FlatLands: Generative Floormap Completion From a Single Egocentric View

1. Problem Definition

The paper addresses the challenge of Single-View Bird's-Eye View (BEV) Floor Completion. In indoor autonomous navigation, robots often operate under partial observability, where a single egocentric RGB image captures only a narrow frustum of the floor, leaving the majority of the traversable area unobserved due to occlusions and limited field of view.

The core task is to infer a complete, metric traversability map (a binary grid indicating floor vs. non-floor) from a single image. Crucially, the paper frames this not as a deterministic point-estimation problem but as a Bayesian inverse problem. Since a single partial observation can correspond to multiple plausible room layouts (e.g., a hallway could continue straight, turn left, or end), the goal is to sample from the posterior distribution $P(F_{unobserved} | F_{observed})$ rather than predicting a single "best guess." This allows downstream planners to reason about uncertainty and risk.

2. Methodology

A. The FlatLands Dataset and Benchmark

To enable rigorous evaluation, the authors introduce FlatLands, the first large-scale benchmark for this task.

• Scale: Aggregates 17,656 real metric indoor scenes from six existing datasets (ZInD, ARKitScenes, Matterport3D, ScanNet, 3RScan, and ScanNet++).
• Observations: Contains 270,575 synthesized observations. For each scene, virtual cameras are placed at floor-valid positions with 24 different yaw headings.
• Data Structure: Each observation includes:
  • $F_{obs}$: The observed floor (projected from the image).
  • $U$: The unobserved mask (valid but unseen regions).
  • $F^*$: The ground-truth full floor map.
  • $V$: A validity mask distinguishing in-bounds from out-of-bounds regions.
• Splits: Includes explicit In-Distribution (ID) and Out-of-Distribution (OOD) splits, with ScanNet++ reserved strictly for OOD testing to ensure generalization is not overfitted to specific architectural styles.

B. Pipeline Architecture

The system operates in two stages (Fig. 1):

1. Perception Front-End: Converts a single RGB image into a BEV observation.
   • Uses DepthPro for metric depth estimation and SegFormer for floor segmentation.
   • Projects these signals orthographically onto a 256×256 BEV grid using camera intrinsics to generate $F_{obs}$ and the unobserved mask $U$.
2. Generative Completion: A conditional generative model takes $(F_{obs}, U)$ as input and predicts completions for the unobserved region $U$.
   • Constraint: The model must strictly preserve the observed evidence ($F_{obs}$) via "hard clamping" (Eq. 3), ensuring the output matches the input where data exists.

C. Baselines and Models Evaluated

The paper benchmarks 11 methods across four categories:

1. Training-Free/Naive: All-Obstacle, All-Floor, Nearest-Neighbor Propagation, Uniform Random.
2. Deterministic Models: U-Net, PartialConv U-Net, and LaMa (adapted for binary maps). These output a single point estimate.
3. Epistemic Ensembles: LaMa Ensemble (4 independent models with different seeds).
4. Stochastic Generative Models:
   • Diffusion: Denoising Diffusion Probabilistic Models (DDPM) with per-step evidence clamping.
   • Flow Matching: ODE-based transport models.
   • FM+XAttn: Flow Matching augmented with Cross-Attention Conditioning, where an encoder processes the conditioning pair $(F_{obs}, U)$ and injects features via cross-attention at coarse resolutions (64×64, 32×32).

D. Evaluation Metrics

Beyond standard fidelity metrics (IoU, F1), the paper introduces metrics to evaluate calibration and diversity:

• UMR (Unobserved-Region Mismatch Rate): Measures error specifically in the unobserved valid region.
• MES (Masked Energy Score): A proper scoring rule that balances fidelity (distance to ground truth) and diversity (spread among samples). Lower is better.
• Boundary Variance Analysis: Decomposes variance into "interior" (geometrically determined) and "boundary" (structurally ambiguous) regions to assess if uncertainty is localized correctly.

3. Key Contributions

1. FlatLands Benchmark: A rigorous, large-scale dataset with aligned observations, visibility masks, and ground truth, specifically designed for single-view BEV floor completion with ID/OOD splits.
2. Formalization of Uncertainty: Establishes that floor completion is a multi-modal problem requiring posterior sampling rather than deterministic prediction.
3. Comprehensive Benchmarking: Evaluates 11 methods, demonstrating that stochastic generative models significantly outperform deterministic predictors in capturing layout ambiguity.
4. Architectural Insight: Identifies that FM+XAttn (Flow Matching with Cross-Attention) achieves the best balance of fidelity and calibration. It successfully localizes uncertainty to structurally ambiguous boundaries, whereas ensemble methods (like LaMa-Ens) conflate seed divergence with genuine layout ambiguity, producing high variance even in geometrically certain regions.
5. End-to-End Validation: Confirms that method rankings hold even when using real monocular RGB inputs with estimated depth and segmentation, proving the pipeline's viability for real-world sensors.

4. Results

• Stochastic vs. Deterministic: Stochastic models with "Oracle Best-of-K" selection (choosing the best sample from 4) consistently outperform all deterministic models in both ID and OOD settings. This confirms that posterior sampling recovers higher-fidelity completions that single-pass estimators miss.
• Top Performer: FM+XAttn achieves the lowest Masked Energy Score (MES) and best calibration. It concentrates variance at layout boundaries (where ambiguity is real) rather than uniformly across the map.
• Failure Modes:
  • LaMa (Deterministic): Prone to mode collapse under sparse conditioning (e.g., when >50% of the floor is unobserved), often outputting near-zero floor area.
  • Boundary Leakage: All generative methods struggle when conditioning is extremely sparse, sometimes over-extending floor into obstacle-heavy areas, though FM+XAttn is the most conservative.
• OOD Generalization: Method rankings are preserved on the ScanNet++ OOD split, indicating that the learned layout priors generalize across different architectural styles and capture conditions.
• End-to-End Performance: When moving from ground-truth BEV inputs to real RGB inputs (via DepthPro/SegFormer), performance degrades for all models, but the relative ranking remains stable. Interestingly, the advantage of stochastic models diminishes in the end-to-end setting because upstream perception errors dominate the error budget.

5. Significance and Impact

• Embodied AI: Provides a critical tool for robots to build probabilistic spatial priors for belief-space planning, active perception, and SLAM. By understanding where they are uncertain, robots can make safer navigation decisions or decide to move to gather more information.
• Generative Modeling: Demonstrates the superiority of conditional flow matching and diffusion models over traditional inpainting (like LaMa) for geometric map completion, particularly when using cross-attention mechanisms to handle global layout constraints.
• Standardization: Fills a gap in the field by providing a standardized benchmark for indoor metric map completion, moving beyond synthetic simulations to real-world metric data.
• Future Directions: The work highlights the need for better front-end perception (depth/segmentation) as the current bottleneck, and suggests future work in multi-view settings, semantic conditioning, and graded traversability (e.g., stairs, slopes).

In summary, FlatLands establishes that generating a distribution of plausible floor maps is essential for robust indoor navigation, and that modern conditional generative models (specifically Flow Matching with Cross-Attention) are the most effective approach for this task.