Shen Cai

Shen Cai, Zhanhao Wu, Lingxi Guo et al.

In this paper, we present two fast and interpretable decomposition methods for 2D homography, which are named Similarity-Kernel-Similarity (SKS) and Affine-Core-Affine (ACA) transformations respectively. Under the minimal $4$-point configuration, the first and the last similarity transformations in SKS are computed by two anchor points on target and source planes, respectively. Then, the other two point correspondences can be exploited to compute the middle kernel transformation with only four parameters. Furthermore, ACA uses three anchor points to compute the first and the last affine transformations, followed by computation of the middle core transformation utilizing the other one point correspondence. ACA can compute a homography up to a scale with only $85$ floating-point operations (FLOPs), without even any division operations. Therefore, as a plug-in module, ACA facilitates the traditional feature-based Random Sample Consensus (RANSAC) pipeline, as well as deep homography pipelines estimating $4$-point offsets. In addition to the advantages of geometric parameterization and computational efficiency, SKS and ACA can express each element of homography by a polynomial of input coordinates ($7$th degree to $9$th degree), extend the existing essential Similarity-Affine-Projective (SAP) decomposition and calculate 2D affine transformations in a unified way. Source codes are released in https://github.com/cscvlab/SKS-Homography.

Yaqing Ding, Viktor Kocur, Zuzana Berger Haladová et al.

In this paper, we propose a novel approach for recovering focal lengths from three-view homographies. By examining the consistency of normal vectors between two homographies, we derive new explicit constraints between the focal lengths and homographies using an elimination technique. We demonstrate that three-view homographies provide two additional constraints, enabling the recovery of one or two focal lengths. We discuss four possible cases, including three cameras having an unknown equal focal length, three cameras having two different unknown focal lengths, three cameras where one focal length is known, and the other two cameras have equal or different unknown focal lengths. All the problems can be converted into solving polynomials in one or two unknowns, which can be efficiently solved using Sturm sequence or hidden variable technique. Evaluation using both synthetic and real data shows that the proposed solvers are both faster and more accurate than methods relying on existing two-view solvers. The code and data are available on https://github.com/kocurvik/hf

Yujie Lu, Long Wan, Nayu Ding et al.

Neural implicit representation of geometric shapes has witnessed considerable advancements in recent years. However, common distance field based implicit representations, specifically signed distance field (SDF) for watertight shapes or unsigned distance field (UDF) for arbitrary shapes, routinely suffer from degradation of reconstruction accuracy when converting to explicit surface points and meshes. In this paper, we introduce a novel neural implicit representation based on unsigned orthogonal distance fields (UODFs). In UODFs, the minimal unsigned distance from any spatial point to the shape surface is defined solely in one orthogonal direction, contrasting with the multi-directional determination made by SDF and UDF. Consequently, every point in the 3D UODFs can directly access its closest surface points along three orthogonal directions. This distinctive feature leverages the accurate reconstruction of surface points without interpolation errors. We verify the effectiveness of UODFs through a range of reconstruction examples, extending from simple watertight or non-watertight shapes to complex shapes that include hollows, internal or assembling structures.

Yu Han, Zhiwei Huang, Yanting Zhang et al.

Point-pixel registration between LiDAR point clouds and camera images is a fundamental yet challenging task in autonomous driving and robotic perception. A key difficulty lies in the modality gap between unstructured point clouds and structured images, especially under sparse single-frame LiDAR settings. Existing methods typically extract features separately from point clouds and images, then rely on hand-crafted or learned matching strategies. This separate encoding fails to bridge the modality gap effectively, and more critically, these methods struggle with the sparsity and noise of single-frame LiDAR, often requiring point cloud accumulation or additional priors to improve reliability. Inspired by recent progress in detector-free matching paradigms (e.g. MatchAnything), we revisit the projection-based approach and introduce the detector-free framework for direct point-pixel matching between LiDAR and camera views. Specifically, we project the LiDAR intensity map into a 2D view from the LiDAR perspective and feed it into an attention-based detector-free matching network, enabling cross-modal correspondence estimation without relying on multi-frame accumulation. To further enhance matching reliability, we introduce a repeatability scoring mechanism that acts as a soft visibility prior. This guides the network to suppress unreliable matches in regions with low intensity variation, improving robustness under sparse input. Extensive experiments on KITTI, nuScenes, and MIAS-LCEC-TF70 benchmarks demonstrate that our method achieves state-of-the-art performance, outperforming prior approaches on nuScenes (even those relying on accumulated point clouds), despite using only single-frame LiDAR.

Siyu Zhang, Hui Cao, Yuqi Liu et al.

Using deep learning techniques to process 3D objects has achieved many successes. However, few methods focus on the representation of 3D objects, which could be more effective for specific tasks than traditional representations, such as point clouds, voxels, and multi-view images. In this paper, we propose a Sphere Node Graph (SN-Graph) to represent 3D objects. Specifically, we extract a certain number of internal spheres (as nodes) from the signed distance field (SDF), and then establish connections (as edges) among the sphere nodes to construct a graph, which is seamlessly suitable for 3D analysis using graph neural network (GNN). Experiments conducted on the ModelNet40 dataset show that when there are fewer nodes in the graph or the tested objects are rotated arbitrarily, the classification accuracy of SN-Graph is significantly higher than the state-of-the-art methods.