💻 computer science

GALoc: Gravity Aligned Wireframes for Depth-Free Monocular Floorplan Localization

GALoc is a geometry-first framework for monocular floorplan localization that replaces brittle depth prediction with gravity-aligned wireframes to achieve robust, depth-free indoor positioning by satisfying verticality and coplanarity constraints.

Original authors: Jeahn Han, Minji Kim, Jeongbin Sohn, Jonghyeok Park, Matthias Wuest, Pyojin Kim

Published 2026-09-09

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CC BY 4.0

Original authors: Jeahn Han, Minji Kim, Jeongbin Sohn, Jonghyeok Park, Matthias Wuest, Pyojin Kim

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside a building, the walls do not change their shape when the lights go out or when the furniture is rearranged. This stability makes architectural floorplans powerful tools for helping computers figure out where they are. Unlike photographs, which can look completely different depending on the time of day or the clutter in a room, a floorplan is a simple, unchanging map of the structure itself. For years, researchers have tried to use these maps to guide robots and augmented reality devices, but most existing methods rely on a fragile step: they first try to guess the distance to every object in a scene using complex software. This guesswork often fails in messy rooms where chairs and tables confuse the computer, or in empty spaces where there is no texture to measure. The result is a system that works well in perfect conditions but breaks down in the real world.

A new approach called GALoc, developed by researchers at GIST, KAIST, and Zurich University of Applied Sciences, bypasses this guessing game entirely. Instead of trying to calculate how far away everything is, the system focuses on the straight lines and corners that define the walls. It treats the camera's view as a set of wireframe sketches that must obey the laws of physics: walls are vertical, and floors and ceilings are flat. By using a sensor that knows which way is down (gravity), the system can mathematically align these wireframes to the real world without ever needing to know the exact distance to the walls. This method allows the computer to match the view from a single camera directly against a floorplan, finding its location with high precision even when the room is cluttered or the lighting is poor.

The core of this innovation is a shift in how the computer understands a room. Traditional systems act like a person trying to estimate distance by squinting, which is prone to error. GALoc acts more like an architect who knows that a wall must stand straight up and that a floor must be level. When the system looks at a room, it first identifies the junctions where walls meet the ceiling or floor. If the camera is tilted, these lines will appear skewed. The system then searches for the specific angle that, if applied to the camera, would make all those lines perfectly vertical and all the floor points perfectly flat. It does this by testing thousands of angles until it finds the one that makes the geometric rules fit together perfectly. Once the system has "straightened" the view, it projects the walls onto a flat, top-down map, much like looking at a building from a helicopter. This top-down view is then compared against the known floorplan to pinpoint the camera's exact location and orientation.

In testing this method, the researchers found that it excels where other methods struggle. They evaluated the system using both simulated environments and real-world footage captured in offices and long corridors. In a simulated dataset called Gibson, which features wide views of rooms, the system successfully located the camera within a tenth of a meter over a sequence of 100 steps in 88 percent of cases. By comparison, a leading method that relies on distance estimation succeeded only 68 percent of the time in the same conditions. The difference becomes even more stark when the system encounters a room full of furniture. While the distance-based method often mistakes a chair for a wall and loses its way, GALoc ignores the clutter because it only cares about the structural lines of the room. When the system cannot see enough of the walls to make a decision, it simply admits uncertainty rather than guessing a wrong location, which prevents it from drifting off course.

The researchers also tested the system in real buildings using a standard smartphone. In a cluttered office and a long corridor, the system managed to track movement with an error of less than half a meter over the length of the path. However, the study also highlighted a current limitation: the system depends on a tool that can accurately draw the wireframe lines from a photo. In the real-world tests, when the researchers used an automatic tool to find the lines, the system was less accurate than when they manually marked the corners. This suggests that the future of this technology depends less on the localization math and more on improving the ability of computers to see and draw the structural lines of a room as clearly as a human can. Until that tool becomes more robust, the system remains a powerful but specialized solution that works best when the walls are visible and the geometry is clear.

The findings demonstrate that a computer does not need to know the depth of a room to know where it is. By relying on the rigid geometry of architecture and the constant pull of gravity, the system achieves a level of stability that distance-based methods cannot match. It proves that for indoor navigation, understanding the shape of the space is often more important than measuring the distance to every object within it. As the tools for detecting these structural lines improve, this gravity-aligned approach could become a standard way for devices to navigate the complex, cluttered interiors of our daily lives.

Technical Summary: GALoc – Gravity Aligned Wireframes for Depth-Free Monocular Floorplan Localization

Problem Definition

Visual localization in indoor environments often relies on dense 3D reconstructions or pre-built maps that degrade under appearance changes. While floorplan-based localization offers a compact, appearance-invariant alternative, existing methods typically depend on depth estimation—either from RGB-D sensors or learned depth networks—to align camera poses with architectural structures. This reliance on depth is fragile: in cluttered scenes, furniture is often mistaken for walls, and depth regressors extrapolate poorly in low-texture or unseen environments. The core issue is that depth is an intermediate representation not strictly required for the task; the fundamental requirement is the geometric structure of walls.

Methodology

GALoc proposes a depth-free, geometry-first framework that replaces depth prediction with gravity-aligned wireframes. The system operates on a temporal sequence of monocular RGB images, camera intrinsics, relative poses, and IMU orientation (roll/pitch). The pipeline consists of the following stages:

1. Wireframe Extraction and Completion

The system employs PolygonHGT to extract wireframes (wall junctions and connectivity) from RGB images. Truncated wall cycles at image boundaries are completed using line intersections and vanishing directions. Each completed cycle is labeled with ceiling/floor status and a Field-of-View (FOV) arc label (Known or Unknown).

2. Null Space Gravity Alignment (Core Contribution)

Instead of optimizing reprojection error or regressing depth, GALoc formulates gravity alignment as a null-space search.

Constraint Formulation: A linear constraint matrix $A(\theta)$ is constructed from 2D wireframe junctions, encoding verticality (ceiling and floor points share $x$ and $z$ coordinates) and coplanarity (all ceiling points share a $y$ height; all floor points share a $y$ height).
Gauge Estimation: The unknown camera yaw ( $\theta$ ) is recovered by finding the angle that minimizes the smallest singular value ( $\sigma_{min}$ ) of $A(\theta)$ . At the correct gauge, the matrix becomes rank-deficient, allowing a non-trivial solution for the depth vector $Z$ .
Structure Recovery: Using the Eckart–Young–Mirsky (EYM) theorem, the system projects the noisy matrix to its nearest rank-deficient form. The null-space vector of this projected matrix yields the depth ratios $Z$ . This process ensures that the recovered 3D wireframe satisfies verticality and coplanarity by construction, without requiring depth supervision.

3. Bird's-Eye-View (BEV) Transformation

The rectified 3D wireframes are projected onto the X–Z plane to generate a BEV layout. A closed-form, scale-free transformation is derived using the inscribed-angle theorem to ensure FOV consistency. This corrects distortions caused by noise, placing the camera on a circle where the subtended angle matches the known FOV.

4. Sequential Localization

The BEV layout is matched against a wall-only floorplan via metric-free SE(2) search.

Raycasting: Observation rays are cast from the camera position across the known FOV sectors.
Scoring: A masked cosine similarity scores the alignment between observed rays and precomputed map profiles.
Fusion: A histogram filter performs sequential fusion, shifting the belief distribution based on odometry and updating it with confidence-weighted log-likelihoods. The system abstains from updating the belief in "structure-blind" scenes (where no full wall panels are visible) to prevent error accumulation.

Key Contributions

Null Space Gravity-Aligned Rectification: A novel approach that recovers the camera gauge (yaw) and 3D wireframe structure simultaneously by minimizing the smallest singular value of an architectural constraint matrix. This eliminates the need for learned depth regression.
Field-of-View Consistent BEV Transformation: A closed-form, scale-free method to project gravity-aligned wireframes into a BEV layout that guarantees FOV consistency, enabling accurate raycasting against floorplans.
Depth-Free Framework: The system operates without learned depth, semantic annotations, or panoramic inputs, relying solely on wireframe geometry and IMU orientation.

Experimental Results

The authors evaluate GALoc on three datasets: Structured3D (synthetic, non-upright), Gibson (synthetic, gravity-aligned), and real-world author-collected sequences.

Single-Image Localization: On Structured3D, GALoc's aggregate recall is lower than depth-based baselines (F3Loc) because it abstains on frames with zero wall coverage (approx. 40% of frames). However, in frames with sufficient coverage (>40%), GALoc matches or outperforms baselines. On Gibson, where over 80% of frames have sufficient coverage, GALoc achieves 3× higher recall at 0.1m compared to F3Loc.
Sequential Localization: On Gibson sequences (100 steps), GALoc achieves an 88% success rate at 0.1m error, significantly outperforming the baseline F3Loc (68%). GALoc converges faster (7–10 frames) and avoids the "confident-but-wrong" observations that corrupt depth-based filters in cluttered scenes.
Real-World Performance: In zero-shot real-world tests, GALoc achieves 20% recall at 1m, while F3Loc fails entirely (0% recall). With hand-labeled junctions (semi-ground truth), GALoc's recall jumps to 80%, indicating that the localization geometry is robust, but the bottleneck lies in the wireframe extractor's domain transfer capabilities.
Runtime: The end-to-end runtime is approximately 2.32 seconds per frame on a consumer GPU, dominated by the wireframe extraction step.

Significance and Claims

The paper claims that GALoc demonstrates a viable alternative to depth-dependent localization by leveraging the geometric priors of indoor environments (verticality and coplanarity).

Complementary Regimes: The authors posit that GALoc and depth-based methods occupy complementary regimes. GALoc excels when wall geometry is visible, offering superior precision and robustness to clutter, while abstaining when structure is absent.
Robustness: By removing the dependency on depth regression, the system avoids the brittleness of depth networks in low-texture or cluttered scenes.
Future Outlook: The authors note that current limitations are tied to the wireframe extractor's performance. As wireframe extraction matures to match the robustness of modern monocular depth, geometry-first localization is expected to become competitive across a wider range of environments. The paper does not claim to solve all localization problems but highlights the potential of "geometry-first" approaches when sufficient structural cues are available.