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.

Yao Huang, Si-Yuan Cao, Yaqing Ding et al.

Planar homography, with eight degrees of freedom (DOFs), is fundamental in numerous computer vision tasks. While the positional offsets of four corners are widely adopted (especially in neural network predictions), this parameterization lacks geometric interpretability and typically requires solving a linear system to compute the homography matrix. This paper presents a novel geometric parameterization of homographies, leveraging the similarity-kernel-similarity (SKS) decomposition for projective transformations. Two independent sets of four geometric parameters are decoupled: one for a similarity transformation and the other for the kernel transformation. Additionally, the geometric interpretation linearly relating the four kernel transformation parameters to angular offsets is derived. Our proposed parameterization allows for direct homography estimation through matrix multiplication, eliminating the need for solving a linear system, and achieves performance comparable to the four-corner positional offsets in deep homography estimation.

Yongdong Huang, Yuanzhan Li, Xulong Cao et al.

Using neural networks to represent 3D objects has become popular. However, many previous works employ neural networks with fixed architecture and size to represent different 3D objects, which lead to excessive network parameters for simple objects and limited reconstruction accuracy for complex objects. For each 3D model, it is desirable to have an end-to-end neural network with as few parameters as possible to achieve high-fidelity reconstruction. In this paper, we propose an efficient voxel reconstruction method utilizing neural architecture search (NAS) and binary classification. Taking the number of layers, the number of nodes in each layer, and the activation function of each layer as the search space, a specific network architecture can be obtained based on reinforcement learning technology. Furthermore, to get rid of the traditional surface reconstruction algorithms (e.g., marching cube) used after network inference, we complete the end-to-end network by classifying binary voxels. Compared to other signed distance field (SDF) prediction or binary classification networks, our method achieves significantly higher reconstruction accuracy using fewer network parameters.

Yuanzhan Li, Yuqi Liu, Yujie Lu et al.

In recent years, neural signed distance function (SDF) has become one of the most effective representation methods for 3D models. By learning continuous SDFs in 3D space, neural networks can predict the distance from a given query space point to its closest object surface,whose positive and negative signs denote inside and outside of the object, respectively. Training a specific network for each 3D model, which individually embeds its shape, can realize compressed representation of objects by storing fewer network (and possibly latent) parameters. Consequently, reconstruction through network inference and surface recovery can be achieved. In this paper, we propose an SDF prediction network using explicit key spheres as input. Key spheres are extracted from the internal space of objects, whose centers either have relatively larger SDF values (sphere radii), or are located at essential positions. By inputting the spatial information of multiple spheres which imply different local shapes, the proposed method can significantly improve the reconstruction accuracy with a negligible storage cost. Compared to previous works, our method achieves the high-fidelity and high-compression 3D object coding and reconstruction. Experiments conducted on three datasets verify the superior performance of our method.

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.

Yuqi Liu, Yin Wang, Haikuan Du et al.

Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or spherical projections, as the sphere is an unstructured grid. In this paper, we present Spherical Transformer which can transform spherical signals into vectors that can be directly processed by standard CNNs such that many well-designed CNNs architectures can be reused across tasks and datasets by pretraining. To this end, the proposed method first uses local structured sampling methods such as HEALPix to construct a transformer grid by using the information of spherical points and its adjacent points, and then transforms the spherical signals to the vectors through the grid. By building the Spherical Transformer module, we can use multiple CNN architectures directly. We evaluate our approach on the tasks of spherical MNIST recognition, 3D object classification and omnidirectional image semantic segmentation. For 3D object classification, we further propose a rendering-based projection method to improve the performance and a rotational-equivariant model to improve the anti-rotation ability. Experimental results on three tasks show that our approach achieves superior performance over state-of-the-art methods.

Ji Luo, Hui Cao, Jie Wang et al.

Voxel-based 3D object classification has been thoroughly studied in recent years. Most previous methods convert the classic 2D convolution into a 3D form that will be further applied to objects with binary voxel representation for classification. However, the binary voxel representation is not very effective for 3D convolution in many cases. In this paper, we propose a hybrid cascade architecture for voxel-based 3D object classification. It consists of three stages composed of fully connected and convolutional layers, dealing with easy, moderate, and hard 3D models respectively. Both accuracy and speed can be balanced in our proposed method. By giving each voxel a signed distance value, an obvious gain regarding the accuracy can be observed. Besides, the mean inference time can be speeded up hugely compared with the state-of-the-art point cloud and voxel based methods.

Hui Cao, Haikuan Du, Siyu Zhang et al.

In this paper, we present an InSphereNet method for the problem of 3D object classification. Unlike previous methods that use points, voxels, or multi-view images as inputs of deep neural network (DNN), the proposed method constructs a class of more representative features named infilling spheres from signed distance field (SDF). Because of the admirable spatial representation of infilling spheres, we can not only utilize very fewer number of spheres to accomplish classification task, but also design a lightweight InSphereNet with less layers and parameters than previous methods. Experiments on ModelNet40 show that the proposed method leads to superior performance than PointNet and PointNet++ in accuracy. In particular, if there are only a few dozen sphere inputs or about 100000 DNN parameters, the accuracy of our method remains at a very high level (over 88%). This further validates the conciseness and effectiveness of the proposed InSphere 3D representation. Keywords: 3D object classification , signed distance field , deep learning , infilling sphere