Hough-SIFT: Robust Image Registration for Linear Structures via Hough Space

Visual front-ends for robotic localization typically rely on point-based features such as Oriented FAST and Rotated BRIEF (ORB), which frequently fail in structured environments dominated by strong linear structures or textureless surfaces. While line-based Simultaneous Localization and Mapping (SLAM) systems mitigate this by utilizing line segments, conventional line extraction and description algorithms are computationally prohibitive for real-time edge robotics. To address this fundamental bottleneck, we propose HOME (Hough-space One-dimensional Matching of Extrema), an ultra-lightweight, training-free feature matching framework. HOME transforms images into Hough space, mapping global linear structures to stable local extrema, which serve as keypoints, thereby reformulating complex line matching into highly efficient one-dimensional point matching. The proposed 1D radial descriptor mathematically guarantees rotational and translational invariance without the overhead of explicit orientation estimation. As a proof of concept to validate the matching accuracy and efficiency of HOME, this paper focuses on homography estimation. Extensive evaluations demonstrate that HOME achieves robust registration in challenging scenarios where point-based methods fail, operating at a much faster speed than existing line-based methods. Extending this robust matching engine to full 3D pose estimation remains a highly promising future direction.

Point cloud registration critically depends on local features that are both distinctive and robust to arbitrary 3D rotations. Existing learning-based methods typically approximate rotation invariance via fragile local reference frames or extensive data augmentation, providing only empirical invariance and often degrading under unseen rotational transformations. In this paper, we propose SHReg, a strictly rotation-equivariant point cloud registration framework grounded in the representation theory of $SO(3)$. By representing local geometric features as irreducible representations of $SO(3)$, SHReg guarantees exact equivariance under arbitrary rotations without relying on local reference frames. Built upon a spherical-harmonics-based equivariant backbone, SHReg jointly learns rotation-invariant descriptors for robust correspondence matching and rotation-equivariant features that preserve fine-grained orientation information. The preserved equivariant structure enables each correspondence to directly hypothesize a rigid transformation, reducing reliance on large-scale hypothesis sampling in conventional RANSAC-based pipelines and leading to improved robustness under challenging rotational variations. Extensive experiments on 3DMatch, 3DLoMatch, and KITTI demonstrate that SHReg consistently outperforms state-of-the-art methods in registration accuracy, particularly under large rotational perturbations.

Image-to-point cloud registration is often challenged by viewpoint changes, cross-modal discrepancies, and repetitive textures, which induce scale ambiguity and consequently lead to erroneous correspondences. Recent detection-free methods alleviate this issue by leveraging multi-scale features and transformer-based interactions. However, they still suffer from attention drift across layers and intra-scale inconsistencies, hindering precise registration. Inspired by human behavior, we propose a ``Focus--Sweep'' paradigm and develop a Hierarchical Focus--Sweep Interaction Module within an SSM-based framework to enhance multi-level cross-modal feature association. In addition, we introduce a Dynamic Layer Allocation Strategy that adaptively determines the iteration depth to better exploit geometric constraints and improve matching robustness. Extensive experiments and ablations on two benchmarks, RGB-D Scenes V2 and 7-Scenes, demonstrate that our approach achieves state-of-the-art performance.