REXO: Radar Detection & Exobase Modeling

• REXO is a dual-purpose framework that leverages 3D diffusion to improve indoor radar object detection and to analyze exobase radius in atmospheric escape models.
• It fuses synchronized multi-view radar data with geometric priors via a denoising diffusion process, yielding efficient and accurate 3D bounding box estimation.
• $R_{exo}$ delineates the exobase radius in planetary atmospheres, marking the transition from collisional to ballistic regimes and influencing escape profile simulations.

REXO refers to “multi-view Radar object dEtection with 3D bounding boX diffusiOn,” a diffusion-based multi-view indoor radar perception framework for explicit 3D object detection, and, in exoplanet escape modeling, to the exobase radius parameter controlling the transition between collisional and ballistic regimes in planetary atmospheres. The REXO approach for indoor radar object detection fundamentally addresses the ambiguity of cross-view feature association in multi-view radar scenarios by fusing explicit 3D bounding-box diffusion with geometric priors, producing significant improvements over earlier methods in complex indoor environments (Yataka et al., 21 Nov 2025). Separately, $R_\mathrm{exo}$ (Rexo) is central in atmospheric escape theory as the threshold radius distinguishing the collisional thermosphere from the collisionless exosphere in hot Jupiter outflow models (Bourrier et al., 2014).

1. Definition and Context

REXO in indoor radar object detection designates a neural architecture for 3D bounding box estimation from synchronized multi-view radar data. The core innovation is lifting the bounding-box diffusion process from image-based 2D (as in DiffusionDet) to full 3D in radar space, integrating radar-specific priors and enforcing explicit, geometry-aware multi-view association (Yataka et al., 21 Nov 2025).

In planetary atmosphere modeling, $R_{\rm exo}$ (“Rexo”) is the exobase radius: the geometrical boundary between an atmospheric region dominated by collisional (hydrodynamic) behavior and an exterior exosphere where mean free paths exceed local scale heights and particle motions become effectively ballistic. For HD 209458b, $R_{\rm exo}$ is tightly coupled to the Roche lobe geometry and critically shapes simulated and observed escape profiles (Bourrier et al., 2014).

2. REXO Framework for Indoor Multi-View Radar Object Detection

The REXO pipeline accepts synchronized horizontal and vertical radar heatmap views per frame (typically range–azimuth and range–elevation), optionally stacked over consecutive frames. Each view is encoded by a shared backbone (e.g., ResNet+FPN) into view-specific, multi-scale feature maps $Z_{\rm hor}$ and $Z_{\rm ver}$.

A set of $N$ noisy 3D bounding boxes, $$x_t^i = [c_x^i,\,c_y^i,\,c_z^i,\,w^i,\,h^i,\,d^i]^\top \in \mathbb{R}^6$$, are maintained and evolved from noise by a denoising diffusion process from $t=T$ to $t=0$. At each reverse diffusion step:

• The ground-contact prior is applied by setting $c^t_y \leftarrow h^t/2$.
• Each box $x_t^i$ projects to both radar views to specify Region-of-Interest (RoI) boxes ($$x_{t,{\rm hor}} = [c_x^t, c_z^t, w^t, d^t],\ x_{t,{\rm ver}} = [c_y^t, c_z^t, h^t, d^t]$$).
• Features from each view are RoI-aligned and concatenated, then processed through a detection head (“DenoisingDet”) to regress clean boxes $\hat x_0$ and object class scores $\hat p$.

At completion, 3D predictions are projected to the image plane using the radar-to-camera transform, refined by a regression subnetwork, and confidence-thresholded. This explicit, box-guided association mitigates the ambiguities of implicit matching approaches (e.g., RFMask’s proposal pairing or RETR’s query cross-attention), and its linear scaling in the number of views improves efficiency compared to quadratic approaches (Yataka et al., 21 Nov 2025).

3. Mathematical Formulation of 3D Diffusion and Ground-Contact Prior

REXO adapts the standard Denoising Diffusion Probabilistic Model (DDPM) formulation for bounding box coordinates:

• Forward (noising) process:

$$q(x_t \mid x_0) = \mathcal{N}\left(x_t; \sqrt{\bar\alpha_t}\, x_0,\, (1-\bar\alpha_t) I_6\right)$$

where $\bar\alpha_t = \prod_{s=1}^t (1-\beta_s)$. Training samples $x_t$ via

$$x_t = \sqrt{\bar\alpha_t}\,x_0 + \sqrt{1-\bar\alpha_t}\,\epsilon, \quad \epsilon \sim \mathcal{N}(0,I_6)$$

• Reverse (denoising) process:

$$p_\theta(x_{t-1} \mid x_t, Z_{\rm hor}, Z_{\rm ver}) = \mathcal{N}(x_{t-1}; \mu_\theta(x_t,t),\,\sigma_t^2 I_6)$$

where the predicted clean box $\hat x_0$ is output by the detection head, and the DDIM-style update incorporates both the estimated denoising and the noise learning schedule.

At each diffusion step, the ground-contact prior $c_y^t = h^t/2$ is enforced, eliminating the need to diffuse the $c_y^t$ coordinate independently and reducing the effective diffusion parameter space by one dimension. This exploits the fact that target subjects (typically people) are assumed in contact with the floor, yielding physically plausible and data-efficient optimization.

Losses combine DETR-style set prediction (Hungarian matching), 3D box regression (L1 + GIoU), and 2D projected box refinement (Yataka et al., 21 Nov 2025).

4. Cross-View Feature Association and Comparison to Existing Methods

REXO uniquely employs explicit, box-guided RoIAlign for cross-view radar feature association at every diffusion step:

1. Each noisy 3D box is projected into both horizontal and vertical radar views.
2. RoIAlign is applied, and resulting features (tensor size $C \times r \times r$ for each view) are concatenated for each proposal.
3. The conditioned feature is processed by a detection head comprising self-attention, dynamic convolution, and a feed-forward network to output refined box parameters and classification scores.

This explicit, geometry-driven mechanism contrasts with RFMask (which matches 2D proposals using a fixed vertical window, leading to quadratic scaling and implicit associations) and RETR (which performs cross-attention from learned queries to features, potentially resulting in ambiguous feature–query matches and less geometric specificity) (Yataka et al., 21 Nov 2025).

5. Quantitative Performance and Ablation Studies

REXO was evaluated on MMVR (345,000 frames) and HIBER (73,500 frames) indoor radar datasets. Using mean average precision (mAP) over $\text{IoU} \in [0.5, 0.95]$ and established baselines:

• On MMVR P2S2 (unseen, cluttered), REXO improved mean AP by +11.02 (RETR: 12.45 $\rightarrow$ REXO: 23.47).
• On HIBER WALK, the gain was +3.24 AP (RETR: 22.09 $\rightarrow$ REXO: 25.33).
• Additional gains observed in less challenging splits as well.

Ablation experiments demonstrate that the ground-contact prior alone yields 0.8–4.2 AP improvement, both 2D and 3D geometric losses are essential, and performance increases with additional diffusion steps. REXO is robust to the number of boxes handled in both training and inference, and adapts to various radar view configurations (Yataka et al., 21 Nov 2025).

Notable limitations include degraded performance when multiple people overlap in depth by less than 20 cm in the vertical view, and runtime constraints with full diffusion sampling (approx. 4 FPS at 5 steps), presenting a trade-off between accuracy and throughput.

6. $R_\mathrm{exo}$: Exobase Radius in Atmospheric Escape Physics

In planetary atmospheric escape modeling, $R_{\rm exo}$ (“Rexo”) denotes the exobase: the boundary between the collisional thermosphere (where hydrostatic equilibrium and local thermodynamic conditions dominate) and the kinetic exosphere (where ballistic escape and radiation acceleration prevail). In the context of exoplanet HD 209458b,

• Best-fit $R_{\rm exo} = 3.0^{+1.3}_{-0.9}\,R_p$ (planet radius), with constraints $2.1 \leq R_{\rm exo}/R_p \leq 4.3$.
• This radius lies at or just above the Roche lobe (critical gravitational equipotential).
• Inside $R_{\rm exo}$, neutral magnesium density follows

$$n_{\rm Mg^0}(r) = n_{\rm Mg^0}(R_{\rm exo}) \exp\left[ \frac{GM_p \bar m}{k_B \overline T } \left( \frac{1}{r} - \frac{1}{R_{\rm exo}} \right) \right], \quad (r \leq R_{\rm exo})$$

• Escape profiles and observed absorption features (depth, width of Mg I line) are highly sensitive to $R_{\rm exo}$, as detailed in grid-based simulations that vary $R_{\rm exo}$, planetary wind velocity, escape rate, and electron density (Bourrier et al., 2014).

If $R_{\rm exo}$ is below $\sim2R_p$, excessive self-shielding and gravitational confinement suppress the high-velocity blue wing in Mg I absorption. Above $4.3R_p$, hydrostatic assumptions break down. Accurate characterization of $R_{\rm exo}$ is thus critical for atmospheric escape modeling, especially in Roche lobe-filling hot Jupiters (Bourrier et al., 2014).

7. Future Directions and Extensions

Potential research avenues for REXO (indoor radar context) include:

• Diffusing box orientation parameters for non-axis-aligned objects.
• Incorporating Doppler features to improve moving target discrimination.
• Fusing radar and RGB views in a joint diffusion and detection framework.
• Optimizing inference speed for real-time or embedded applications.

For $R_{\rm exo}$ in exoplanet escape modeling, research will further explore coupling $R_{\rm exo}$ to hydrodynamic wind solutions, treatment near Roche potentials, and detailed line-profile modeling under varying planetary/stellar irradiation conditions.

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References:

• “REXO: Indoor Multi-View Radar Object Detection via 3D Bounding Box Diffusion” (Yataka et al., 21 Nov 2025)
• “Modeling magnesium escape from HD209458b atmosphere” (Bourrier et al., 2014)