Let C represent an irreducible algebraic space curve defined by the real polynomials f i ( x 1 , x 2 , x 3 ) for i = 1 , 2 . It is a recognized fact that a birational relationship invariably exists between the points on C and those on an associated irreducible plane curve, denoted as C p . In this work, we leverage this established relationship to delineate the asymptotic behavior of C by examining the asymptotes of C p . Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of C , given that the asymptotes of C p have been ascertained. • Let C represent an irreducible algebraic space curve defined by the real polynomials f i ( x 1 , x 2 , x 3 ) , i = 1 , 2 . • A birational relationship always exists between the points on C and those on an associated irreducible plane curve C p . • We use this relationship to analyze the asymptotic behavior of C by examining the asymptotes of C p . • We introduce a novel algorithm designed to efficiently compute the asymptotes of C by studying the asymptotes of C p .

When using digital cameras to capture video from a display screen, the occurrence of moiré patterns can lead to color distortions, significantly degrading the quality of both images and video. Given the escalating demand for video acquisition, designing algorithms for video demoiréing is a significant topic. In this paper, we introduce a novel attention-based network for this task, the spatiotemporal fusion transformer (STFT). By introducing temporal and spatial attention encoders and a multi-scale feature fusion method, STFT can learn dynamic spatial and temporal variations in moiré patterns. In the decoding phase, a self-attention mechanism is employed to learn temporal dependencies at both image-level and video-level, enhancing model moiré removal performance. Experimental results demonstrate a significant improvement in the performance of the proposed model over existing methods on public datasets. Furthermore, STFT can output visual attention maps for analyzing the distribution of moiré and the focus of model learning. STFT's outstanding performance on the video rain removal task also demonstrates the robustness of our model, highlighting its potential for application to other restoration tasks.

Image demoiréing is a complex image-restoration task because of the color and shape variations of moiré patterns. With the development of mobile devices, mobile phones can now be used to capture images at multiple resolutions. This difficulty increases when attempting to remove moiré from both low- and high-resolution images, as different resolutions make it challenging for existing methods to match the scales and textures of moiré. To solve these problems, we built a mixed attention residual module (MARM) by combining multi-scale feature extraction and mixed attention methods. Based on MARM, we propose a multi-scale adaptive mixed attention network (MA2Net) that can adapt to input images of different sizes and remove moiré of various shapes. Our model achieved the best results on four public datasets with resolutions ranging from 256×256 to 4k. Extensive experiments demonstrated the effectiveness of our model, which outperformed state-of-the-art methods by a large margin. We also conducted experiments on image deraining to validate the effectiveness of our model in other image-restoration tasks, and MA2Net achieved state-of-the-art performance on the Rain200H dataset.

Abstract As a fundamental problem in computer vision, 3D point cloud registration (PCR) aims to seek the optimal transformation to align point cloud pairs. Meanwhile, the equivariance lies at the core of matching point clouds at arbitrary pose. In this paper, we propose GETr, a geometric equivariant transformer for PCR. By learning the point‐wise orientations, we decouple the coordinate to the pose of the point clouds, which is the key to achieve equivariance in our framework. Then we utilize attention mechanism to learn the geometric features for superpoints matching, the proposed novel self‐attention mechanism encodes the geometric information of point clouds. Finally, the coarse‐to‐fine manner is used to obtain high‐quality correspondence for registration. Extensive experiments on both indoor and outdoor benchmarks demonstrate that our method outperforms various existing state‐of‐the‐art methods.

We introduce IGF-Fit, a novel method for estimating surface normals from point clouds with varying noise and density. Unlike previous approaches that rely on point-wise weights and explicit representations, IGF-Fit employs a network that learns an implicit representation and uses derivatives to predict normals. The input patch serves as both a shape latent vector and query points for fitting the implicit representation. To handle noisy input, we introduce a novel noise transformation module with a training strategy for noise classification and latent vector bias prediction. Our experiments on synthetic and real-world scan datasets demonstrate the effectiveness of IGF-Fit, achieving state-of-the-art performance on both noise-free and density-varying data.

Tool-path planning is a crucial factor of computer-aided design (CAD) and computer-aided manufacturing (CAM). Previous path generation methods often transform the problem into local or global optimization methods to solve it, leading to a long computational time. With the development of modern industry, real-time path planning is becoming an urgent issue in advanced manufacturing. This article proposes an efficient neural network-based direct tool-path generation method on B-spline surface for subtractive end milling. In order to build the first corresponding dataset, adaptive iso-scallop height method is proposed, which can effectively avoid generating breakpoints at the boundary. B-Spline reparameterization is used to fit discrete tool paths to obtain regular control points data structure for further deep learning. After that, an intelligent neural network is proposed to learn the relationship between the input B-Spline surface and the reparameterized tool paths. Finally, experimental results and case study are provided to illustrate and clarify our method, which only needs a few microseconds of planning time while ensuring the quality of the generated paths. Due to its simple structure and low computational burden, this method can be easily applied to CAD/CAM software.

Smooth surfaces from an arbitrary topological control grid have been widely studied, which are mostly generalized from splines with uniform knot intervals. These methods fail to work well on extraordinary points (EPs) whose edges have varying knot intervals. This article presents a patching solution for arbitrary topological 2-manifold control grid with non-uniform knots that defines one bi-cubic Bézier patch per control grid face except those faces with EPs. Experimental results demonstrate that the new solution can improve the surface quality for non-uniform parameterization. Applications in surface reconstruction, arbitrary sharp features on the complex surface and tool path planning for the new surface representation are also provided in the paper.

Reconstructing a spline surface from a given arbitrary topological triangle mesh is a fundamental and challenging problem in computer-aided design and engineering. This article introduces a novel surface fitting method utilizing G-NURBS capable of handling control meshes with arbitrary topologies. This method employs adaptive control point adjustment, guided by the geometric attributes of the input model, ensuring precise representation of sharp features such as edges and corners. Two primary strategies are employed: A parameter correspondence approach designed for sharp features and a control mesh iterative refinement technique that incorporates geometrical feature information. The proposed method has been tested and evaluated on various CAD models to demonstrate its effectiveness. This method can achieve higher fitting accuracy while faithfully preserving the geometrical features with fewer control points.

We present a novel implicit neural representation to reconstruct CAD models from point clouds with high quality. Our method first extracts edge points from input points by an edge detection network and then recovers implicit surfaces while preserving the sharp features of ground-truth models. The edge detection network uses a U-Net structure for feature encoding, and the attention module is introduced to improve the accuracy in the CAD models. This detection network is light weighted and runs fast. Afterward, we propose an MLP-based network to train an implicit representation from input points with its extracted edge points. A two-stage training process is proposed, and loss functions are designed for each stage to ensure that the sharp features of the input points are learned while the surface details are fitted. Comparing our method with other SOTA methods in the ABC dataset, our method is significantly superior to the existing nonlearning and learning 3D reconstruction methods in terms of surface approximation quality and sharp feature preservation. Moreover, we can gain spline representations from learned shapes for CAM as the application of our method.

Given an algebraic surface implicitly defined by an irreducible polynomial, we present a method that decides whether or not this surface can be parametrized by a polynomial parametrization without base points and, in the affirmative case, we show how to compute this parametrization.

We introduce a neural network, MixNet, for learning implicit representations of 3D subtle models with large smooth areas and exact shape details in the form of interpolation of two different implicit functions. Our network takes a point cloud as input and uses conventional MLP networks and SIREN networks to predict different implicit fields. We use a learnable interpolation function to combine the implicit values of these two networks and achieve the respective advantages of them. The network is self-supervised with only reconstruction loss, leading to faithful 3D reconstructions with smooth planes, correct details, and plausible spatial partition without any ground-truth segmentation. We evaluate our method on ABC, the largest and most diverse CAD dataset, and some typical shapes to test in terms of geometric correctness and surface smoothness to demonstrate superiority over current alternatives suitable for shape reconstruction.

The detection of possible defects on the steel surface is the last step and considered as the last line of defense for manufacturers to ensure the quality of products. To identify defects on the steel surface more quickly and accurately, this paper proposes a modified network based on RetinaNet in view of the current difficulties in detecting large-area steel defects and the overall performance to be improved of detectors. The depth of the FPN is increased to improve the ability to extract semantic information; the detail information enhancement structure, the feature information optimization structure, and the semantic information enhancement structure are combine into the augmented feature information to make the network better in using of image information; finally, we increase the sub-network’s layers to improve the ability to classify. Experiments were carried out on DGAM 2007 and PASCAL VOC. DGAM 2007 is a steel defect dataset, and PASCAL VOC is a general dataset to verify the overall performance of the detector. The results show that our proposed network has greatly improved the detection accuracy of the steel surface defects to 99.73%, and to some extent, large-area defects can be easily detected, and the mAP on DGAM 2007 and PASCAL VOC is both higher than that of the original RetinaNet network, which proves that the modified algorithm can play as an outstanding detector.

Implicitizing rational surfaces is a fundamental computational task in Computer Graphics and Computer Aided Design. Ray tracing, collision detection, and solid modeling all benefit from implicitization procedures for rational surfaces. The univariate resultant of two moving lines generated by a μ-basis for a rational curve represents the implicit equation of the rational curve. But although the multivariate resultant of three moving planes corresponding to a μ-basis for a rational surface is guaranteed to contain the implicit equation of the surface as a factor, μ-bases for rational surfaces are difficult to compute. Moreover, μ-bases for a rational surface often have high degrees, so these resultants generally contain many extraneous factors. Here we develop fast algorithms to implicitize rational tensor product surfaces by computing the resultant of three moving planes corresponding to three syzygies with low degrees. These syzygies are easy to compute, and the resultants of the corresponding moving planes generally contain fewer extraneous factors than the resultants of the moving planes corresponding to μ-bases. We predict and compute all the possible extraneous factors that may appear in these resultants. Examples are provided to clarify and illuminate the theory.

Summary form only given. In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.

The μ-bases of rational curves/surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of the rational curves/surfaces. They provide efficient algorithms to implicitize rational curves/surfaces as well as algorithms to compute singular points of rational curves and to reparametrize rational ruled surfaces. In this paper, we present an efficient algorithm to compute the μbasis of a rational curve/surface by using polynomial matrix factorization followed by a technique similar to Gaussian elimination. The algorithm is shown superior than previous algorithms to compute the μ-basis of a rational curve, and it is the only known algorithm that can rigorously compute the μ-basis of a general rational surface. We present some examples to illustrate the algorithm.