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

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

cs.CVOct 15, 2026

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

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

Organizations: School of Artificial Intelligence, Jilin University, China. · School of Computer Science and Technology, Changchun University of Science and Technology, China.

Abstract

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.

Figures & tables

Fig. 1 : Overview of our framework. Given RGB images from different viewpoints, initial matches are obtained through ORB feature extraction and refined using RANSAC. A Delaunay triangulation is then built over the inliers to capture neighborhood relationships, followed by the computation of spatial distribution and geometric consistency losses. Finally, a weighted matrix is used to optimize the geometric parameters.

Panel of Figure 2 — Fig. 2 : Edge-based geometric consistency models: (a) rotation and (b) translation.

Fig. 3 : Illustration of an instance of edge-based geometric consistency.

Panel of Figure 4 — Fig. 4 : Delaunay triangulation results and corresponding matching instances for image evaluation benchmarks: (a) TUM, (b) KITTI, (c) T&T, (d) CPC, (e) EVD.

			RANSAC [ 11 ]	LO-RANSAC [ 12 ]	$\text{LO}^{+}$ - RANSAC [ 13 ]	GC-RANSAC [ 14 ]	PSC-RANSAC [ 15 ]	DLOSAC (ours)
Fundamental Matrix	TUM	$\epsilon_{\text{avg}}$ (px)	0.482	0.294	0.247	0.139	0.148	0.116
		$\epsilon_{\text{std}}$ (px)	0.478	0.230	0.225	0.193	0.190	0.130
		$f_{imp}$ (%)	75.93	60.54	53.04	16.55	21.62	0.00
	T&T	$\epsilon_{\text{avg}}$ (px)	0.538	0.402	0.329	0.229	0.204	0.197
		$\epsilon_{\text{std}}$ (px)	0.501	0.398	0.394	0.263	0.250	0.214
		$f_{imp}$ (%)	63.38	51.00	40.12	13.97	3.43	0.00

TABLE I : The error and improvement rates for all methods (1st row) across tasks (1st column) and datasets (2nd column) are presented, along with the average performance (Avg.) of each task across benchmarks. The optimal results are indicated in bold , and the second-best results are marked with underline .

Method	F-Matrix	Rel. Pose	Homo.	Avg.
RANSAC	18.24	24.62	8.26	17.04
LO-RANSAC	29.66	41.18	16.41	29.08
LO + -RANSAC	26.43	38.08	14.24	26.25
GC-RANSAC	65.32	92.56	45.11	67.66
PSC-RANSAC	72.17	98.32	48.22	72.90
DLOSAC (Ours)	42.65	58.90	22.73	41.43

TABLE II : Comparison of average runtime (ms). Our method is highlighted in blue . Bold and underlined values indicate the best and second-best performance, respectively.

Method	Fund. Matrix		Rel. Pose		Homo.
Method	$\epsilon_{\text{avg}}$ (px)	$\epsilon_{\text{std}}$ (px)	$\epsilon_{\text{R}}$ ( ∘ )	$\epsilon_{\text{t}}$ ( ∘ )	$\epsilon_{\text{avg}}$ (px)	$\epsilon_{\text{std}}$ (px)
w/o ( $\mathcal{L}_{\text{edge}}+\mathcal{L}_{\text{spatial}}$ )	0.573	0.580	4.133	13.061	1.447	1.411
w/o ( $\mathcal{L}_{\text{edge}}$ )	0.295	0.371	2.755	9.122	0.935	1.173
w/o ( $\mathcal{L}_{\text{spatial}}$ )	0.181	0.212	2.643	10.90	0.736	0.928
DLOSAC (Ours)	0.156	0.191	2.320	7.501	0.588	0.902

TABLE III : Ablation Study. Mean errors and standard deviations across all datasets for three geometric estimation tasks. For relative-pose estimation, rotation and translation errors are reported separately. The best results are highlighted in bold .

Panel of Figure 8 — Fig. 5 : Parameter analysis: (a) Weighting coefficient for the spatial distribution loss $\lambda_{\text{spatial}}$ ; (b) Regularization weight $\sigma$ .

Multi-View Geometry

Multi-view geometry studies how images from different viewpoints reveal camera motion, scene structure, and consistent 3D measurements.

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DS-SAC: Density Search for Sample Consensus

Suraj Thapa, Muhammad Aminul Islam

Tagliatela College of Engineering, University of New Haven, 300 Boston Post Rd, West Haven, 06516, CT, USA.

Multi-View Geometry Robust Estimation

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Robust geometric model estimation is a fundamental problem in computer vision. RANSAC and its variants remain widely used for this task; however, they rely on stochastic minimal sampling. In this article, we propose Density Search Sample Consensus (DS-SAC), a deterministic robust estimation framework, that avoids repeated random sampling by searching dense regions. Starting from an initial model estimated from the available points, the method performs local exploration via forward and backward search. To facilitate global exploration, DS-SAC recursively partitions the point set using signed residuals and searches each valid partition for high-consensus models. We show that DS-SAC has polynomial complexity with respect to the number of points, making it an efficient alternative to stochastic consensus-based methods. Experiments on large-scale real-world datasets for homography, fundamental matrix, and essential matrix estimation show that DS-SAC achieves higher AUC scores, competitive or lower median pose errors, and faster runtime compared with widely used robust estimators, including RANSAC, MAGSAC, LO-RANSAC, and GC-RANSAC.

Abstract

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