PaperlayerView exact revision on arXiv

Source-linked AI summary

DLOSAC: Joint Spatial-Geometric Image Estimation via Delaunay-Guided Local Optimization RANSAC

Yu Liu, Meiqi Zhou, Zipei Fan, Guanyuan Feng, Xuan Song

arXiv:2610.21215v1cs.CV

TL;DR

Noisy matching points and residual-centric local optimization leave spatial distribution and geometric refinement insufficiently integrated. DLOSAC jointly uses Delaunay-based neighborhood structure, edge-level geometric consistency, spatial descriptors, and point-level constraints; it reports state-of-the-art performance across three tasks, with gains over the strongest baseline on each.

  • Problem

    Existing local optimization emphasizes point-level geometric residuals, while spatial bucketing heuristics separate distribution optimization from residual minimization.

    Source: §I · p. 1

  • Method

    DLOSAC triangulates candidate inliers and combines edge-level geometric consistency, triangle- and edge-derived spatial descriptors, and point-level constraints in local optimization.

    Source: §I · p. 1, 3) Delaunay-Guided Local Optimization · p. 4

  • Results

    DLOSAC improves over the strongest baseline to date by +12.85% on fundamental-matrix estimation, +13.85% on relative-pose estimation, and +15.88% on homography estimation.

    Source: 1) Quantitative Geometry Estimation… · p. 5

  • Takeaways & Limitations

    Across six public datasets and three geometric estimation tasks, DLOSAC consistently achieves superior performance compared with existing state-of-the-art methods.

    Source: §VI · p. 7

    Gains are relatively modest in wide-baseline settings such as CPC and T&T, where strong parallax, depth variation, and non-coplanar structures can break approximate Euclidean invariance.

    Source: §VI · pp. 7–8

Abstract

from arXiv · show

Reliable image geometric estimation from noisy matching points is typically addressed using RANSAC, often combined with local optimization to refine inliers and model parameters. However, existing paradigms are predominantly residual-centric; even heuristic attempts to enforce spatial uniformity suffer from a sequential, two-stage nature that inherently decouples distribution optimization from geometric refinement, preventing an effective trade-off. In this paper, we propose DLOSAC, a local optimization framework that jointly incorporates both geometric consistency and spatial distribution information. We begin by constructing a Delaunay triangulation over candidate inliers to explicitly encode neighborhood topology. The geometric module introduces an edge-based consistency metric to evaluate geometric errors, while the spatial module derives distribution descriptors from triangle areas and edge attributes to quantify the clustering of inliers. Finally, we combine edge-based geometric constraints, spatial distribution regularization, and traditional point-level geometric constraints to improve the quality of geometric parameters. Extensive experiments on six publicly available real-world datasets, covering three types of geometric estimation tasks, achieve state-of-the-art performance.

I. INTRODUCTION

Noisy matches complicate geometric estimation, while existing local-optimization approaches leave spatial distribution and geometric refinement insufficiently integrated. DLOSAC combines these cues and is reported to outperform state-of-the-art methods across three estimation tasks.

  • Existing local optimization remains focused on point-level residuals, while bucketing-based spatial heuristics separate distribution optimization from residual minimization.This motivates a unified framework for balancing spatial uniformity and geometric consistency.Source: §I · p. 1
  • DLOSAC combines geometric consistency and spatial distribution by triangulating inliers, evaluating edge-level consistency, and deriving clustering descriptors from triangle areas and edge attributes.These cues are fused into an inlier weighting function for inlier selection and model estimation.Source: §I · p. 1
  • The framework couples a novel edge-based geometric measure with traditional point-based metrics and a spatial distribution model to assess inlier clustering.Source: §I · p. 1
  • DLOSAC significantly outperforms state-of-the-art methods in accuracy and robustness across six public real-world datasets and three geometric estimation tasks.Source: §I · p. 1

A. Image Geometric Estimation

Geometric estimation uses matched image features to fit model parameters despite noise and outliers. The paper motivates local optimization that jointly accounts for geometry and spatial distribution, and formulates parameter fitting as weighted least squares.

A. Image Geometric Estimation

  • Image correspondences may contain noisy inliers and gross outliers, motivating robust estimation; the section frames joint optimization of geometric consistency and inlier distribution as the goal.Source: A. Image Geometric Estimation · p. 2

B. Local Optimization RANSAC

  • Prior local optimization centers on point-level geometry, while the proposed edge-patch strategy adds edge-level consistency and patch-level spatial distribution as complementary cues.Source: B. Local Optimization RANSAC · p. 2

III. PROBLEM FORMULATION

  • The problem is formulated as weighted least-squares fitting of geometric parameters to correspondence-induced constraints, with weights modulating each correspondence’s influence.Source: §III · p. 2

1) Delaunay triangulation:

Delaunay triangulation turns matched points into a neighborhood graph, while local optimization refines RANSAC’s geometric estimate using its inliers. The framework overview places triangulation after RANSAC refinement and before loss computation and parameter optimization.

1) Delaunay triangulation:

  • Delaunay triangulation partitions planar points into triangles and induces a graph whose edges encode point adjacency.Its empty-circumcircle property excludes other points from each triangle’s circumcircle, and the triangulation maximizes the minimum triangle angle.Source: 1) Delaunay triangulation · p. 2

2) Local Optimization RANSAC:

  • RANSAC estimates parameters by maximizing the number of correspondences whose geometric residual falls below an inlier threshold.It repeatedly samples minimal subsets, scores hypotheses, and retains the highest-scoring model.Source: 2) Local Optimization RANSAC · pp. 2–3
  • LO-RANSAC re-estimates the current best model from its inliers or a filtered subset to improve accuracy and stability.The framework overview then builds a Delaunay triangulation over RANSAC inliers before computing losses and optimizing geometric parameters.Source: 2) Local Optimization RANSAC · p. 3, Figure 1 · p. 3

B. Proposed Local Optimization RANSAC

The proposed local optimization uses neighboring-edge length consistency as a geometric regularizer and triangle-derived descriptors to measure inlier spatial distribution. The edge cue is a discriminative prior, while point-level geometric errors remain the primary constraints.

1) Edge-Based Geometric Consistency Loss:

  • Under pure rotation, correctly matched neighboring points tend to preserve edge lengths, whereas mismatches can produce larger length changes.Under translation, even correct matches may have inconsistent edge lengths when neighboring points differ substantially in depth.Source: 1) Edge-Based Geometric Consistency Loss · p. 3
  • The edge loss weights neighboring-edge length variation by 1−d_ab, where d_ab is pixel distance normalized by the image diagonal.Closer points receive greater weight because they are more likely to have similar depths and satisfy the edge-consistency constraint.Source: 1) Edge-Based Geometric Consistency Loss · p. 3
  • L_edge is a discriminative prior derived under a simplified camera model, used only as a regularizer rather than a physical law.Point-based geometric errors, such as epipolar constraints or homography residuals, remain the primary constraints.Source: 1) Edge-Based Geometric Consistency Loss · p. 4

2) Spatial Distribution Loss:

  • The spatial loss uses adjacent-triangle areas and largest internal angles to describe each matched point’s spatial distribution.Smaller descriptor values indicate adjacent triangles closer to equilateral and with areas nearer the global mean.Source: 2) Spatial Distribution Loss · p. 4

3) Delaunay-Guided Local Optimization:

DLOSAC builds a Delaunay graph over inliers and combines edge-consistency and spatial-distribution losses into point-specific weights. Those weights are used in weighted least squares to estimate geometric parameters.

3) Delaunay-Guided Local Optimization:

  • DLOSAC builds a Delaunay triangulation over inliers and computes each node’s mean adjacent-edge and incident-triangle losses.These losses represent geometric consistency and spatial distribution, respectively.Source: 3) Delaunay-Guided Local Optimization · p. 4
  • Each node’s unified loss adds its mean edge loss to its mean spatial loss scaled by λ_spatial.The resulting loss is converted to a weight by exponential decay, so lower-loss nodes receive higher weights.Source: 3) Delaunay-Guided Local Optimization · p. 4
  • The node-specific weights are used in weighted least squares to solve for the geometric parameters.Nodes with higher geometric consistency and better spatial distribution receive exponentially higher weights.Source: 3) Delaunay-Guided Local Optimization · p. 4

V. EXPERIMENTS

The experiments are organized around comparisons with state-of-the-art methods, ablations of the proposed losses, and hyperparameter sensitivity. The supplied description states the study plan but gives no outcomes.

V. EXPERIMENTS

  • The comparative study evaluates DLOSAC against state-of-the-art geometric estimation techniques.The passage describes the study’s purpose but does not report comparative results.Source: §V · p. 4
  • The ablation study is designed to quantify the benefits of the edge–geometry consistency and spatial-distribution losses.No ablation outcomes are reported in the supplied passage.Source: §V · p. 4
  • The hyperparameter study evaluates how critical parameter choices influence final estimation quality.The supplied passage identifies this evaluation but does not state its findings.Source: §V · p. 4

A. Experimental Setup

The benchmark covers three geometric-estimation tasks across six public datasets, using established robust-estimation methods as baselines and task-specific error metrics.

1) Benchmark:

  • Fundamental- and essential-matrix estimation use TUM, KITTI, T&T, and CPC; homography estimation uses Homo and EVD.The benchmark uniformly samples 1,000 image pairs from each dataset with more than 1,000 images.Source: 1) Benchmark · p. 5

2) Baselines:

  • Comparisons include RANSAC, LO-RANSAC, LO+-RANSAC, GC-RANSAC, and PSC-RANSAC.RANSAC is the no-local-optimization baseline; the other methods add local refinement, graph-cut labeling, or displacement-space clustering and refinement.Source: 2) Baselines · p. 5

3) Evaluation Metrics:

  • Fundamental-matrix and homography accuracy use mean and standard deviation of pixel error; relative pose uses rotation and translation errors in degrees.The evaluation also defines an improvement rate relative to the proposed method and an overall relative-pose error measure.Source: 3) Evaluation Metrics · p. 5

B. Comparison with state-of-the-art methods

DLOSAC is compared with strong baselines across three estimation tasks and six datasets. It outperforms the strongest baseline on every task, with gains varying by baseline regime.

1) Quantitative Geometry Estimation Evaluation:

  • RANSAC has the weakest overall performance, while LO-RANSAC and LO+-RANSAC can incur added computation and become trapped in suboptimal solutions.The passage attributes RANSAC's sensitivity to its lack of local optimization and identifies uneven inlier distributions and local minima as risks for the LO methods.Source: 1) Quantitative Geometry Estimation… · p. 5
  • DLOSAC improves over the strongest baseline by (+12.85%) on fundamental-matrix estimation, (+13.85%) on relative-pose estimation, and (+15.88%) on homography estimation.The comparison reports cross-dataset averages under a unified evaluation protocol.Source: 1) Quantitative Geometry Estimation… · p. 5, Table I · p. 6
  • DLOSAC couples spatial geometric consistency and correspondence-distribution regularization with point-wise constraints, mitigating cluster-induced overfitting.GC-RANSAC and PSC-RANSAC also use neighborhood consistency priors alongside point-wise errors.Source: 1) Quantitative Geometry Estimation… · pp. 5–6
  • Gains are larger on short-baseline datasets; long-baseline perspective changes and scale or deformation effects undermine the geometric-consistency term and limit improvements.T&T and CPC are identified as long-baseline datasets, while the other evaluated datasets are primarily short-baseline.Source: 1) Quantitative Geometry Estimation… · p. 6

2) Runtime Analysis:

The section compares runtime with competing methods and describes ablations that remove DLOSAC's two regularization terms to assess their contributions.

2) Runtime Analysis:

  • DLOSAC reduces runtime by approximately 39% versus GC-RANSAC, with Delaunay triangulation performed only on candidate inliers.RANSAC and LO-RANSAC have lower latency but reduced estimation accuracy; the passage identifies triangulation as DLOSAC's primary computational overhead.Source: 2) Runtime Analysis · pp. 6–7, Table II · p. 7

C. Ablation study

  • The ablation compares full DLOSAC with variants removing the spatial-distribution term, the edge-based consistency term, or both.Table III reports mean errors and standard deviations across three tasks and all datasets, with rotation and translation errors reported separately for relative pose.Source: C. Ablation study · p. 7, Table III · p. 7

D. Sensitivity Analyses

The sensitivity analyses identify low-error regions around λspatial = 0.6–0.8 and σ = 0.8, with smooth curves around the selected settings. The conclusion reports superior performance across six public datasets and three tasks, while noting smaller gains in wide-baseline settings and limits under strong viewpoint or scene variation.

D. Sensitivity Analyses

  • λspatial = 0.6–0.8 reaches a low-error region across three tasks; the curves are smooth there, and λspatial = 0.6 is used in all experiments.The sweep spans [0, 1]; the plotted errors are average pixel error for fundamental-matrix and homography estimation and average rotation and translation errors for relative-pose estimation.Source: D. Sensitivity Analyses · p. 7, Figure 5 · p. 7
  • σ = 0.8 lies in a stable low-error region across three tasks and is adopted as the default value.The passage describes smooth error curves and says this setting balances stability and performance across the tasks.Source: D. Sensitivity Analyses · p. 7, Figure 5 · p. 7

VI. CONCLUSION

  • DLOSAC consistently achieves superior performance to existing state-of-the-art methods across six public datasets and three geometric estimation tasks.The conclusion attributes the approach to integrating geometric consistency and spatial distribution information, including Delaunay triangulation, edge-level consistency metrics, and distribution descriptors.Source: §VI · p. 7
  • DLOSAC’s gains are relatively modest in wide-baseline settings, including CPC and T&T.The stated limitation is tied to geometric regularizers’ reliance on approximate Euclidean invariance, which can break down under significant viewpoint or scale changes.Source: §VI · pp. 7–8
  • Strong parallax, pronounced depth variation, and non-coplanar structures can break the approximate Euclidean-invariance assumption and inflate true-inlier residuals.The passage says this reduces inlier–outlier separability and weakens mismatch discrimination; it also affects GC-RANSAC and PSC-RANSAC.Source: §VI · pp. 7–8
  • Future work proposes projective- and affine-invariant regularizers, multi-scale triangulation with adaptive weighting, and integration into a complete RANSAC framework.The stated aims include stability under large viewpoint changes and strong parallax, mitigating bias from unstable local statistics, and integration into a framework such as USACv20.Source: §VI · p. 8

Related papers

Loading 2610.21215v1…