitz restoration networks maintain smooth optimization trajectories, while high-Lipschitz detection networks ex- perience sharp gradient transitions and unstable convergence. improve harmony between these tasks and ensure training stability, we constrain the Lipschitz constant of the detection networks in the parameter space. We introduce parameter-space regularization term to stabilize gradient flows, promoting smoother optimization dynamics.

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Remark 4 (Lipschitz Regularization via Parameter- Space Smoothing). Let 0 = 8, U is the full parameter set of the detection model. The parameter-spen spacerr-peeeeeee regularization term is defined as the gradient norm with respect to the model parameters, denoted by (Vooo(z)
Full framework. The Lipschitz-regularizze object detection (LROD) framework incorporates the above two regularizations to ensure stable and efficient training. The total loss function is defined as:
Liotal = Lett + Lres + >p [ooo(())]
where Laet is the detection loss, fres is the restoration loss, computed as a Charbonnier loss 22 between the restored image and the ground truth clean image, and || [ is the regularization term. The weights À and Xp used to balance the restoration and regularization terms, respectively.
We implement this framework as Lipschitz-regularzzz detectors. As illustrated in Figure 3 ConvIR [II] and YOLOv8 [9 are employed as representative restoration and detection methods, respectively. LR-YOLO smooths the loss landscape of object detection compared to traditional cascade frameworks, better aligning with image restoration during training. This results in smooth gradient flow, improved stability, and more efficient optimization.
YOLO (LR- YOLO), which builds upon YOLO
Experiments
5.1 Experimental Settings
Dataset. Datasets cover two challenging conditions: hazy weather and low-light environments. For both settings, we use Pascal VOC (26] and COCO [29] datasets for training and validation following the degradation setting from 2 51, and real-world datasets for oft-of-domain evaluation.
Val consist of 8, 111 and 2, 734 images respectively. Haze is synthesized online during training using the atmospheric scattering model with 5 E [0.5, 1.5), while validation images are synthesized offline once for reproducibility; b) DOC__Drk_Tiin Train and VOC_ YOC_Dark_WWe Val consist of 12, 334 and 3, 760 images respectively. Low-light is simulated online during training and offline for validation via gamma correction with E [1.5, 5]. The classes in both the training and validation datasets for haze and low-light conditions align with those in the real-world datasets; c) COCO @DDCO_Haze_iae Hae_Haaa__rrre TTrize and COCO Dark__rrttt consist of 118, 287 training images, and COCO Haze_ Val and coCO_Dark__ Val contain 5, 000 validation images.
1) Training and Validation Data: a) VOC Harzeeaee_ Train and
2) Real-world Test Data. We adopt two benchmark datasets for the out-of of-domain evaluation: a) RTTS (30) contains 4, 422 real-world hazy images annotated with 5 object categories, i.e., Person, Car, Bus, Bicycle, and Motorbike; b) ExDark [31] contains 2, 563 real-world low-light images labeled with 10 categories, i.e., People, Car, Bus, Bicycle, Motorbike, Boat, Bottle, Chair, Dog, and Cat.
Metrics. We evaluate object detection performance using mean Average Precision (mAP) an IoU threshold of 50%, which excludes difficult objects by default. Additionally, we report dificatt. which includes all objects, including challenging cases (e.g., occluded targets) on the Pascal VOC (26) and RTTS 30 datasets. For the COCO dataset (29] we adopt standard COCO-style metrics, including mAP averaged over IoU thresholds from 0.5 to 0.95 (in 0.05 increments), along
Evaluation
MAPaificat.
with APso. AP75. and scale-specific scores: AP3 (small), APM (medium), and AP (large).
Implementation Details: We adopt Y0LOv10-s and YOLOv8-s as the baseline detectors. For training, the loss weights are to À 10 and A 0.01. We use the SGD optimizer with initial learning rate of 1 x 10 and weight decay of 5 x 10-4. The model is trained on an RTX 4090 GPU for 100 epochs with a batch size of 16, requiring approximately hours. Input images are resized to 640 x 640, and standard YOLO data augmentation techniques (e.g., random flipping and affine transformation) are applied. For experiments on the COCO dataset, we use 8 RTX 4090 GPUs with a batch size of 16 per GPU. Training is conducted for 300 epochs and takes approximately 48 hours.
5.2 Object Detection under Adverse Conditions
T presents a method comparison of object detection under two adverse conditions: hazy weather, evaluated on the YOC_Haze Val and RTTS (30) datasets, and low-light environments, evaluated on the DoC__ark___ Val and ExDark [3T datasets. We compare various image restoration methods, including SFNet 110, ConvIR [T. LLFommer 12], and RetinexFormer (13), all of which are trained
7

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79.1
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46.5
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Table 1: Comparison under two adverse conditions: haze weather and low-light environment. Left: Results on VOC_Haze Val and RTTS [30), with models trained on YOC_Haze JoC_Haze_Train. Right: Results on VOC_ VOC_Dark_ Val and ExDark (II, with models trained VOC_Dark Train. In the cascade framework, indicates adversarial training [2]. and $ denotes alternating training [16].
Methods
COCO COCO__Hate Val
COCCO_Dad Vol
mAP
AP50
AP15
AP3:
AF
AP
mAP
AP50
AP1z
AF'S
AP
APr.
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20.3
23.8
22.0
22.8
29.1
31.3
85.2
34.2
45.1
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InsuucUR
14
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8
33.4
47.7
36.1
15.2
36.8
49.0
30.2
43.8
32.3
14.3
32.9
44,5
+YOLOx5
YOLOx8
36.4
51.4
180
39.8
51.6
33.5
47.8
17.7
48.
GDMP 0 YOLDV8
3666
51.8
90.4
18.1
40.6
51.5
33.4
47.6
36.0
17.5
35.9
43.6
ReatEniTancer
YYLO08
36.7
52.2
39.7
18.3
40.5
52.1
36.1
89.2
37.1
17.9
37.0
48.5
JR-YOLLOv8:0nm (Ouns)
37.7
53,3
19.5
41.6
52.7
35.3
90.5
37.9
19.0
38.3
49.7
Table Comparison COCO COCO_Haze Haze Val and COCO Dark Val datasets under haze and low- light conditions. All models are trained from scratch on COCO Haae_HHzeeeha Truin and COCO Dark _Train respectively. The indicates adversarial training 2 and denotes alternating training (16).
Methods
ComvR
LLFomer
Retinesfomee
EnstruedR 14
LA
GDIP 3
FeuEaHaneer
17
Ours
(M)
31.15
Pleps (C)
775.17
22:52
15.57
Table 3: Computational complexity comparison. Our method shows lower computational complex- ity in terms of the number of parameters (Params) and floating point operations (FLOPs).
on degraded images and used to restore inputs before detection. We further consider two joint training strategies: 1) Adversarial training [2], where restoration networks are fine-tuned to generate detection- friendly images; 2) Alternating training [16), where restoration is supervised using detection- perceptual losses and detection is trained on restored outputs. Furthermore, we include end-to-end
methods for comparison, including IA []], GDIP [3) and FeatEnHancer [17]. They trained directly on degraded inputs. All models are trained from scratch on the VOC HDC__Hzee Haze_Train Dark_Train
Train and Train datasets, respectively. Our method outperforms other methods when using both YOLOv10 and YOLOv8 as object detectors, achieving mAP improvements 2.0 and 2.9 on RTTS, and 2.9 and 2.7 ExDark, respectively. Table 2 shows comparison COCO Haze Val and COCO coro_Dark___ Val datasets, trained on COCO Haze _rain and COCO Dark Train, respectively. We compare the all-in-one restoration method InstructIR [14]. Our method consistently improves performance across all evaluation metrics, achieving mAP improvements of 1.0 and 1.2, respectively.
5.3 Evaluation and Analysis
Computational Complexity Evaluation. Table presents comparison of parameters (Params) and floating point operations (FLOPs), showcasing the inference efficiency of our framework.
Lipschitz Regularization Ablation Study. We evaluate the impact of two Lipschitz regularization parts (low-Lipschitzz restoration learning Lres and parameter-space smoothing [[)))o(=)))) The evaluation is conducted on the RTTS and ExDark for out-of-domain performance, presented in

---

fres [aaso(a))
Detection Nusus Featura Map
YOLOv YOLOv10
46.0
50.6
48.1
47.2
51.5
49.2
53,8
51.3
53.6
50.1
53.2
54.5
w/o Restoration Learning
W Restoration Learning
Table 4: Lipschitz regularization ablation study. We evaluate the effect of two Lipschitz regulariza- tion parts fres and | [=)
Figure 4: Feature visualization. We visualize the feature maps in the backbone of our model trained without and with Lres.
Table Incorporating both restoration learning and parameter space smoothing during training improves synergy between detection and restoration, leading to mAP gains of 3.2 for YOLOv 10 and 3.9 for YOLOv8 in R77S, and 3.2 and 2.9 on ExDark, respectively, compared to baseline methods.
Restoration Learning Aallysis We visualize the backbone features our model trained with and without restoration learning fres shown in Figure[4 Integrating restoration learning into the detector's 's feature learning facilitates the enhancement of degraded image features in the backbone, resulting improved detection (e.g. complete detections of objects like the stop sign and motorcycle).
Alternative Regularization Ablation Study. We com-
Method
Hoseline
SNK
PGD
3R
Ours
pare method with two alternative regularization strategies-SSeccralll Norm Regularization (SNR (22)) and adversarial training via PGD [32-bb by training on
RI7S
49.3
20.1
40.8
$3.2
Table 5: Alternative regularization ablation study.
VOC_Haze Train and evaluating out-of-domain on RITS.
As presented in Table 5 our approach attains the best R77S performance, surpassing both SNR and PGD. Unlike SNR, which constrains weights globally, our method penalizes [ reducing output sensitivity to parameter changes and enabling input- aware smoothness. Compared to PGD-based adversarial training, which requires generating perturbed inputs and increases training cost, our approach achieves implicit robustness without adversarial examples, resulting in more stable and efficient training and no observed degradation on clean inputs.
Architectural Variants Ablation Study. We ablate how deeply to share the encoder between detection and restora- tion by varying the number of shared stages, training VOC_Haze_Tvvee Train and evaluating out-of-domain on RITS.
Sharing Baseline F1-22
PI-23 (Ous) FI-F4
Table 6: Alternative variants abla- tion study.
As summarized in Table 6 shallower sharing (F1-F2) provides insufficient regularization, while deeper sharing (F1-F4) introduces task interference, supporting our design choice of the first three stages (FI-F3).
Regularization Coefficients Ablation Study. We ab- late the input-space and parameter-space regularization strengths by sweeping À E {0, 10, 20} and X {0, 0.005, 0.01, 0.02), training on VOC Haze Train and evaluating
0
10
10
20
2,
0.005
0.02
0.01
0.01
0.01
RITS
49.3
$2.9
53.0
53.2
53.1
52.8
on RTTS. As reported in Table 7 method consistently outperforms the baseline across range of coefficient values, with only minor performance variation over the sweep, demonstrating robustness to the choice of regularization magnitudes.
Table 7: Regularization coefficients ablation study.
Lipschitz Continuity Analysis. We analyze changes in Lipschitz continuity both the input and parameter spaces during training. Specifically, we monitor the upper bound of the Jacobian norm sup=edom(() || fe(x)) in the input space, where dom(f) represents the domain of input images from Pascal VOC. Additionally, we track the gradient norm || V [x))l in the parameter space. As shown in Figure 5 LR- LR-LOL trained with Lres reduces the Lipschitz constant in both the input and parameter spaces compared to with [x)) further promotes Lipschitz continuity in the input and parameter spaces.
and YOLOv8 during training. Training
Generalization on Other Detection Paradigm. We further validate the generalizability of our LROD by integrating it into the shared backbones of a transformer-basel detector (RT-DETR (33)

---

Input Space
Parameter Space
Jacobian Norm (Upper Bound)
Gradient Norm
400
125
100
VOLOvB
300
ConvIR->
YOLOv8
75
200
60
LR YOLOVE (Ours)
LR. YO (Ours)
25
YOLVVL (Ours)
LR-VOLOVE (Ours)
20
40
60
80
100
10000 20000
30000
40000
50000
Epoch
Iteration
Figure 5: Comparison of changes in Lipschitz continuity in both the input space and parameter space during training. Methods include ConvIR R YOLLO88 C- (Cascade), YOLOv8 (Baseline), LR- YOLOv8* (only trained with Lres), and LR-YOLOv8 (trained with both Lrss and [V)](
Method
RE-DETR
Mation
Rain
HazeHaze_
VOC_Hazr__ Val RITS
YOLO.E
50.8
53.1
60.8
50.1
ConviR
11
YOLLON
30.1
79.9
80.5
79.2
CoaviR 11
76.0
43.7
78.5
44.1
[T YOLOKS
78.0
1A
0
76.8
43.6
78.6
41.3
GDIP
YULOWS
80.4
78.3
FeunerFancer
73.3
42.4
77.7
39.4
FeateeHanneer
T
YOLO08
80.2
79.6
79.6
78.9
LROD (Oun)
78.9
45.1
90.2
45.9
TR-YDLLOvS (Durs)
82.3
82.5
83.0
81.6
Table 8: Generalization on other detection paradigm. We integrate our LROD into RT-
Table 9: Generalization on other degradation. We assess the robustness of our method under motion blur, rain, snow, and haze-raie rain mixture.
DETR 33 and Faster-RCNN (34..
and a two-stage detector (Faster R-CNN +4 ). All models are trained on VOC Haze Train and
evaluated on both the synthetic
Val and real-world RTTS dataset. As shown in Table X LROD consistently outperforms other methods when using other detection paradigms, achieving mAP improvements of 1.4 on R77S, supporting LROD as plug-and-play regularization framework.
Generalization on Other Degradation. We further assess robustness under additional adverse con- ditions-motion blur, rain, snow, and a haze-rain mixture-by constructing matched train/valide aain//vlidation splits for each degradation and retraining all methods per setting. As reported in Table our method consistently outperforms existing methods, achieving mAP gains of 2.1, 2.6, 2.5, and 2.4, respectively. These results highlight the versatility and robustness of our method across diverse degradation.
Conclusion
In this paper, we revisit the integration of image restoration and object detection under adverse conditions through the lens of Lipschitz continuity in both the input and parameter spaces. Our analysis reveals that the inherent mismatch in Lipschitz continuity between these tasks introduces instability and moothnsthssss when directly cascaded. To address this, we propose a Lipschitz- regularized framework that harmonizes the two tasks by constraining the Lipschitz continuity of object detection. This is achieved through low-Lipschitz restoration learning to smooth perturbations before detection, alongside parameter-span regularization to stabilize gradient flows during training. We implement this approach as Musschiz--Reglariize YOLO (LR-YC YOLO), which extends to existing YOLO detectors with minimal overhead. Extensive experiments on haze and fow-light benchmarks show that method improves detection stability and optimization smoothness, contributing to more robust performance challenging environments.
Limitation and Future Direction. While our method has been validated across range of adverse conditions-inn including haze, rain, snow, low-light, and mixed weather current limitation that each input is assumed to contain only single type of degradation. A valuable future direction would be extend our framework to handle inputs affected by multiple, concurrent degradations. Another promising direction is to extend our Lipschitz-continil
analysis to camouflaged object detection (COD 35 36)), as COD involves detecting objects with ambiguous, low-contrast boundaries, posing challenges similar to those in cascaded systems under adverse conditions.
10

---

Acknowledgements
This work supported in part by the National Natural Science Foundation of China (NSFC) under Grant Nos. 62376292, 62325605, and U21A20470; the Guangdong Provincial General Fund under Grant No. 2024A1515010208; and the Guangzhou Science and Technology Program Project under
Grant Nos. 2025A0435465 and 2024A0406365.
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12

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Appendix
A Detailed Proofs
Remark 3 (Lipsehitz Regularization via Low-Lipschitz Restoration). Let: f6,.04 Sox So denote the object detection model, where fo, (:; 0.) is the backbone network parameterized by 0b, and (: Oa) the detection head parameterized by 6a- Similarly, let: 90,.0. fo. fo, represent the image restoration model, where fo, (o. 0.) 3 is the restoration head parameterized by 0r, sharing the same backbone foy. Given a weighted combination of the detection loss and the restoration loss:
L(0b, Bas 0,) fdet (fo,,e) x fres (905.0.),
x>
Let Lip(Jo.) == sup fo, (a)) be the Lipschitz constant of fo, defined by jacobian norm. If:
Cres is Lipschitz continuous and || o, Cre )l S for G < [1 Ldet (fo
There exists a training sample x² and 7 > 0 such that: (Vo, II (x*) (x*)), Va, Cres (90).0)) 2 7
then under continuous-tin timm gradient descent 0g (t+1) t 0, (1)
Ve, C(o, 0s. 0,) (p denotes the
learning rate), the evolution of the Lipschitz constant satisfies:
dt [Tip(So.)] +
where E(t) == 1o, (x=")l, Vo, Laet (for.o)))))) the unconstrained change induced by the detection loss and is the regularization via the restoration task.
This suggests that integrating the image restoration task directly into the detector's 's feature learning by sharing the detector's 's backbone helps suppress the model's sensitivity to input perturbations during training, effectively acting as a Lipschitz regularization.
Proof. Using Theorem in 25 the Lipschitz constant of fo, is:
Lip(fe,) = sup || (=)l
Let xt be the input that attains or approximates this supremum. Then, during continuous-time gradient descent:
dt [Lp((o.)) dt 1J (x=))I (VollJ
d
(=v))l=(VVllJJ,, (a*))l2, - Vo, C(0, 0.))
Substituting the joint loss:
d
dt [Lip(f.)] - -vo (x')ll, Vo, (fee(oo X Vo, (9000))))
Breaking into components:
d [Lip(fo.) (Vo,,1JJo, (o"J,(("""1 (x") - Vo, Lact (Fon x. (VoillJ (a*)1l, Vo, (90
By Assumption 2, the second term is lower bounded:
V [ Vo 2g
Define the first term as {(t), then:
Lip(fo) < -xy E(t)
dt
which completes the proof.
13

---

Low-Lave Featines
Upsample
CSPLayer
CSPLayer
F1
Downsample
CSPLaaerr
CSPLayer
CSPLayer
CSPLayer
Feature Extraction
Restored Image
Low-Lipschitz Restoration Module
res
YOLO
Head
YOLO Backbone
YOLO Neck
YOLO
Head
YOLO
Degraded Image
Head
Detection Results
YOLO Detector
ddet
Figure 6: The overall architecture of Lipschitz- YOLO (LR-YOLO).
Dotsset
bicycle
Dus
motorbike
Total
VOC Train
8111
13256
1064
3267
922
1052
19561
VOC Huze objects)
2734
4528
1201
213
325
6601
7674
RTTS
50
4522
7950
334
18413
1838
802
29577
KTTS (all objects)
4322
11366
698
25317
2590
1232
41203
Table 10: Statistics of haze datasets in terms of image count and object annotations per class.
B
Detailed Model
To efficiently and effectively harmonize image restoration and object detection, we integrate image restoration learning into the feature extraction process of the object detection backbone. This integration implicitly enforces Lipschitz continuity during training, thereby enhancing the stability of the detector under varying degradation intensities. As illustrated in Figure 6 we extend existing YOLO detectors by extracting low-level features from the first three stages of the backbone without modifying the original network architecture. These features are then processed by lightweight restoration-awart module, which reconstructs clean version of the input image and facilitates the learning of smoother and more stable representations within the detection network.
The YOLO architecture is one-stage object detection framework that performs detection in single forward pass, achieving high efficiency and speed. It consists of three main components, i.e., Backbone, which extracts visual features from the input image; the Neck, which aggregates multi-scale features to enhance representation; and the Head, which predicts bounding boxes, class scores, and objectness. Due its high computational efficiency and ease of deployment on edge devices, YOLO is widely used in real-time detection applications.
YOLO Detector.
Low-Lipschitz Restoration Module. To improve the stability of object detection under adverse imaging conditions, we introduce Restoration-Aware Module integrated into the YOLO framework. As illustrated in Figure 6 we extract low-level features from the first three stages of the YOLO backbone (denoted as Fl, F2, and F3), which preserve rich spatial and textural information essential for image restoration. Inspired by the design of the YOLO Neck and Head, these features are passed through restoration-specife neck and decoder composed of multiple Cross Stage Partial layers (CSPLayer). The module adopts densely connected architecture that facilitates multi-scale feature fusion, which is crucial for effective restoration learning. By progressively refining the low-level representations, the module reconstructs a restored version of the input image that is less affected by visual degradation. This restoration-awant module not only contributes to the stability of YOLO detectors during training due the inherently smoothness of restoration, but also enhances the low-level features used by the detector for downstream detection tasks.
14

---

Dataset
image
person
bieycle
car
bus
motorbike
bost
bottle
cat
chair
dogg
Total
KOC_Dark_
12334
13256
1064
5267
822
1052
1140
1764
1593
5152
2025
29135
VOC, DiC_Dark
3760
4528
337
1301
213
325
263
400
358
756
489
8939
VOC_Duk_War (all objocts)
3760
5183
389
254
393
646
308
1268
10930
2563
515
Table 11: Statistics of low-light datasets in terms of image count and object annotations per class.
C
Detailed Datasets
Datasets cover two challenging conditions: hazy weather and low-light environments, For both settings, use real-world datasets for out-of-domain evaluation and construct synthetic train-
ing/validation sets based on PASCAL VOC [26]. following IA-YOLO [1. ReForDe [ and Vat [5]
1) Training and Validation Data: We construct synthetic datasets by selecting PASCAL VOC [26
images containing the relevant object categories:
VOC Haze Train and VOC Haze Val consist of 111 and 2, 734 images respectively. Haze is synthesized online during training using the atmospheric scattering model with E [0.5, 1.5). while validation images are synthesized offline once for reproducibility.
vOC Dark Train and VOC Dark Val consist of 12, 334 and 3, 760 images respectively. Low-light is simulated online during training and offline in validation via gamma correction with E [1.5,5].
2) Real-world Test Data. We adopt two benchmark datasets for the out-of-domain evaluation:
contains 4, 322 real-world hazy images annotated with 5 object categories, i.e., Person, Car, Bus, Bicycle, and Motorbike.
RTTS 330
contains 2, 563 real-world low-light images labeled with 10 categories, i.e., People, Car, Bus, Bicycle, Motorbike, Boat, Bottle, Chair, Dog, and Cat.
ExDark [3
The object annotations per class the above datasets are presented in Table 10 and Table II
D Detailed Detection Results
We report the average precision for each category on the VOC_Haze Val and RTTS datasets, as shown in Table and on the VOC_Dark_Val and ExDark datasets, as presented in Table 14
E Image Restoration Evaluation
evaluate the restoration performance our LR- YOLO under haze and low-light conditions using peak signal-to-noies ratio (PSNR) for pixel-level fidelity and learned perceptual image patch similarity
(LPIPS) [37] for perceptual similarity. Table 13 presents the restoration results on VOC VOC_Haze Val and VOC Dark Val. We compare
method with the image dehazing technique ConvIR [II]. low-light enhancement method Retinexformer [13), and image adaptive methods IA M and GDIP (3). Our full model achieves the best LPIPS score and competitive PSNR on both VOC Haze Val and VOC Dark_ Val, outperforming the baseline YOLOv8 and image adaptive pipelines. Additionally, restoration-only variant 1R-YOLLO8 (Restoration-One trained only with restoration learning) achieves a balanced improvement in reconstruction fidelity.
F Qualitative Comparison
Figure 2 (a) illustrates that the detector features of the cascade method are highly sensitive to minor haze density variations Az, while our Lipschitz-eegularized framework maintains stability. A qualitative comparison detection result stability is presented Figure When two haze inputs and æ: + Ae with slight haze density variations Ar are fed into the model, the detection results of the cascade method (ConvIR- (ConvIR-+OLLOR YOLOV8) exhibits significant instability even though those haze can be mitigated by the image dehazing method. For example, car is detected in one case but
15

---

Methods
mAP
Ponun
Car
VOL. Hase Val
Bas
Ricycle
Mutcehike
mAp
Rensm
Car
RIT3 59
Rix
Ricycle
Motecbik
YOLOvIO
50.
55.3
63.5
46.3
68.1
19.55
42.6
10.7
48.9
20.5
41.0
31.5
SPNo-YYLLOKU
35,4
SFNG-YY0L.vi0
79.1
80.5
83.6
77.
76.9
77.3
46.5
75.4
54.8
24.9
42.1
38.0
SPNa-YYOLOvuf
72.4
ComdR-Y0LO0v00
72.6
36.3
Com1R-1Y0L0v100
80.1
80.9
$4.4
79.2
77.3
78.6
46.6
73.2
55.3
25.0
42.4
37.0
CowdR->YOLOv100
72.0
10
79.2
79.3
83.4
76.8
79.4
77.4
47.2
73.2
54.6
24.6
45.3
38.1
Feaffaftnnee=-DD Ov
79
79
82.9
78.4
RO.0
78.6
46.7
72.0
53.4
22.9
43.8
36.6
IR-YOL.0v10
82.5
82.0
86.6
79.7
83.4
81.8
49.2
74
58.5
27.7
44.9
42.0
SPNoO-YY
77.1
37.8
SPNu-+YOUL0sa
808
82.0
85.2
78.2
79.4
78.9
49.1
75.6
59.2
25.2
47.3
36.0
CondR-=YOLO08
80.
81.3
34.8
78.2
79.7
78.5
49.3
75.3
59.5
24.2
45.9
28.5
Yom
80.9
$5.6
77.3
79.7
79.6
49.5
75.3
25.7
47.7
39,0
Y
8144
35.9
77.
$1.3
79.9
30.1
75.6
00:1
25.8
69.4
29.5
IA-YOLOGE
8015
81.6
85.5
77.2
90.8
75.0
47.7
75.3
58.7
25.6
44.6
36.5
GDIP-
$1.0
81.7
85.9
78.1
79.9
79..
50.3
75.8
59.7
27.8
49.9
38.0
ReatFnHanczrr- YDL Ov8
81.2
81.4
85.3
77.0
81.8
80.4
45.4
74.8
57.9
76.1
47.1
40.7
IR-YOLO&
Methods
mAP
VOC Haze Val (all object))
Car
Motochike
RTTS (all obfeeas)
50]
Dicycle
Motechike
40.6
SPNo-+Y00.0v10
71.1
67.5
70.1
36
19.5
29.1
SINe-+Y000+00
738
76.7
70.4
71.5
73.3
39.3
60.4
48.3
20.7
38.0
28,9
SPNa-YYOLOvi0
728
69.1
71.6
29.1
OmmRR-Y0H.0010
72.8
7644
75.0
69.3
71.5
71.6
38.7
58.1
46.4
19.9
40.0
20.4
ComdR=>YULov10f
1m
74.0
77.3
77.0
69.3
72.3
74.3
39.9
60-2
40.0
20.2
59.8
30.2
IA-YOLOV-10
73.0
76.5
15.7
69.4
72.8
70,9
37.3
$6.5
45.8
19.5
35.6
28.7
GDIP-YOLLOv10
73.1
76.4
75.4
69.5
71.0
73.0
39.8
60.5
46.5
22.6
59.8
29.5
Ieataalances---0e
73.4
LR
71.1
77.4
YOLOvs
44.7
50.1
53.8
41.7
42.1
35.6
35.8
$4.2
40.8
15.1
33.5
23,4
SPNa
70.1
72.7
71.7
68.2
69.4
68.6
35.9
55.7
41.6
18.8
35.7
27.9
37Ne-=YOLO<a
SPNo--Y00.00a
71.7
75.1
73.2
68.9
69.5
71.4
36.0
$5.0
42.6
19.1
34.4
38.2
OmmRR-X00.008
72.2
75.3
73.3
70.5
7088
70.9
36.0
55.7
42.0
19.3
35.8
27.3
CowtR->YULOvs
72.9
37.2
28.4
YomdR-YYOLOusf
72.6
76.0
33.7
7012
7088
72.5
36.5
55.9
42.8
19.4
35.3
20.0
MA-YOLO4S
72.0
74.5
74.0
68.1
70.8
35.8
55.5
43.4
18.3
34.3
27.8
GDIP-
PeatEallance-- YOLOvs
71.2
LR-YOLOs8 (Ouns)
74.4
76.7
713
74.8
39.1
45.9
21.3
37.3
33.0
Table 12: Detailed results on YOC_Haze Val and RTTS
130 with models trained on
Train.
VOC Dark
Methods
Methods
LPIPS +
PSNR
LPIPS
PSNR
ConviR 11 YOLOVS
0.180
25,44
Retinexformer
13 YOLOV8
0.293
21.46
IA
0 YOLOv8
0.270
13.12
IA [ YOLO.S
0.195
20.73
GDIP 3 YOLOV8
0.234
15.75
GDIP B YOLOv8
0.189
(Baseline)
13.51
YOLOvw (Baseline)
LR-YOLOvE (Restoration-Only)
0.195
23.72
LR-YOLOvE (Restoration-Only
0.245
21.19
LR-YOLOv8 (Ours)
0.133
22.72
LR-YOLOv8 (Ours)
0.179
21.05
Table 13: Restoration results on
Val and YOC_Dark_L_ Val.
not in another, and person is suddenly undetected. This highlights the instability inherent in the cascade framework. Visual examples in Figure (haze condition) and Figure 9 lig-tight condition) qualitatively illustrate the effectiveness of method in improving detection accuracy and perceptual quality, thereby enhancing human trust in detection results.
16

---

Methods
VOC Dark
maA
Person
Car
Bus
Blcysle
Matcebike
Reat
Bortle
Chair
Dog
Car
YOLOv10
62.1
68.7
72.9
69.0
70.2
67.1
56.2
47.0
43.0
61.7
65.3
YOLOv10
65.6
72.6
78.0
71.8
74,0
70.7
59.0
46.9
46.2
66.1
70.3
L..ormer -YOLOv00
64.7
73.9
77.4
69.7
73.5
71.7
56.4
47.2
43.1
65.0
68.6
Fororrrr YOLOV10
78.2
71.8
70.6
66.3
73.3
78.8
73.6
72.9
70.7
39.8
49.7
46.0
66,4
71.7
Reinen
66.0
74.8
78.5
72.7
75.4
72.7
$7.2
49.5
45.2
64.9
69.2
Reineafonset-
IA > YOLO.10
66.0
73.1
78.5
68.2
74.5
69.4
60.6
52.0
48.2
67.1
68.0
-
65.8
74.3
77.9
71.2
77.4
72.5
56.5
49.4
45.4
67.0
66.8
FestEaHancer 1Y0LOv1D
75.3
79.1
73.6
LR (O0)
70.6
77.6
82.5
76.3
78.3
75.9
65
56.3
52.1
69.3
72.5
76.1
66.2
74.5
80.0
71.5
74,3
71.7
99.0
45.4
47.2
67.9
70.3
L.Fomeer-YOLOvS
66.2
76.3
80.6
71.9
75.1
71.7
59.2
45.8
46.2
65.3
70.0
LLFormer- YOLOvS
ReiineFoomer .YOLO.8
67.8
76.5
81.1
73.5
73,8
71.0
62.9
49.8
47.7
69.4
72.2
ReinexFommrr>>O00000
77.5
80.9
72.8
70.2
Reinossommxr=>OLLL4
IA-> YOLDv8
66.5
73.2
79.8
70.7
73.1
73.0
61.6
50.1
48.6
66.1
68.4
GDIP CDIP-YOLO+s
68.9
77.1
81.6
73.1
76.2
75.0
61.9
51.4
49.9
69.2
73.3
PeatPaHancer YOL.0
75.8
79.7
73.2
71.3
LR- LR-YOLOV8 (Ours)
71.7
78.5
82.9
77.2
79.7
78.3
62.9
60.1
52.6
70.3
74.3
VOC Dark Val (ell objects)
Methods
Mutorbike
YOLOvTO
55.8
63.8
66.2
61.3
64.0
61.3
46.1
36.7
33.9
66..6
64.3
58.7
69.6
70.1
64.1
67.3
65.5
46.3
36.1
36.6
63.9
67.8
L..oormer YOLOv10!
58.8
70.3
71.0
64.6
67.2
66.1
45.7
36.9
36.6
61.9
67.6
-
59.2
70.3
71.1
64.4
67.7
67.2
46.9
37.8
36.5
63.0
67.4
ScinesFomx==YYLO0
59.5
70.2
70.9
66.0
65.3
64.5
18.4
38.6
37.2
64.55
69.4
Reineefoomee--OLLo00
60.0
71.5
71.5
65.1
67.4
67.8
47.5
38.7
38.5
62.8
69.0
61.0
71.4
72.2
69.1
68.8
40.9
38.6
64.6
69.4
[A YO1.D01
59.2
68.5
70.5
64.7
65.4
66.9
48.0
40.1
38.4
62.9
66.9
71.5
61.8
69:7
69.9
65.6
69.3
70.0
47.0
41.9
40.7
65.4
68.9
(R-YOLOv100Ours)
73.3
70.1
72.3
48.2
42.3
67.1
72.7
YOL
55.0
62.3
64.2
61.7
62.9
60.9
42.9
37.5
34.4
SK.7
64.2
58.0
67.3
68.1
64.7
66.3
61.1
45.3
37.5
36,9
62.1
67.6
LLFoma=YYLOv8
57.5
68.0
67.9
63.8
65.3
64.9
43.4
37.9
34.7
61.5
67.4
LLFormer- YOLOvs
59.2
70.3
71.1
64.4
67.7
67.2
46.9
37.8
63.5
63.0
67.4
ReinexFemer--XOOl..
58.6
68.3
68.5
65.7
64.9
63.3
45.9
4000
36.8
62.9
70.1
58.4
68.9
68.3
65.0
66.8
66.5
43.7
40.1
36.9
61.0
67.1
59.2
68.3
68.7
65.5
67.8
65.8
46.6
39.5
37.3
63.4
69.1
IA 1A-+YOLOv8
58.7
68.5
68.8
62.0
67.8
64.1
47.7
41.9
67.9
63.2
64.9
-YOL-+
FestEaHancer- YOLOvv
59.9
69.1
69.0
65.5
68.5
68.2
45.7
41.1
40.0
64.2
67.3
LR- LR-YOLO'S (Ours)
62.7
71.5
72.4
68.1
71,1
70.1
50.1
45.6
41.3
66.2
71.1
ErDark 31
Methods
Bicycle
Boat
YOLOv10
50.0
55.5
52.4
63.3
58.9
31.8
42.0
48.4
42.2
58.0
47.5
YOLOV10
47.9
53.5
50.6
57.9
60.7
32.7
39.6
49.3
38.4
52.2
43.8
LLFarmer Noomerr-YOLOv10 YOLOv10
48.6
$3.9
49.6
$7.9
60.9
33.3
41.7
50.0
40.0
$2.6
45.9
ReinesFomme-
49.5
54.5
51.6
60.6
60.8
34,6
42.5
50.6
40.0
$3.3
46.5
Reine-FommxxYOLLLp0t
49.5
55.1
50,2
58.5
60.7
31.1
11.9
$1.0
42.6
55.0
15.8
GDIP-YOLO+10
51.2
57.1
51.0
61.7
65.1
36.0
14.8
47.7
43.6
57.1
18.4
51.8
55.5
50.0
63.6
61.7
36.5
43.5
$1.1
45.7
59.5
50,9
LR-YOL.0010((0rr)
56.3
52.1
YOLOva
49.2
$3.1
$0.00
63.8
58.9
$4.0
43.3
46.3
43.6
53.8
44.8
LLFomeer+YOLOv
LLFormer- YOLOv8
47.0
51.7
46.8
58.1
62.6
37.4
40.5
43.2
38.9
50.2
41,0
LLForma
49.5
51.3
47.9
60.0
63.9
37.0
14.3
46.0
42.0
$3.9
15.6
ReinesFoomxr=>OO..00
45.8
49.8
46.9
55.6
60.9
35.3
11.6
42.9
39.0
47.7
38.2
ReinexHemer--YOl000
47.5
$2.2
46.7
$7.0
61.4
35.1
43.4
44.0
40.8
51.6
42.9
JA YOLOO8
50.1
64.2
61.9
34.5
45.5
48.5
43.1
$4.1
46.2
CDIL-S
48.9
51.7
47.8
63.4
61.1
36.7
42.3
43.7
39.1
55.5
47.9
PenEaHancer sYOLOw
50.9
34.0
48.9
65.9
61.8
37.1
45.4
45.4
43.0
58.3
49.4
(Ours)
Table 14: Detailed results on VOC_Dark Val and ExDark 31, with models trained on
VOC Dark Train.
17

---

AX
Input
ConvIR->YOLOW
LR-YOLOV8
Input
ConviR YOLOV8
LR-YOLOv8
Figure 7: Qualitative comparison of detection result stability between the cascade method (ConvIR-+YOLOn and our LR-YOLE YOLOv8.
GDIP->YOLOV8
LR-YOLOv8 (Ours)
Figure 8: Qualitative comparisons on both Val and R7TS between our LR- YOLOv8 and other methods.
Retinexformer-
GDIP-SYOLOV8
(Ours)
Figure 9: Qualitative comparisons on both VOC_Dark Val and ExDark between our LR- YOLOV8 and other methods.
18

---

G Broader Impacts
Improving object detection in adverse weather and low-light environments has significant implications for safety-critical applications, such autonomous driving, traffic surveillance, and search-and- rescue missions. particular, autonomous vehicles often operate under unpredictable environmental conditions. Failure to accurately detect pedestrians, vehicles, obstacles in foggy or nighttime scenarios can lead to life-threatening consequences. Our method aims to fill this gap by jointly enhancing visual clarity and detection accuracy, offering potential safety upgrade existing perception pipelines.
Nevertheless, this line of research also entails broader considerations. First, the deployment of advanced visual detection systems could increase surveillance capabilities in urban and rural areas. While this may improve public security, it also raises concerns about privacy and the potential for misuse by authoritarian entities.
Second, performance across different demographic and geographic contexts should be evaluated. Adverse weather conditions may vary significantly between regions (e.g., smog marine fog), and ensuring that models generalize fairly across different environments and communities is crucial to avoid biased deployment outcomes.
Lastly, we acknowledge that improved detection in low-visibility environments might be repurposed for military security applications. While the proposed method is designed for civilian safety and transportation enhancement, dual-use risks exist.
19

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Reviews:
[{"review_id": "dwEbr26sYE", "reviewer": "Reviewer_te96", "summary": "This paper investigates the instability in cascaded image restoration and object detection pipelines under adverse conditions (e.g., haze, low light), attributing the issue to a mismatch in Lipschitz continuity between the two tasks. Restoration networks exhibit smooth, continuous mappings, whereas detection networks are highly sensitive and discontinuous. To address this, the authors propose Lipschitz-Regularized Object Detection (LROD), a framework that integrates low-Lipschitz restoration directly into the detection backbone and applies parameter-space smoothing to stabilize the training process. Implemented as LR-YOLO on top of YOLO detectors, the method improves detection robustness, stability, and accuracy across challenging benchmarks, demonstrating its effectiveness and efficiency over traditional cascaded or jointly trained approaches.", "questions": "1. Generality Beyond YOLO-based Detectors\nQuestion: The proposed method is closely connected to the YOLO architecture. Have you tried or considered applying LROD to other object detection frameworks, such as Transformer-based models (e.g., DETR, RT-DETR) or two-stage detectors like Faster R-CNN? Are there any gradient flow or optimization issues with the models mentioned above?\n\n2. Clarification of Restoration Loss Contribution During Inference\nQuestion: Is the restoration module used during inference, or is it only for training regularization? If it’s discarded after training, how does its supervision affect feature stability during inference?\n\n3. Ablation on Alternative Regularization Strategies\nQuestion: What are the primary advantages of this method compared to other regularization techniques or some adversarial training methods?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe paper presents a well-motivated and original perspective on the instability of cascaded image restoration and object detection systems by analyzing their functional mismatch through the lens of Lipschitz continuity. The theoretical analysis is thorough and clearly articulated, spanning both input and parameter spaces, which enhances the paper's clarity and depth. The proposed solution—Lipschitz-Regularized Object Detection (LROD)—is simple yet effective, demonstrating strong empirical results across multiple benchmarks and outperforming existing cascaded and joint training baselines. The integration into YOLO detectors also highlights the practical significance and deployability of the method in real-time applications.\n\nWeaknesses:\nWhile the paper provides a compelling analysis and effective solution, it focuses exclusively on YOLO-based detectors, thereby limiting its generalizability to other detection paradigms, such as Transformer-based models (e.g., DETR). Additionally, the paper lacks an ablation on alternative regularization strategies or deeper architectural variants. The experimental scope, while strong in haze and low-light conditions, could be broadened to include other forms of degradation (e.g., motion blur, rain, snow, or a combination of these), further validating the robustness and versatility of the approach.", "was_revised": true, "final_justification": "Thank you for the strong submission and the well-prepared rebuttal. The paper addresses an important and challenging problem with a clear motivation, novel methodology, and good experimental validation. I appreciate the work and the clarity in both the paper and the rebuttal.", "rebuttal": "Thank you very much for the constructive comments. We validate the effectiveness of our framework across different detector paradigms (Q1-1) and degradation scenarios (Q3), and conduct ablation studies on regularization strategies (Q2-1) and architectural designs (Q2-2). Below, we provide our point-by-point responses.\n\n***\n\n> **Q1-1: Generalizability to other detection paradigms (e.g., DETR, RT-DETR) or two-stage detectors like Faster R-CNN?**\n\n**A1-1:** Our LROD framework is both compatible with and effective across other detection paradigms. Following the suggestion, we applied it to the shared backbone of both the transformer-based RT-DETR and the two-stage Faster R-CNN. In both cases, LROD remains effective, as demonstrated by the results reported in the tables below.\n\n*All models are trained on VOC_Haze_Train and evaluated on both the synthetic dataset *VOC_Haze_Val* and the real-world dataset RTTS.*\n\n* **1. Transformer-based detector RT-DETR**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|RTDETR|51.5|43.7|\n|ConvIR$\\rightarrow$RTDETR|76.0|43.7|\n|IA$\\rightarrow$RTDETR|76.8|43.6|\n|GDIP$\\rightarrow$RTDETR|72.6|43.5|\n|FeatEnHancer$\\rightarrow$RTDETR|73.3|42.4|\n|LR-RTDETR|**78.9**|**45.1**|\n\n* **2. Two-stage detector Faster R-CNN Results**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|FasterRCNN|69.1|43.2|\n|ConvIR$\\rightarrow$FasterRCNN|78.5|44.1|\n|IA$\\rightarrow$FasterRCNN|78.6|41.3|\n|GDIP$\\rightarrow$FasterRCNN|76.6|44.5|\n|FeatEnHancer$\\rightarrow$FasterRCNN|77.7|39.4|\n|LR-FasterRCNN|**80.2**|**45.9**|\n\nWe will include the above experiments in Section 5.3.\n\n***\n\n> **Q1-2: Any gradient flow or optimization issues with the models mentioned above?**\n\n**A1-2:** We observe that RT-DETR and Faster R-CNN exhibit similar gradient flow and optimization issues to those in YOLO. Both models suffer from sharp gradient transitions and unstable optimization behavior. Our proposed regularization facilitates smoother gradient propagation, and the overall training process is more stable.\n\nThis is evidenced by the upper bounds on the Lipschitz constant, as presented in the table below.\n\n| Paradigm | | Faster R-CNN | | | RT-DETR | |\n|:--------|:-------------:|:---------------------------:|:-------------:|:-----:|:-----------------------:|:---------:|\n| Method | FasterRCNN | ConvIR$\\rightarrow$FasterRCNN | LR-FasterRCNN | RTDETR | ConvIR$\\rightarrow$RTDETR | LR-RTDETR |\n| Upper Bounds on Lipschitz Constant $\\downarrow$ | 287.6 | 691.7 | **174.3** | 246.3 | 619.4 | **155.6** |\n\n***\n\n> **Q2-1: Ablation on alternative regularization strategies.**\n\n**A2-1:** During the rebuttal, we conducted an ablation study comparing our method with two alternative regularization strategies: Spectral Norm Regularization (SNR) [a] and the adversarial training method Projected Gradient Descent (PGD) [b].\n\nOur approach consistently outperforms both SNR and PGD, as shown in the table below.\n\n*All models are trained on VOC_Haze_Train and evaluated on RTTS to assess out-of-domain generalization.*\n\n|Method|Baseline|SNR [a]|PGD [b]|Ours|\n|:--:|:-:|:-:|:-:|:-:|\n|RTTS|49.3|50.1|40.8|**53.2**|\n\n[a] Spectral Normalization for Generative Adversarial Networks, ICLR 2018\n\n[b] Towards Deep Learning Models Resistant to Adversarial Attacks, ICLR 2018\n\nWe further discuss the advantages over the two regularization techniques as follows,\n\nFirst, compared to SNR, which constrains weights globally, our method penalizes $\\lVert \\nabla_{\\mathbf{\\theta}} f_{\\mathbf{\\theta}}(x) \\rVert$,  reducing output sensitivity to parameter changes and enabling input-aware smoothness. Further, the restoration network promotes feature smoothness aligned with detection.\n\nSecond, compared to adversarial training (e.g., PGD), which requires generating perturbed inputs and increases training cost, our approach achieves implicit robustness without adversarial examples, resulting in more stable and efficient training. Moreover, while PGD often compromises performance on clean images, our method maintains accuracy on both clean and degraded inputs.\n\n***\n\n> **Q2-2: Ablation on deeper architectural variants.**\n\n**A2-2:** To explore the impact of backbone sharing depth, we conducted an ablation study using different configurations of shared encoder stages between the detection and restoration heads. \n\nOur method shares the first three stages (F1–F3), aiming to strike a balance between feature smoothness and task-specific specialization. As shown in the table below, shallower sharing (F1–F2) limits regularization, while deeper sharing (F1–F4) introduces task interference, supporting our design choice of the first three stages (F1–F3).\n\n*All strategies are trained on *VOC_Haze_Train* and evaluated on *RTTS* to assess out-of-domain generalization.*\n\n|Stage Sharing|Baseline|F1,F2|F1,F2,F3 (Ours)|F1,F2,F3,F4|\n|:--:|:-:|:-:|:-:|:-:|\n|RTTS|49.3|51.9|**53.2**|52.8|\n\nThe above two ablation studies will be included in Section 5.3. \n\n***\n\n> **Q3: Include other forms of degradation (e.g., motion blur, rain, snow, or a combination of these).**\n\n**A3:** As suggested, we evaluated our method on additional degradation types, including motion blur, rain, snow, and haze–rain mixtures. \n\nAcross all scenarios, our method consistently outperforms existing approaches, demonstrating its versatility and robustness under diverse adverse conditions, as shown in the tables below.\n\n*We construct new training and validation sets under each degradation setting. All models are retrained on the respective training sets and evaluated on the corresponding validation sets.*\n\n|Method|Motion Blur|Rain|Snow|Haze + Rain|\n|:--|:-:|:-:|:-:|:-:|\n|YOLOv8|50.8|53.1|60.8|50.1|\n|ConvIR$\\rightarrow$YOLOv8|80.1|79.9|80.5|79.2|\n|IA$\\rightarrow$YOLOv8|79.6|79.9|80.3|78.0|\n|GDIP$\\rightarrow$YOLOv8|80.1|79.6|80.4|78.3|\n|FeatEnHancer$\\rightarrow$YOLOv8|80.2|79.6|79.6|78.9|\n|LR-YOLOv8 (Ours)|**82.3**|**82.5**|**83.0**|**81.6**|\n\nThe above results will be included in Section 5.3.\n***\n\n> **Q4: Clarification of Restoration Loss Contribution During Inference: \n> Is the restoration module used during inference, or is it only for training regularization? If it’s discarded after training, how does its supervision affect feature stability during inference?**\n\n**A4:** The restoration and detection networks share a common backbone. During inference, since the primary task is object detection, the restoration head can be removed without affecting detection performance. Furthermore, if both detection results and restored images are desired, the restoration head can be retained to generate the restored outputs.\n\nWe clarify that the primary role of restoration supervision is during training, which helps suppress the model’s sensitivity to input perturbations, thereby constraining the Lipschitz constant of the detection network (Figure 5) and enhancing both its robustness and feature stability at inference time (Table 4).\n\n***"}, {"review_id": "UFEGjskzUH", "reviewer": "Reviewer_419p", "summary": "Generally in adverse visual conditions (like haze or low light), it is common to apply image restoration before object detection. But this cascade often suffers from instability, where small artifacts from restoration get amplified in detection. The paper investigates this issue through Lipschitz continuity, showing that the mismatch in smoothness between restoration and detection leads to poor performance. The authors had the following key observations: i) Restoration networks are low-Lipschitz (smooth). ii) Detection networks are high-Lipschitz (non-smooth). iii) Cascading the two causes gradient amplification and instability in both input and parameter space. Therefore, they proposed a unified framework called LROD (Lipschitz-Regularized Object Detection) that integrates image restoration within the detector’s feature extraction stage and adds parameter-space regularization to smooth training dynamics. This results in LR-YOLO, an enhanced YOLO-based detector that outperforms traditional cascades under adverse conditions. The Authors argued that LR-YOLO achieves higher mAP scores, better training stability and lower Lipschitz constants.", "questions": "i) Can there be a discussion about how you see the framework extends to more adverse scenarios as you mentioned in the future direction, if not extendable what are the limitations there? \nii) Analysis about adversarial robustness is preferred, e.g. with the presence of Gaussian noise.\niii) For regularization coefficients, it is better to include a sensitivity analysis to see how that affects mAP.\niv) It would be good to also include non-YOLO detectors as baselines in the experiments although they are not fully studied.", "limitations": "The authors have listed a few limitations of their work, however I don't see discussion about potential negative societal impact.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe discussion around restoration and detection instability is through Lipschitz continuity, which is both novel and mathematically sound.\nAccording to the authors, the LROD framework is a lightweight modification and low computational overhead. Moreover, the authors provided analytical derivations in both input and parameter spaces, including smoothness bounds and optimization stability. Personally I like its clear architectural design, and that it is designed to be lug-and-play for most YOLO variants.\n\nWeaknesses:\ni) It is nice that the authors have shown their extensive evaluation on synthetic and real-world datasets. However, the focus seems to be on only haze and low-light scenarios. Other degradation types (rain, motion blur, snow, etc.) are only mentioned as future work. It would be interesting to see how well this framework generalizes to other conditions and if the difference between these condition types are clearly stated.\nii) In Lipschitz constants estimation, empirical Jacobian norms are used to estimate Lipschitz continuity, which may be noisy or dataset-specific. A discussion on estimation variance or robustness would be preferred.\niii) Although the two-part regularization is evaluated, the backbone-sharing choice and stage-wise contribution of restoration to detection aren’t dissected in detail.\niv) While Figure 6 helps, more clarity on how gradients flow jointly through detection and restoration heads would help readers understand the training interaction.", "was_revised": true, "final_justification": "The authors have provided clear answers to address the concerns I raised earlier about the sensitivity of Jacobian, and have added more experiments/baselines to further address the robustness of the model performance. Therefore, I agreed to increase my rating by 1.", "rebuttal": "We sincerely appreciate your constructive comments. In response, we extend our evaluation to diverse degradations (Q1), provide analyses on Lipschitz estimation and robustness (Q2), conduct ablations on regularization and architecture (Q3), and validate generalizability across detectors (Q4). Our detailed point-by-point responses are provided below.\n\n***\n\n> **Q1: Extend to other degradation types (rain, motion blur, snow, etc.).**\n\n**A1:** Our method effectively extends to a variety of adverse conditions, including motion blur, rain, and snow. As shown in the table below, our method consistently outperforms existing approaches across all these scenarios.\n\n*We construct new training and validation sets under each degradation setting. All models are retrained on the respective training sets and evaluated on the corresponding validation sets.*\n\n|Method|Motion Blur|Rain|Snow|Haze + Rain|\n|:--|:-:|:-:|:-:|:-:|\n|YOLOv8|50.8|53.1|60.8|50.1|\n|ConvIR$\\rightarrow$YOLOv8|80.1|79.9|80.5|79.2|\n|IA$\\rightarrow$YOLOv8|79.6|79.9|80.3|78.0|\n|GDIP$\\rightarrow$YOLOv8|80.1|79.6|80.4|78.3|\n|FeatEnHancer$\\rightarrow$YOLOv8|80.2|79.6|79.6|78.9|\n|LR-YOLOv8 (Ours)|**82.3**|**82.5**|**83.0**|**81.6**|\n\nThe above results will be included in Section 5.3.\n\n***\n\n> **Q2-1: Empirical Jacobian norms estimate Lipschitz continuity, which may be noisy or dataset-specific ... Discussion on the Lipschitz constant estimation variance.**\n\n**A2-1:** We agree that empirical Jacobian norms can be sensitive to noise and data distribution. To reduce this effect, we follow prior work [a, b] and compute norms over many randomly sampled validation inputs, which helps stabilize estimates and limit dataset-specific bias.\n\n[a] Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach, ICLR 2018\n\n[b] Some Fundamental Aspects about Lipschitz Continuity of Neural Networks, ICLR 2024\n\nFurthermore, we include an analysis of the estimation variance and report confidence intervals to assess robustness in the table below. To complement the empirical approach, we also compute certified upper bounds using the dataset-independent LipSDP method [c]. Together, these results validate the use of Jacobian norms as a stable proxy for estimating Lipschitz continuity while accounting for variance and distribution sensitivity.\n\n|Method|Mean $\\downarrow$|Variance $\\downarrow$|Confidence Interval|Upper Bounds on Lipschitz Constant $\\downarrow$|\n|:--|:-:|:-:|:-:|:-:|\n|YOLOv8|19.5|18.9|[17.4,21.7]|215.9|\n|ConvIR$\\rightarrow$YOLOv8|43.4|46.2|[38.3,48.7]|530.8|\n|LR-YOLOv8 (Ours)|**8.9**|**9.8**|**[8.3,9.7]**|**136.4**|\n\n[c] Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks, NeurIPS 2019\n\n***\n\n> **Q2-2: Analysis about adversarial robustness is preferred.**\n\n**A2-2:**  As suggested, we analyze adversarial robustness by evaluating performance under varying levels of Gaussian noise. \n\nOur method maintains higher absolute performance and exhibits the smallest drop from the clean setting, demonstrating stronger resilience to input perturbations. Results are provided in the tables below.\n\n|Method|Clean|$\\sigma=0.01$|$\\sigma=0.02$|$\\sigma=0.03$|$\\sigma=0.04$|\n|:--|:-:|:-:|:-:|:-:|:-:|\n|YOLOv8|45.3|45.1 (-0.2)|44.1 (-1.2)|42.3 (-3.0)|40.1 (-5.2)|\n|ConvIR$\\rightarrow$YOLOv8|49.3|48.7 (-0.6)|47.5 (-1.8)|45.3 (-4.0)|43.3 (-6.0)|\n|LR-YOLOv8 (Ours)|**53.2**|**53.1 (-0.1)**|**52.2 (-1.0)**|**50.4 (-2.8)**|**48.5 (-4.7)**|\n\n***\n\n> **Q3-1: Ablation Study on the Backbone-Sharing Strategy.**\n\n**A3-1:** As suggested, we conducted an ablation study on backbone sharing and found that sharing the first three stages (F1–F3) yields the best balance between stability and task synergy. Shallower sharing (F1–F2) limits regularization, while deeper sharing (F1–F4) introduces interference. This supports our design choice of using the first three stages.\n\n\nPlease refer to the detailed results presented in the tables below.\n\n*All strategies are trained on *VOC_Haze_Train* and evaluated on *RTTS* to assess out-of-domain generalization.*\n\n|Stage Sharing|Baseline|F1,F2|F1,F2,F3 (Ours)|F1,F2,F3,F4|\n|:--:|:-:|:-:|:-:|:-:|\n|RTTS|49.3|51.9|**53.2**|52.8|\n\n***\n\n> **Q3-2: Ablation Study on the Regularization Coefficients.**\n\n**A3-2:** As suggested, we conducted an ablation study on the regularization coefficients $\\lambda$ (input space) and $\\lambda_p$ (parameter space). The results show that our method consistently outperforms the baseline across a range of coefficient values, with only minor variation in performance. \n\n*All settings are trained on *VOC_Haze_Train* and evaluated on *RTTS*.*\n\n| |Baseline| | |Ours| | |\n|:--:|:-:|:-:|:-:|:-:|:-:|:-:|\n|$\\lambda$|0|10|10|10|20|5|\n|$\\lambda_p$|0|0.005|0.02|0.01|0.01|0.01|\n|RTTS|49.3|52.9|53.0|53.2|53.1|52.8|\n\nThe above two ablation studies will be included in Section 5.3.\n\n***\n\n> **Q4: Include non-YOLO detectors as baselines.**\n\n**A4:** Our LROD framework is both compatible with and effective across other detection paradigms. During the rebuttal, we integrated it into the shared backbone of both the transformer-based RT-DETR [a] and the two-stage Faster R-CNN [b]. In both settings, it consistently enhances performance, as evidenced by the results in the tables below.\n\n*All models are trained on VOC_Haze_Train and evaluated on both the synthetic dataset *VOC_Haze_Val* and the real-world dataset RTTS.*\n\n* **1. Transformer-based detector RT-DETR**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|RTDETR|51.5|43.7|\n|ConvIR$\\rightarrow$RTDETR|76.0|43.7|\n|IA$\\rightarrow$RTDETR|76.8|43.6|\n|GDIP$\\rightarrow$RTDETR|72.6|43.5|\n|FeatEnHancer$\\rightarrow$RTDETR|73.3|42.4|\n|LR-RTDETR|**78.9**|**45.1**|\n\n* **2. Two-stage detector Faster R-CNN Results**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|FasterRCNN|69.1|43.2|\n|ConvIR$\\rightarrow$FasterRCNN|78.5|44.1|\n|IA$\\rightarrow$FasterRCNN|78.6|41.3|\n|GDIP$\\rightarrow$FasterRCNN|76.6|44.5|\n|FeatEnHancer$\\rightarrow$FasterRCNN|77.7|39.4|\n|LR-FasterRCNN|**80.2**|**45.9**|\n\nWe will include the above experiments in Section 5.3.\n\n[a] DETRs Beat YOLOs on Real-time Object Detection, CVPR 2024\n\n[b] Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks, NeurIPS 2015\n\n***\n\n> **Q5: Clarity on how gradients flow jointly through detection and restoration heads.**\n\n**A5:** We clarify that the detection and restoration heads share the first three backbone stages, and their losses jointly update these parameters. The detection loss provides task-specific supervision, while the restoration loss contributes smooth gradients that regularize training. As shown in Figure 5, incorporating the restoration loss (LR-YOLOv8*) stabilizes both Jacobian and gradient norms, highlighting the benefit of joint gradient flow. \n\nWe will also include a gradient flow diagram in Figure 6 for clarity.\n\n***\n\n> **Q6: The authors have listed a few limitations of their work, however I don't see discussion about potential negative societal impact.**\n\n**A6:** We discuss potential societal impacts in Appendix G: Broader Impacts. Specifically:\n\n1.\tImproved detection capabilities in low-visibility conditions may enhance public safety but also raise privacy concerns in surveillance applications.\n    \n2.\tThe proposed method’s effectiveness in challenging environments may attract interest from security-related applications, which, while unintended, highlights the importance of responsible deployment.\n\n***"}, {"review_id": "MekUZsPzXm", "reviewer": "Reviewer_AYoA", "summary": "This paper proposes a Lipschitz-regularized object detection framework (LROD) to address the functional mismatch between image restoration and detection networks in adverse conditions. The key innovation lies in analyzing the Lipschitz continuity disparity between restoration (low-Lipschitz) and detection (high-Lipschitz) tasks, which causes instability in traditional cascade frameworks.", "questions": "1. ​​Limited Generalization Tests​​: While haze and low-light conditions are covered, other adverse conditions (rain, snow, mixed weather) mentioned in Limitations are not experimentally validated. \n\n2. The claim of \"extending to diverse detection architectures\" lacks supporting evidence.\n\n3. I am excited to see this theoretical support between restoration and detection. Actually, i  am wondering if some interesting findings are also in Camouflaged Object Detection. These relevance reference are encouraged to be discussed, [2] also mentioned the high-resolution is beneficial for object detection:\n\n[1] Camouflaged Object Detection;\n\n[2] High-resolution Iterative Feedback Network for Camouflaged Object Detection", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths：The Lipschitz continuity analysis in both input and parameter spaces provides theoretical grounding for the instability issues in cascade frameworks.\nThe dual regularization approach  is well-motivated and demonstrates superior performance over existing methods.\nExtensive experiments on multiple datasets with detailed per-class results  validate the method's robustness.\n\nWeaknesses:\n1. ​​Limited Generalization Tests​​: While haze and low-light conditions are covered, other adverse conditions (rain, snow, mixed weather) mentioned in Limitations are not experimentally validated. \n2. The claim of \"extending to diverse detection architectures\" lacks supporting evidence.", "was_revised": true, "final_justification": "I lean to accept this paper due it addresses all my concerns.", "rebuttal": "Thank you very much for the insightful comments. In response, we extend our evaluation to diverse degradation types (Q1), validate our framework on additional detection architectures (Q2), and discuss its relevance to camouflaged object detection (Q3). Detailed responses are provided below.\n\n***\n\n> **Q1: Generalization to other adverse conditions (rain, snow, mixed weather)**\n\n**A1:** Our method naturally extends to a range of adverse conditions. To validate this, we extended our evaluation to additional adverse conditions, including motion blur, rain, snow, and mixed degradations (e.g., haze + rain). \n\nAcross all settings, our approach consistently outperforms existing baselines. Please refer to the results provided in the tables below for detailed comparisons.\n\n*We construct new training and validation sets under each degradation setting. All models are retrained on the respective training sets and evaluated on the corresponding validation sets.*\n\n|Method|Motion Blur|Rain|Snow|Haze + Rain|\n|:--|:-:|:-:|:-:|:-:|\n|YOLOv8|50.8|53.1|60.8|50.1|\n|ConvIR$\\rightarrow$YOLOv8|80.1|79.9|80.5|79.2|\n|IA$\\rightarrow$YOLOv8|79.6|79.9|80.3|78.0|\n|GDIP$\\rightarrow$YOLOv8|80.1|79.6|80.4|78.3|\n|FeatEnHancer$\\rightarrow$YOLOv8|80.2|79.6|79.6|78.9|\n|LR-YOLOv8 (Ours)|**82.3**|**82.5**|**83.0**|**81.6**|\n\nThe above results will be included in Section 5.3.\n\n***\n\n> **Q2: Extend to diverse detection architectures.**\n\n**A2:** Our LROD framework is both compatible with and effective across different detection paradigms. During rebuttal, we applied it to the shared backbone of both the transformer-based RT-DETR [a] and the two-stage Faster R-CNN [b]. In both cases, LROD consistently remains effective. \n\nPlease refer to the detailed results presented in the tables below.\n\n*All models are trained on VOC_Haze_Train and evaluated on both the synthetic dataset *VOC_Haze_Val* and the real-world dataset RTTS.*\n\n* **1. Transformer-based detector RT-DETR**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|RTDETR|51.5|43.7|\n|ConvIR$\\rightarrow$RTDETR|76.0|43.7|\n|IA$\\rightarrow$RTDETR|76.8|43.6|\n|GDIP$\\rightarrow$RTDETR|72.6|43.5|\n|FeatEnHancer$\\rightarrow$RTDETR|73.3|42.4|\n|LR-RTDETR|**78.9**|**45.1**|\n\n* **2. Two-stage detector Faster R-CNN Results**:\n\n|Method|VOC_Haze_Val|RTTS|\n|:--|:-:|:-:|\n|FasterRCNN|69.1|43.2|\n|ConvIR$\\rightarrow$FasterRCNN|78.5|44.1|\n|IA$\\rightarrow$FasterRCNN|78.6|41.3|\n|GDIP$\\rightarrow$FasterRCNN|76.6|44.5|\n|FeatEnHancer$\\rightarrow$FasterRCNN|77.7|39.4|\n|LR-FasterRCNN|**80.2**|**45.9**|\n\nWe will include the above experiments in Section 5.3.\n\n[a] DETRs Beat YOLOs on Real-time Object Detection, CVPR 2024\n\n[b] Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks, NeurIPS 2015\n\n***\n\n> **Q3: If some interesting findings also in Camouflaged Object Detection [1] ... high-resolution is beneficial for object detection [2]**\n\n**A3:** Thanks for raising this discussion. We believe that our analysis on the Lipschitz continuity disparities between restoration and detection networks extends naturally to camouflaged object detection (COD), where similar challenges in boundary stability arise.\n\nIn particular, COD involves detecting objects with ambiguous, low-contrast boundaries, posing challenges similar to those in cascaded systems under adverse conditions. Our findings suggest that instability around object boundaries in COD may stem from the non-smooth behavior of detection networks. The high-resolution preservation enabled by restoration modules can help address this, as fine edge and texture details are essential for accurate localization. This observation is consistent with [2], which highlights the importance of high-resolution features in improving COD performance.\n\nWe will incorporate the above discussion and include the related works [1, 2] in Lines 320-325.\n\n[1] Camouflaged Object Detection\n\n[2] High-resolution Iterative Feedback Network for Camouflaged Object Detection\n\n***"}, {"review_id": "vDwDKnZjKu", "reviewer": "Reviewer_KmkB", "summary": "This paper investigates the instability in cascaded fashion, image restoration, and object detection, under adverse conditions, and proposes a smooth Lipschitz continuity framework,  namely LR-YOLO, which integrates restoration into the detection network and adds regularization in both input and parameter spaces.\nLR-YOLO attributes the instability problem to a mismatch in Lipschitz continuity—restoration networks are smooth, while detection networks are sensitive to small changes. \n LR-YOLO improves detection robustness and stability with low computational cost, outperforming prior approaches on haze and low-light benchmarks.", "questions": "Please see my review.", "limitations": "No potential negative societal impact.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1) This paper's motivation is quite clear and straightforward.\n2) The implementation looks simple and effective.\n\nWeaknesses\n- The low-light images are synthesized by the gamma correction. However, in real scenes, low-light images are typically accompanied by noise.\n\n-  In row 206. It seems that the detection loss can also suppress the Lipschitz constant.  Since the main task is detection, the gradient of the detection loss is generally aligned with the Jacobian norm of one. Thus, the detection loss also satisfies the assumption in row 204. \nOverall, suppressing the Lipschitz constant doesn't seem to be solely driven by the restoration loss.\n\nI am concerning that the penalty of $$\\| \\nabla_{\\theta} f_{\\theta}(x) \\|$$ is enough to harmonize the instability.  \n\n\n**Presentation**:\n\n- Figure 2 (a) does not clearly explain why the purple dot cannot be seen in 'ours'.\n\n- In Row 203, what does 'small' mean?  \n\n**Experiments**:\n\n- In the Experiment Section, it looks like the Image enhancement methods are just training on the synthesis image pairs. I think the author should also compare with the pretrained image enhancement methods. (For example, using the Image enhancement methods to yield clear images for training and testing).", "was_revised": true, "final_justification": "Thanks to the author's detailed answer, which addressed my concerns, I chose to raise my score to 5: Accept.", "rebuttal": "We sincerely appreciate your insightful comments. In response, we clarify the low-light setting and evaluate robustness to noise (Q1), clarify the role of regularization and gradient dynamics (Q2), revise visualizations and expressions for improved clarity (Q3–Q4), and compare with pretrained enhancement methods (Q5). Detailed responses are provided below.\n\n***\n\n> **Q1: The low-light images are synthesized by the gamma correction. However, in real scenes, low-light images are typically accompanied by noise.**\n\n**A1:** Thanks for the insightful comment. We follow standard protocols [a, b, c] using gamma correction to ensure consistency with existing benchmarks. \n\nWe agree that real-world low-light images often contain noise. To evaluate robustness under such conditions, we introduce Poissonian-Gaussian noise during testing. As shown in the table below, our method maintains strong performance, indicating good generalization to more realistic low-light scenarios.\n\n\n|Method|VOC_Dark_Noise_Val|ExDark|\n|:--|:-:|:-:|\n|YOLOv8|49.7|50.0|\n|Retinexformer$\\rightarrow$YOLOv8|64.3|48.7|\n|IA$\\rightarrow$YOLOv8|63.1|50.1|\n|GDIP$\\rightarrow$YOLOv8|65.8|51.5|\n|FeatEnHancer$\\rightarrow$YOLOv8|64.9|51.9|\n|LR-YOLOv8 (Ours)|**67.8**|**54.8**|\n\n\n[a] Image-Adaptive YOLO for Object Detection in Adverse Weather Conditions, AAAI 2022\n\n[b] Rethinking Image Restoration for Object Detection, NeurIPS 2022\n\n[c] Unsupervised Variational Translator for Bridging Image Restoration and High-Level Vision Tasks, ECCV 2024\n\n***\n\n> **Q2-1: It seems that the detection loss can also suppress the Lipschitz constant, as its gradient is generally aligned with the Jacobian norm. Suppressing the Lipschitz constant doesn't seem to be solely driven by the restoration loss.**\n\n**A2-1:** The effect of detection loss on Lipschitz suppression is inconsistent. While it can occasionally reduce the Lipschitz constant when its gradient aligns with the Jacobian norm (i.e., $\\xi(t) < 0$), object detection involves non-smooth components such as bounding box matching, which often introduce sharp gradient changes. These can result in $\\xi(t) > 0$, increasing the Lipschitz constant and destabilizing training.\n\nIn contrast, *the restoration loss plays a primary and consistent role* in suppressing the Lipschitz constant by providing smooth, stable gradients. As shown in Figure 5, its inclusion lowers and stabilizes both Jacobian and gradient norms.\n\nWe will add this discussion to Line 206 to clarify the effect of the detection loss.\n\n> **Q2-2: I am concerning that the penalty of $\\lVert \\nabla_{\\mathbf{\\theta}} f_{\\mathbf{\\theta}}(\\boldsymbol{x}) \\rVert$ is enough to harmonize the instability.**\n\n**A2-2:** We clarify that $\\lVert \\nabla_{\\theta} f_{\\theta}(\\boldsymbol{x}) \\rVert$ enforces Lipschitz regularization by promoting smoothness in the parameter space. When applied alone, it can improve performance over the baseline. For example, YOLOv10 improves from 46.0 to 47.2 mAP on RTTS.\n\nFurthermore, when combined with input-space regularization via the restoration loss $\\mathcal{L}_{\\text{res}}$, performance further increases to 49.2 mAP: a further gain of 2.0%. This indicates the complementarity of the two regularizers: gradient norm stabilizes parameters, while restoration loss smooths input supervision.\n\nFigure 5 also supports this, LR-YOLOv8 (ours) achieves lower Jacobian norms than LR-YOLOv8* (using only $\\mathcal{L}_{\\text{res}}$), leading to more stable training.\n\n\n\n***\n\n> **Q3: Figure 2 (a) does not clearly explain why the purple dot cannot be seen in 'ours'.**\n\n**A3:** The points corresponding to $x$ (purple) and $x + \\Delta x$ (yellow) are nearly overlapping, appearing as dark yellow. To improve clarity, we will update the Figure 2 using distinct marker shapes to better distinguish the two points.\n\n***\n\n> **Q4: In Row 203, what does 'small' mean?**\n\n**A4:** Thanks for your meticulous comment. We have fixed this typo:\n\n> $\\lVert \\nabla\\_{\\mathbf{\\theta}\\_b} \\mathcal{L}\\_{\\mathrm{res}}(g\\_{\\mathbf{\\theta}\\_b, \\mathbf{\\theta}\\_r}) \\rVert \\le G$ for ~~small~~ $G < \\lVert \\nabla\\_{\\mathbf{\\theta}\\_b} \\mathcal{L}\\_{\\mathrm{det}}(f\\_{\\mathbf{\\theta}\\_b, \\mathbf{\\theta}\\_d}) \\rVert$\n\nWe refer to the gradient norm of the restoration loss, $\\lVert \\nabla\\_{\\mathbf{\\theta}\\_b} \\mathcal{L}\\_{\\mathrm{res}}({g}\\_{\\mathbf{\\theta}\\_b, \\mathbf{\\theta}\\_r}) \\rVert$, being smaller than that of the detection loss, $\\lVert \\nabla\\_{\\mathbf{\\theta}\\_b} \\mathcal{L}\\_{\\mathrm{det}}(f\\_{\\mathbf{\\theta}\\_b, \\mathbf{\\theta}\\_d}) \\rVert$. \n\n***\n\n> **Q5: Using the pretrained image enhancement methods to yield clear images for training and testing.**\n\n**A5:** Our method achieves consistently better performance than the pretrained image enhancement methods. As suggested, we include the Transformer-based pretrained method OneRestore [a] and the Diffusion-based pretrained method PromptFix [b] for evaluation. Please see the results in the table below.\n\n|Method|VOC_Haze_Val|RTTS|VOC_Dark_Val|ExDark|\n|:--|:-:|:-:|:-:|:-:|\n|YOLOv8|54.3|45.3|63.4|50.0|\n|OneRestore$\\rightarrow$YOLOv8|62.1|38.4|68.9|51.3|\n|PromptFix$\\rightarrow$YOLOv8|78.2|49.3|63.6|50.1|\n|LR-YOLOv8 (Ours)|**83.3**|**53.2**|**71.7**|**54.5**|\n\n[a] OneRestore: A Universal Restoration Framework for Composite Degradation, ECCV 2024\n\n[b] PromptFix: You Prompt and We Fix the Photo, NeurIPS 2024\n\n***\n\n> **Q6: No potential negative societal impact.**\n\n**A6:** We discuss potential societal impacts in Appendix G: Broader Impacts. Specifically:\n\n1.\tImproved detection capabilities in low-visibility conditions may enhance public safety but also raise privacy concerns in surveillance applications.\n    \n2.\tThe proposed method’s effectiveness in challenging environments may attract interest from security-related applications, which, while unintended, highlights the importance of responsible deployment.\n\n***"}]

Author rebuttal:

Meta-review: The paper received all positive recommendations. After rebuttal, all reviewers acknowledged the strengths of the paper and agreed that the authors have addressed their concerns. Reviewers achieved a final consensus of positive rating of this paper. AC agrees with this recommendation and therefore is happy to accept the paper. Authors are required to update the rebuttal and discussion contents to the camera-ready version of the paper to improve it so as to address the raised concerns in the final paper.
Decision: Accept (poster)