We propose POLAR, a novel radar-guided depth estimation method that introduces polynomial fitting to efficiently transform scaleless depth predictions from pretrained monocular depth estimation (MDE) models into metric depth maps. Unlike existing approaches that rely on complex architectures or expensive sensors, our method is grounded in a fundamental insight: although MDE models often infer reasonable local depth structure within each object or local region, they may misalign these regions relative to one another, making a linear scale and shift (affine) transformation insufficient given three or more of these regions. To address this limitation, we use polynomial coefficients predicted from cheap, ubiquitous radar data to adaptively adjust predictions non-uniformly across depth ranges. In this way, POLAR generalizes beyond affine transformations and is able to correct such misalignments by introducing inflection points. Importantly, our polynomial fitting framework preserves structural consistency through a novel training objective that enforces local monotonicity via first-derivative regularization. POLAR achieves state-of-the-art performance across three datasets, outperforming existing methods by an average of 24.9% in MAE and 33.2% in RMSE, while also achieving state-of-the-art efficiency in terms of latency and computational cost.

翻译：我们提出POLAR，一种新颖的雷达引导深度估计方法，引入多项式拟合将预训练单目深度估计（MDE）模型的无尺度深度预测高效转换为公制深度图。与依赖复杂架构或昂贵传感器的现有方法不同，我们的方法基于一个基本洞察：尽管MDE模型通常能推断每个物体或局部区域内合理的局部深度结构，但这些区域之间的相对对齐可能不准确，使得当存在三个或更多区域时，线性尺度与偏移（仿射）变换不再足够。为解决这一局限，我们利用从廉价、普适的雷达数据中预测的多项式系数，自适应地对不同深度范围的预测进行非均匀调整。通过这种方式，POLAR超越了仿射变换，并能通过引入拐点来修正此类对齐偏差。重要的是，我们的多项式拟合框架通过一项新颖的训练目标保持了结构一致性，该目标利用一阶导数正则化强制局部单调性。POLAR在三个数据集上达到了最先进的性能，平均MAE降低24.9%、RMSE降低33.2%，同时在延迟和计算成本方面也实现了最优效率。