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.

In this supplementary material, we will provide more analyses of mask prior in Section 1 and similarity transfer in Section 2. We will show the visualization results in Section 3 and the performance variance with iteration in Section 4. We will also conduct experiments to mine base categories in the target dataset in Section 5. Besides, the hyper-parameters analyses will be provided in Section 6. Finally, we will discuss the limitations in Section 7. As mentioned in Section 3.2 in the main paper, mask prior provides coarse pixel-wise category information to improve the ability of the object detection network to locate and identify objects. Our ablation studies (Table 3 in the main paper) have already proved the advantage of mask prior. To further evaluate the effectiveness of mask prior, we evaluate object detection network with/without mask generator on VOC test set. Considering that the target dataset may contain both base categories and novel categories, in which only novel categories have ground-truth bounding boxes, we evaluate our method on novel categories.

Object detection has achieved promising success, but requires large-scale fullyannotated data, which is time-consuming and labor-extensive. Therefore, we consider object detection with mixed supervision, which learns novel object categories using weak annotations with the help of full annotations of existing base object categories. Previous works using mixed supervision mainly learn the classagnostic objectness from fully-annotated categories, which can be transferred to upgrade the weak annotations to pseudo full annotations for novel categories. In this paper, we further transfer mask prior and semantic similarity to bridge the gap between novel categories and base categories. Specifically, the ability of using mask prior to help detect objects is learned from base categories and transferred to novel categories. Moreover, the semantic similarity between objects learned from base categories is transferred to denoise the pseudo full annotations for novel categories. Experimental results on three benchmark datasets demonstrate the effectiveness of our method over existing methods.

For both GP-VAE and CP-VAE, the number of attention heads is empirically set to 4. We customize a fixed weight 0.2 to the KL divergence such that we can bias more towards the reconstruction loss in Eq. (5) and Eq.

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Image Signal Processors (ISPs) play a fundamental role in camera systems.

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For both GP-V AE and CP-V AE, the number of attention heads is empirically set to 4. We customize

Duplicate removal is a critical step to accomplish a reasonable amount of predictions in prevalent proposal-based object detection frameworks.