geometric consistency calibration

This work addresses the physical inconsistency in conventional multi-view satellite image evaluation, which relies on unconstrained 2D matching and ignores the epipolar geometry implicitly encoded in Rational Polynomial Coefficients (RPCs). The paper proposes the first geometry-aware evaluation protocol tailored to the RPC framework: it constructs a geometrically constrained search manifold via 3D projection and employs dense matching as a proxy task to assess the local uniqueness of features within a physically plausible space. By integrating geometric constraints into foundational model evaluation for the first time, this approach reveals a decoupling between semantic consistency and geometric localization capability, and establishes a reproducible, geometry-faithful benchmark for satellite imagery. Experiments demonstrate that, under RPC-consistent evaluation, generic 2D backbone networks outperform specialized 3D-aware models, underscoring the fundamental importance of geometric constraints in task formulation.

This paper addresses text-driven scene-consistent image generation: synthesizing images that simultaneously preserve geometric/appearance fidelity to a reference scene graph and accurately realize textual descriptions of target entities and their spatial relationships. To overcome the trade-off between these competing objectives in existing methods, we propose a geometry-guided diffusion framework comprising: (1) a multi-view geometric modeling pipeline for constructing scene-consistent training data; (2) self-supervised spatial regularization incorporating cross-view geometric constraints; and (3) a scene-text joint attention mechanism. Notably, this work is the first to explicitly integrate geometric priors into attention optimization for text-to-image generation. On our newly established benchmark, our method achieves +12.6% CLIP-Scene score, +9.3% TIFA score, and 78.4% human preference rate, demonstrating strong capability in generating complex geometric compositions.

Existing spatial pattern matching methods are largely confined to two-dimensional space and struggle to handle three-dimensional entity matching involving elevation or height information in real-world scenarios. This work extends spatial pattern matching to 3D environments for the first time, introducing a general problem formulation and proposing a subgraph-matching-based algorithm that explicitly models distance relationships in three-dimensional space. To support empirical evaluation, the authors construct the first 3D spatial pattern matching dataset, integrating both synthetic data and real-world building structures from the city of Hamburg. Experimental results on this benchmark demonstrate the effectiveness of the proposed approach, establishing a foundational algorithmic framework and experimental platform for future research in 3D spatial pattern analysis.

To address the lack of global geometric consistency constraints in local feature matching for point cloud registration, this paper proposes iMatcher—a fully differentiable, end-to-end matching framework. Its core contributions are threefold: (1) constructing local graph embeddings to explicitly model neighborhood structural relationships; (2) introducing a bidirectional source–target matching relocation mechanism to enhance the robustness of initial correspondences; and (3) designing a global geometric consistency learning module that jointly optimizes match confidence scores and rigid-body transformation constraints. Evaluated on KITTI, KITTI-360, and 3DMatch benchmarks, iMatcher achieves inlier ratios of 95–97%, 94–97%, and 81.1%, respectively—substantially outperforming state-of-the-art methods. These results validate the effectiveness of synergistic local–global modeling for robust and accurate point cloud registration.

In spatial prediction tasks—such as weather forecasting and pollution modeling—the validation and prediction locations are fixed and non-overlapping, violating the i.i.d. assumption underlying conventional validation methods (including those correcting for covariate shift), which presume stochastic sampling rather than deterministic spatial sampling. This work formally introduces the notion of *validation consistency*: as the density of validation locations tends to infinity, the validation error must converge arbitrarily closely to the true prediction error. Building upon this principle, we propose the first theoretically guaranteed consistent spatial validation framework, integrating spatial sampling theory with weighted density estimation to accommodate both gridded and irregularly spaced observational structures. We prove its consistency under mild regularity conditions. Empirical evaluation on meteorological and air pollution datasets demonstrates that our method significantly outperforms standard cross-validation and importance-weighting baselines, achieving an average 37% reduction in estimation error.

This study addresses the insufficient robustness and accuracy of local feature matching in overlapping regions of satellite imagery. To this end, the authors construct a manually curated satellite image dataset annotated with GPS coordinates and conduct a systematic evaluation of SIFT and ORB algorithms across the entire matching pipeline—including keypoint detection, descriptor extraction, feature matching, and RANSAC-based geometric verification. Using the inlier ratio as the primary metric for matching quality, the work quantitatively analyzes the impact of keypoint quantity on matching performance. The results reveal a nonlinear relationship between the number of detected keypoints and the inlier ratio, offering empirical evidence and theoretical guidance for algorithm selection and parameter tuning in remote sensing image matching tasks.

This work addresses the challenge of automatically formalizing and verifying proofs for International Mathematical Olympiad (IMO)-level Euclidean geometry problems. It introduces GeoFormalizer, a Mathlib-native agent framework that translates informal problem statements into a geometric intermediate representation (GeoIR) and then into Lean 4, iteratively refining the formalization through structural diagnosis and semantic evaluation. Complementing this, GeoProver generates lemmas via geometric proof planning and algebraizes subgoals, producing algebraic certificates using Singular or SymPy, all verified by the Lean kernel. The approach achieves the first large-scale, kernel-verified automated proofs and counterexample generation for IMO geometry, incorporating a counterexample-guided diagnostic mechanism that significantly enhances weak models’ formalization performance. On 43 historical IMO problems, it proves 29 directly, generates Lean-verified counterexamples for the remaining 14—later proving corrected versions—and establishes the largest automated, kernel-verified IMO geometry proof set to date, including 12 new proofs and formal refutations of two previously conjectured statements on Lean-IMO-Bench.

This work addresses the challenge of inconsistency among problem statements, diagrams, constraints, and solutions in automatic geometry problem generation by proposing a controllable generation framework grounded in executable reasoning traces. The framework employs collaborative Author and Solver agents to generate aligned problem-solution pairs and introduces, for the first time, a three-stage verification mechanism that integrates numerical consistency, analytical feasibility, and global coherence checks. Invalid samples are either filtered or corrected through a verification-guided reflection-and-repair strategy. Experimental results demonstrate that the proposed method significantly reduces invalid generations across five large language models. Furthermore, models fine-tuned on the 8.7k-sample VeriGeo dataset achieve state-of-the-art or competitive performance on GeoQA, PGPS9K, and MathVista-GPS benchmarks.

This work addresses the challenge of high-definition (HD) map generation in regions lacking professional surveying infrastructure, where conventional approaches rely on costly dense sensor suites and high-precision reference data. The authors propose a lane-level HD map construction pipeline that operates solely on publicly available geospatial engineering data and adopts a lanelet-based representation. Notably, they introduce a constraint-driven validation mechanism that requires no external reference, enabling self-consistency checks through geometric, topological, and elevation-based regulatory constraints. This approach substantially enhances the modularity and auditability of the mapping workflow. Evaluated on real-world road networks across four cities in Lower Saxony, Germany, the method demonstrates robust performance, achieving a 100% defect detection rate with zero false positives in controlled defect-injection experiments.

This work addresses the poor performance of large reasoning models on spatial reasoning tasks, which typically rely on costly annotated data. The authors propose the first unsupervised reinforcement learning framework that aligns the model’s internal reasoning process through geometric and semantic consistency verifiers, eliminating the need for ground-truth labels. Key innovations include a novel consistency verification mechanism, the design of an optimal transport–based OT-GRPO algorithm, and the integration of self-supervised learning with multimodal transformations. Experimental results demonstrate that the method achieves accuracy comparable to supervised approaches under label-free conditions and exhibits strong generalization across multiple tasks and domains.