GeoComplete: Geometry-Aware Frameworks

• GeoComplete is a geometry-aware framework that integrates explicit 3D structure into both image completion and geospatial reasoning.
• It employs a dual-branch diffusion network that fuses masked target features with point-cloud geometry using joint self-attention to maintain spatial consistency.
• The framework also features an LLM-based georeferencing method to accurately process complex, relative spatial descriptions in natural language.

GeoComplete denotes a family of geometry-aware computational frameworks, most prominently associated with reference-driven image completion and advanced geospatial natural language processing. Recent usage centers around two distinct, state-of-the-art implementations: a geometry-conditioned diffusion framework for multi-view image inpainting (Lin et al., 3 Oct 2025) and a large-language-model-based approach for georeferencing complex, relative spatial descriptions in text data (Fernando et al., 16 Dec 2025). Both methodologies explicitly leverage geometric structure to enhance inference, fidelity, and usability in spatial tasks previously dominated by either vision-only or text-only models.

1. Geometry-Aware Diffusion for Reference-Driven Image Completion

GeoComplete (Lin et al., 3 Oct 2025) introduces a structured approach to reference-driven image completion, designed to handle missing content in a target image by synthesizing plausible regions using one or more auxiliary reference views. This framework distinguishes itself by conditioning the generative process on explicit 3D geometry, derived from camera calibration (intrinsics and extrinsics) and depth maps, to maintain spatial consistency even across significant view changes.

Fundamental variables include:

• $x_0^{tgt} \in \mathbb{R}^{H\times W\times 3}$, denoting the ground-truth target image,
• $\{x_0^{ref,i}\}$, a set of $N$ reference images,
• $P^{tgt} \in \mathbb{R}^{3\times 4}$ and $P^{ref,i}\in \mathbb{R}^{3\times 4}$, the associated camera projection matrices,
• $d^{tgt}(u,v)$ and $d^{ref,i}(u,v)$, dense depth maps per pixel.

Each view's pixels are back-projected into $\mathbb{R}^3$ to create a union point cloud $Q$, which is then projected into the target view, forming $$Q^{tgt} = \pi(P^{tgt}, \bigcup \pi^{-1}(P^{ref,j}, d^{ref,j}))$$.

2. Dual-Branch Diffusion Network and Target-Aware Masking

GeoComplete's architecture employs a dual-branch UNet:

• A "target branch" encodes the masked target image into features $\{x_0^{ref,i}\}$0,
• A "point-cloud branch" encodes the projected geometric features $\{x_0^{ref,i}\}$1.

Features are concatenated and processed with joint self-attention, regulated by a masking matrix $\{x_0^{ref,i}\}$2 to enforce structured inter- and intra-branch attention: only corresponding spatially-overlapping tokens are permitted cross-branch interaction. Mathematically, for $\{x_0^{ref,i}\}$3, the joint-attention computation is:

$\{x_0^{ref,i}\}$4

where $\{x_0^{ref,i}\}$5 are learned projections and $\{x_0^{ref,i}\}$6 is the feature size.

To address occlusions—regions present in references yet missing from the target—the framework computes, per reference, a redundancy mask $\{x_0^{ref,i}\}$7 by projecting the target's support into each reference via calibrated warping. Conditional masking then ensures the model is trained to selectively leverage only genuinely informative areas during completion.

3. Training Procedure, Loss Formulation, and Ablations

GeoComplete leverages standard denoising diffusion probabilistic modeling with the forward noising:

$\{x_0^{ref,i}\}$8

and the learned denoising process:

$\{x_0^{ref,i}\}$9

with point-cloud conditioning.

The primary loss is the $N$0 denoising error on masked pixels, with auxiliary losses for geometric consistency:

• $N$1: $N$2 depth discrepancy over informative pixels,
• $N$3: $N$4 image reconstruction error over visible target regions, resulting in

$N$5

with $N$6.

Algorithmic pseudocode details the generation of point clouds, mask computation, and diffusion steps for both training and inference.

Ablation studies document that removing geometric conditioning or joint attention degrades PSNR from $N$7 dB to $N$8 and $N$9 respectively, emphasizing the criticality of explicit geometry.

4. Empirical Performance and Evaluation

Comprehensive evaluation of GeoComplete is performed on the RealBench and QualBench datasets against prompt-based (Stable-Diffusion Inpaint, Adobe Generative Fill) and reference-based (Paint-by-Example, TransFill, RealFill) baselines. Key metrics:

Model	PSNR (dB)	SSIM	LPIPS	DINO	CLIP	DreamSim	User Study (5pt)
RealFill	14.78	0.424	0.431	0.948	0.962	0.077	3.98
GeoComplete	17.32	0.578	0.197	0.986	0.987	0.036	4.61

Qualitative inspection reveals that geometry-unaware approaches hallucinate or misalign in extrapolative completions, whereas GeoComplete preserves 3D plausibility, especially under extreme viewpoint shifts.

Ablation confirms geometric branch and joint-attention each contribute substantially to cross-view consistency.

5. LLM-Based Georeferencing of Relative Locality Descriptions

A separate thread of GeoComplete (Fernando et al., 16 Dec 2025) addresses the automatic georeferencing of relative spatial descriptions in natural language, critical for biodiversity informatics. Traditional gazetteer-based methods falter with complex, narrative locality statements lacking explicit toponyms. The GeoComplete-inspired pipeline fine-tunes LLMs (Mistral-7B, QLoRA adapters) to interpret text like “10 km north of Lake Wanaka, 1 km north of Makarora, near Pipson Creek.”

Prompt engineering identifies "Context Manager" patterns as optimal: $P^{tgt} \in \mathbb{R}^{3\times 4}$4 These achieve the most consistent outputs across LLMs.

Fine-tuning is performed on diverse regional datasets (~29–32k records each from NZ, USA, AUS, MX), using 4-bit quantization and rank=32 adapters on a single A100 24GB GPU. LLM reasoning follows known spatial calculation formulations; e.g., for distance $P^{tgt} \in \mathbb{R}^{3\times 4}$0 and bearing $P^{tgt} \in \mathbb{R}^{3\times 4}$1 from $P^{tgt} \in \mathbb{R}^{3\times 4}$2, \begin{align*} \varphi_2 &= \arcsin(\sin\varphi_1 \cos(d/R) + \cos\varphi_1 \sin(d/R) \cos\theta) \ \lambda_2 &= \lambda_1 + \arctan2(\sin\theta \sin(d/R)\cos\varphi_1, \cos(d/R) - \sin\varphi_1\sin\varphi_2) \end{align*}

Error is assessed via the Haversine metric: $P^{tgt} \in \mathbb{R}^{3\times 4}$3

6. Quantitative Results and Pipeline Integration

On standard benchmarks, the fine-tuned LLM achieves significant improvements on georeferencing tasks:

Dataset	Model	Acc@10km	Acc@1km	Median SAE	Mean SAE
New Zealand	Fine-tuned Mistral-7B	70.43%	25.36%	3.55 km	41.95 km
New York	Fine-tuned Mistral-7B	84.89%	66.71%	0.083 km	17.59 km
Mexico	Fine-tuned Mistral-7B	75.82%	51.41%	0.89 km	20 km

Integration into practical pipelines typically combines SpaCy NER-based gazetteer pre-filtering with the LLM resolver, with results validated using Haversine clustering or map overlays. Long, information-rich descriptions benefit most; cross-region transfer is limited unless local examples are included.

7. Limitations and Prospective Directions

Both GeoComplete paradigms manifest limitations:

• For diffusion completion, geometry conditioning relies on depth and calibration accuracy; failure cases involve ambiguous or sparse views.
• For LLM georeferencing, training data density is critical for large-area domains; absence of built-in uncertainty estimation and handling highly ambiguous or multi-clause localities remain open issues.

A plausible implication is that future iterations will incorporate retrieval augmentation for external gazetteer lookups, explicit uncertainty quantification, and interactive correction mechanisms. For the generative vision branch, enhanced multi-modal fusion and real-world scale awareness are promising directions.

In summary, GeoComplete encompasses geometry-aware image synthesis and advanced LLM-based geospatial reasoning, each integrating explicit geometric structure to advance spatial inference and completion beyond previous attribute- or appearance-only systems (Lin et al., 3 Oct 2025, Fernando et al., 16 Dec 2025).