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arxiv: 2505.17732 · v2 · submitted 2025-05-23 · 💻 cs.CV · cs.AI· cs.LG

RQR3D: Reparametrizing the regression targets for BEV-based 3D object detection

Ozsel Kilinc , Cem Tarhan This is my paper

Pith reviewed 2026-05-19 13:35 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LG
keywords 3D object detectionBEV perceptionoriented bounding boxradar camera fusionnuScenes datasetkeypoint regressionautonomous driving
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The pith

RQR3D reparametrizes BEV 3D regression targets using restricted quadrilateral offsets to avoid discontinuities in angle-based losses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Existing BEV 3D object detectors estimate oriented bounding boxes using angles, which leads to discontinuous loss functions during training. The paper proposes to instead regress the axis-aligned bounding box that encloses the oriented one along with the offsets from its corners to the oriented box corners. This reparametrization converts the task into keypoint regression, which the authors integrate into an anchor-free detector. Combined with a simple 2D convolution-based radar fusion, it delivers state-of-the-art results on nuScenes for camera-radar 3D detection. Readers interested in autonomous driving would care because lower errors in object position and orientation support more reliable planning and safety.

Core claim

The authors establish that the restricted quadrilateral representation defines 3D regression targets by the smallest horizontal bounding box and the offsets between the corners of this box and the oriented box. This approach transforms the oriented object detection problem into a keypoint regression task, enabling an anchor-free single-stage detector to achieve 67.5 NDS and 59.7 mAP on nuScenes while reducing translation and orientation errors.

What carries the argument

Restricted quadrilateral representation (RQR), which regresses an enclosing horizontal box and four corner offsets to represent rotated 3D objects without explicit angle prediction.

If this is right

  • The proposed method achieves state-of-the-art camera-radar 3D object detection on nuScenes.
  • Translation and orientation errors are reduced compared to prior approaches.
  • The representation is compatible with different object detection frameworks.
  • The simplified radar fusion backbone uses standard 2D convolutions for efficiency without voxel or sparse operations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This corner-offset approach may extend naturally to 2D aerial oriented detection where similar angle issues arise.
  • The lightweight fusion design could enable faster inference in resource-constrained autonomous systems.
  • Testing the method on additional datasets would help confirm its robustness across different sensor configurations.

Load-bearing premise

The claim rests on the premise that angle discontinuities are the main limiter for BEV 3D detection performance and that the quadrilateral offset encoding resolves them cleanly.

What would settle it

Training both the angle-based and offset-based models on the same data and plotting the loss values specifically for objects oriented near 45 degrees or other discontinuity points would reveal whether the new representation produces smoother optimization.

Figures

Figures reproduced from arXiv: 2505.17732 by Cem Tarhan, Ozsel Kilinc.

Figure 1
Figure 1. Figure 1: a) First, we identify the smallest axis-aligned 2D bounding box (yellow) that encapsulates the oriented box (orange). We [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a) The overall model architecture, comprising an image backbone, radar backbone, 2D to BEV projection module, temporal [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Orientation stability of RQR3D head (left) compared to [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
read the original abstract

Accurate, fast, and reliable 3D perception is essential for autonomous driving. Recently, bird's-eye view (BEV)-based perception approaches have emerged as superior alternatives to perspective-based solutions, offering enhanced spatial understanding and more natural outputs for planning. Existing BEV-based 3D object detection methods, typically using an angle-based representation, directly estimate the size and orientation of rotated bounding boxes. We observe that BEV-based 3D object detection is analogous to aerial oriented object detection, where angle-based methods are known to suffer from discontinuities in their loss functions. Drawing inspiration from this domain, we propose \textbf{R}estricted \textbf{Q}uadrilateral \textbf{R}epresentation to define \textbf{3D} regression targets. RQR3D regresses the smallest horizontal bounding box encapsulating the oriented box, along with the offsets between the corners of these two boxes, thereby transforming the oriented object detection problem into a keypoint regression task. We employ RQR3D within an anchor-free single-stage object detection method achieving state-of-the-art performance. We show that the proposed architecture is compatible with different object detection approaches. Furthermore, we introduce a simplified radar fusion backbone that applies standard 2D convolutions to radar features. This backbone leverages the inherent 2D structure of the data for efficient and geometrically consistent processing without over-parameterization, thereby eliminating the need for voxel grouping and sparse convolutions. Extensive evaluations on the nuScenes dataset show that RQR3D achieves SotA camera-radar 3D object detection performance despite its lightweight design, reaching 67.5 NDS and 59.7 mAP with reduced translation and orientation errors, which are crucial for safe autonomous driving.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes RQR3D, a Restricted Quadrilateral Representation for reparametrizing the regression targets in BEV-based 3D object detection. Drawing an analogy to aerial oriented object detection, it replaces direct angle regression with regression of the smallest enclosing axis-aligned box plus four corner offsets, converting oriented box detection into a keypoint regression task. The method is embedded in an anchor-free single-stage detector augmented by a simplified radar fusion backbone that uses standard 2D convolutions, and it reports state-of-the-art camera-radar 3D detection results on nuScenes (67.5 NDS, 59.7 mAP) with reduced translation and orientation errors.

Significance. If the performance claims are substantiated by detailed ablations and error analysis, the reparametrization could provide a practical way to mitigate periodicity and discontinuity issues in angle-based losses for BEV detectors, which are important for downstream planning in autonomous driving. The lightweight radar backbone is a secondary contribution that avoids voxel grouping and sparse convolutions while preserving geometric consistency.

major comments (3)
  1. [§3.2] §3.2 (RQR3D formulation): the claim that regressing the smallest enclosing axis-aligned box plus corner offsets eliminates discontinuities is not accompanied by a proof or explicit verification that the composite loss remains continuous and that the mapping from the four offsets to yaw is bijective for all valid oriented boxes when height and z-center are regressed independently.
  2. [§5] §5 (Experiments): the reported reductions in translation and orientation errors on nuScenes are not supported by an ablation that isolates the effect of the RQR3D representation from the new 2D-convolution radar backbone; without this separation it is unclear whether the gains are attributable to the reparametrization or to the backbone change.
  3. [Table 1] Table 1 / main results: the SOTA comparison does not indicate whether competing methods were re-trained with the same simplified radar backbone or whether the RQR3D head was substituted into existing detectors while keeping all other components fixed, weakening the claim of compatibility and superiority.
minor comments (2)
  1. [Figure 2] Figure 2: the diagram illustrating the quadrilateral offsets would benefit from explicit labels for the four corner vectors and the resulting oriented box to make the geometric consistency constraints visually clear.
  2. [§4.3] §4.3 (loss function): the weighting between the keypoint offset loss and the separate height/z regression terms is not stated; a brief sensitivity analysis would help confirm robustness.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and indicate planned revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (RQR3D formulation): the claim that regressing the smallest enclosing axis-aligned box plus corner offsets eliminates discontinuities is not accompanied by a proof or explicit verification that the composite loss remains continuous and that the mapping from the four offsets to yaw is bijective for all valid oriented boxes when height and z-center are regressed independently.

    Authors: We appreciate the referee's observation. The RQR3D formulation is motivated by converting oriented box regression into a keypoint regression task to sidestep periodicity and discontinuity issues inherent in direct angle regression. We agree that an explicit verification would improve rigor. In the revised manuscript, we will expand §3.2 with a formal analysis proving continuity of the composite loss and bijectivity of the offset-to-yaw mapping for all valid oriented boxes, accounting for independent regression of height and z-center. revision: yes

  2. Referee: [§5] §5 (Experiments): the reported reductions in translation and orientation errors on nuScenes are not supported by an ablation that isolates the effect of the RQR3D representation from the new 2D-convolution radar backbone; without this separation it is unclear whether the gains are attributable to the reparametrization or to the backbone change.

    Authors: We acknowledge the value of isolating contributions for clear attribution. The current experiments report overall performance of the integrated system. To address this, we will add an ablation in the revised §5 that applies the RQR3D representation to a detector using the prior radar backbone, allowing direct comparison against the full proposed method to separate the effects of the reparametrization from the backbone changes. revision: yes

  3. Referee: [Table 1] Table 1 / main results: the SOTA comparison does not indicate whether competing methods were re-trained with the same simplified radar backbone or whether the RQR3D head was substituted into existing detectors while keeping all other components fixed, weakening the claim of compatibility and superiority.

    Authors: We thank the referee for this clarification request. Table 1 primarily reports published results of competing methods. To better support the compatibility claim, we will include additional experiments in the revision where the RQR3D head is substituted into existing detectors with other components held fixed, reporting the resulting performance to isolate the contribution of the representation. revision: yes

Circularity Check

0 steps flagged

Independent geometric reparametrization with no load-bearing circularity

full rationale

The paper's derivation introduces a Restricted Quadrilateral Representation by re-expressing oriented BEV boxes as the smallest enclosing axis-aligned box plus four corner offsets, converting angle regression into keypoint offsets. This mapping is defined directly from geometry and evaluated on the external nuScenes benchmark; no equation reduces a claimed prediction to a fitted input by construction, and no uniqueness theorem or ansatz is imported via self-citation to force the result. The central performance claims rest on empirical results rather than self-referential definitions, yielding only a minor (non-load-bearing) circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the domain assumption that angle discontinuities are the dominant issue and on the empirical superiority of the new representation; the RQR3D construct itself is the main added element.

axioms (1)
  • domain assumption Angle-based representations for oriented bounding boxes suffer from discontinuities in their loss functions
    Explicitly stated in the abstract as the motivation drawn from aerial oriented object detection.
invented entities (1)
  • Restricted Quadrilateral Representation (RQR3D) no independent evidence
    purpose: To define 3D regression targets by regressing the smallest horizontal bounding box and corner offsets
    New representation introduced by the paper to transform oriented detection into keypoint regression.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Control Your Queries: Heterogeneous Query Interaction for Camera-Radar Fusion

    cs.CV 2026-04 unverdicted novelty 7.0

    ConFusion reaches 59.1 mAP and 65.6 NDS on nuScenes validation by combining heterogeneous queries with QMix cross-attention and QSwap feature exchange.

Reference graph

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    Obtaining the 3D bounding box parameters Evaluation tool from nuScenes [44] requires 3D bounding boxes to be defined as (xctr, yctr, zctr, w, l, h, θ). In this sec- tion, we provide the details about how we obtain this repre- sentation using RQR3D outputs, (xmin, ymin, xmax, ymax) and (u, v,arg min u,arg min v dx, dy, zctr, h). Recalling that u represents...

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    Additional Experiments 8.1. Projection Methods In Table 8, we evaluate the contribution of various projection methods to the overall performance. Our baseline model employs Lift-Splat projection with BEVDepth’s depth dis- tribution module, denoted as DN. We compare this base- line with three different versions: i) Lift-Splat projection with a simpler dept...

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