Reference-based remote sensing super-resolution (RefRS-SR) method shows great potential for improving both spatial resolution and coverage area of remote sensing images, by which high-resolution (HR) reference images can supplement fine details for low-resolution (LR) but wide coverage images. However, most RefRS-SR methods treat the reference as a static template and unidirectionally transfer the high-frequency information to the LR input. To address the issue of inefficient and inaccurate guided super-resolving, we propose a new RefRS-SR method with dynamic reference textures exploitation dubbed DTESR. The key referenced restoration (Ref Restoration) module consists of three components: correlation generation, texture enhancement and refinement (TER), and adaptive similarity-based fusion to progressively reconstruct high correlation and delicate textures for the LR input. Specifically, both the LR input and reference features are utilized for precise correlation generation. Next, both features are enhanced and refined with the most suitable reference under the guidance of the correlation map. Moreover, a learnable fusion method is designed to maintain the consistency of adjacent pixels. These operations will be iteratively applied to the three reconstruction scales to promote the exploitation of the Ref features. Through comprehensive quantitative and qualitative evaluations, our experimental results demonstrate that DTESR surpasses the current state-of-the-art RefRS-SR methods.

Self-intersections of NURBS surfaces are unavoidable during the CAD modeling process, especially in operations such as offset or sweeping. The existence of self-intersections might cause problems in the subsequent simulation and manufacturing process. Therefore, fast detection of self-intersections of NURBS is highly demanded in industrial applications. Self-intersections are essentially singular points on the surface. Although there is a long history of exploring singular points in mathematics community, the fast and robust determination and computation of self-intersections have been a challenging problem in practice. In this article, we construct an algebraic signature whose non-negativity is proven to be sufficient for excluding the existence of self-intersections from a global perspective. An efficient algorithm for determining the existence of self-intersections is provided by recursively using this signature. Once the self-intersection is detected, if necessary, the self-intersection locus can also be computed via a further recursively cross-use of this signature and the surface-surface intersection function. Various experiments and comparisons with existing methods, as well as geometry kernels, including OCCT and ACIS, validate the robustness and efficiency of our algorithm. We also adapt our algorithm to self-intersection elimination, self-intersection trimming, and applications in mesh generation, Boolean operation, and shelling.

The detection and computation of the overlap region between two NURBS surfaces, as a special case of the intersection problem, are essential components of CAD systems, directly influencing the robustness of the entire system. Despite their importance, efficient, topologically correct, and numerically robust algorithms for detecting overlap regions remain lacking. To address this issue, we propose an optimization approach for computing the overlap region between two NURBS surfaces within a given error threshold. Based on a bilevel optimization framework, our algorithm first employs cubic Bézier simplices to approximate the boundary of the overlap region. The boundary points of the overlap region are computed iteratively, followed by a Delaunay triangulation to establish the boundary topology. Additional refinement of the boundary edge is applied to ensure the topological correctness and maintain the precision of the overlap region within the specified error threshold. Our main contribution lies in the development of a novel and robust algorithm to calculate the boundary of the overlap region. This approach differs from previous overlap computation methods, which seldom account for error thresholds and are difficult to implement in floating-point arithmetic in CAD systems. We demonstrate the robustness and topological accuracy of our method through extensive experiments on a diverse set of complex examples with varying error thresholds.

Boolean operations for Boundary Representation (B-Rep) models are among the most commonly used functions in Computer Aided Design (CAD) systems. They are also one of the most delicate soft modules, with challenges arising from complex algorithmic flows and efficiency and accuracy issues, especially in extreme cases. Common issues encountered in processing complex models include low efficiency, missing results, and non-watertightness. In this paper, we propose a novel algorithm for efficient and accurate Boolean operations on B-Rep models. This is achieved by establishing a bijective mapping between B-Rep models and the corresponding triangle meshes with controllable approximation error, thus mapping B-Rep Boolean operations to mesh Boolean operations. By using conservative intersection detection on the mesh to locate all surface intersection curves and carefully handling degeneration and topology errors, we ensure that the results are consistently watertight and correct. We demonstrate the superior efficiency of the proposed method using the open-source geometry engine OCCT, the commercial engine ACIS, and the commercial software Rhino as benchmarks.

Reconstructing CSG trees from CAD models is a critical subject in reverse engineering. While there have been notable advancements in CSG reconstruction, challenges persist in capturing geometric details and achieving efficiency. Additionally, since non-axis-aligned volumetric primitives cannot maintain coplanar characteristics due to discretization errors, existing Boolean operations often lead to zero-volume surfaces and suffer from topological errors during the CSG modeling process. To address these issues, we propose a novel workflow to achieve fast CSG reconstruction and reliable forward modeling. First, we employ feature removal and model subdivision techniques to decompose models into sub-components. This significantly expedites the reconstruction by simplifying the complexity of the models. Then, we introduce a more reasonable method for primitive generation and filtering, and utilize a size-related optimization approach to reconstruct CSG trees. By re-adding features as additional nodes in the CSG trees, our method not only preserves intricate details but also ensures the conciseness, semantic integrity, and editability of the resulting CSG tree. Finally, we develop a coplanar primitive discretization method that represents primitives as large planes and extracts the original triangles after intersection. We extend the classification of triangles and incorporate a coplanar-aware Boolean tree assessment technique, allowing us to achieve manifold and watertight modeling results without zero-volume surfaces, even in extreme degenerate cases. We demonstrate the superiority of our method over state-of-the-art approaches. Moreover, the reconstructed CSG trees generated by our method contain extensive semantic information, enabling diverse model editing tasks.

This work presents an accurate and robust method for estimating normals from point clouds. In contrast to predecessor approaches that minimize the deviations between the annotated and the predicted normals directly, leading to direction inconsistency, we first propose a new metric termed Chamfer Normal Distance to address this issue. This not only mitigates the challenge but also facilitates network training and substantially enhances the network robustness against noise. Subsequently, we devise an innovative architecture that encompasses Multi-scale Local Feature Aggregation and Hierarchical Geometric Information Fusion. This design empowers the network to capture intricate geometric details more effectively and alleviate the ambiguity in scale selection. Extensive experiments demonstrate that our method achieves the state-of-the-art performance on both synthetic and real-world datasets, particularly in scenarios contaminated by noise. Our implementation is available at https://github.com/YingruiWoo/CMG-Net_Pytorch.

Despite their ill-posedness and inherent ambiguity, recent deep learning approaches have demonstrated promising capability to estimate plausible height information from single spaceborne and airborne imagery. However, accurately predicting the height and preserving the rich geometric detailing of aerial images with limited resolution and complex structural variations remains a challenge. To address these issues, we introduce a novel transformer-based architecture for single-imagery height estimation (SIHE) dubbed as HeightFormer. Specifically, the building-block multiscale vision transformer (MViT) constitutes the encoder and decoder of HeightFormer to facilitate the capturing of long-range dependencies across a feature pyramid. Furthermore, we propose the bilateral feature pyramid fusion scheme, which consists of step-by-step and one-stop decoder feature map augmentation, to enhance global and local information reconstruction. The stepwise fusion module (SFM) iteratively fuses encoder and decoder features, while the multiscale fusion module (MFM) combines the final decoder feature with multiscale encoder features. In the end, the Heightbins module is designed to generate the attention map and the adaptive bin width. Then, the bin centers at each pixel are linearly combined as the final estimated height. Extensive experiments validate the effectiveness of HeightFormer on the Vaihingen dataset, the Potsdam dataset, and the DFC2019 dataset. Compared with the state-of-the-art, our method improves accuracy metrics and provides the ability to preserve structure and details. Building height estimation, transformer, attention, progressive refinement.

This work presents a novel and effective method for fitting multidimensional ellipsoids (i.e., ellipsoids embedded in [Formula: see text]) to scattered data in the contamination of noise and outliers. Unlike conventional algebraic or geometric fitting paradigms that assume each measurement point is a noisy version of its nearest point on the ellipsoid, we approach the problem as a Bayesian parameter estimate process and maximize the posterior probability of a certain ellipsoidal solution given the data. We establish a more robust correlation between these points based on the predictive distribution within the Bayesian framework, i.e., considering each model point as a potential source for generating each measurement. Concretely, we incorporate a uniform prior distribution to constrain the search for primitive parameters within an ellipsoidal domain, ensuring ellipsoid-specific results regardless of inputs. We then establish the connection between measurement point and model data via Bayes' rule to enhance the method's robustness against noise. Due to independent of spatial dimensions, the proposed method not only delivers high-quality fittings to challenging elongated ellipsoids but also generalizes well to multidimensional spaces. To address outlier disturbances, often overlooked by previous approaches, we further introduce a uniform distribution on top of the predictive distribution to significantly enhance the algorithm's robustness against outliers. Thanks to the uniform prior, our maximum a posterior probability coincides with a more tractable maximum likelihood estimation problem, which is subsequently solved by a numerically stable Expectation Maximization (EM) framework. Moreover, we introduce an ε-accelerated technique to expedite the convergence of EM considerably. We also investigate the relationship between our algorithm and conventional least-squares-based ones, during which we theoretically prove our method's superior robustness. To the best of our knowledge, this is the first comprehensive method capable of performing multidimensional ellipsoid-specific fitting within the Bayesian optimization paradigm under diverse disturbances. We evaluate it across lower and higher dimensional spaces in the presence of heavy noise, outliers, and substantial variations in axis ratios. Also, we apply it to a wide range of practical applications such as microscopy cell counting, 3D reconstruction, geometric shape approximation, and magnetometer calibration tasks. In all these test contexts, our method consistently delivers flexible, robust, ellipsoid-specific performance, and achieves the state-of-the-art results.

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon , is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points (see the teaser figure). Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

We propose a novel and efficient method for reconstructing manifold surfaces from point clouds. Unlike previous approaches that use dense implicit reconstructions or piecewise approximations and overlook inherent structures like quadrics in CAD models, our method faithfully preserves these quadric structures by assembling primitives. To achieve high-quality primitive extraction, we use a variational shape approximation, followed by a mesh arrangement for space partitioning and candidate primitive patches generation. We then introduce an effective pruning mechanism to classify candidate primitive patches as active or inactive, and further prune inactive patches to reduce the search space and speed up surface extraction significantly. Finally, the optimal active patches are computed by a binary linear programming and assembled as manifold and watertight surfaces. We perform extensive experiments on a wide range of CAD objects to validate its effectiveness.

Face recognition has always been courted in computer vision and is especially amenable to situations with significant variations between frontal and profile faces. Traditional techniques make great strides either by synthesizing frontal faces from sizable datasets or by empirical pose invariant learning. In this paper, we propose a completely integrated embedded end-to-end Lie algebra residual architecture (LARNeXt) to achieve pose robust face recognition. First, we explore how the face rotation in the 3D space affects the deep feature generation process of convolutional neural networks (CNNs), and prove that face rotation in the image space is equivalent to an additive residual component in the feature space of CNNs, which is determined solely by the rotation. Second, on the basis of this theoretical finding, we further design three critical subnets to leverage a soft regression subnet with novel multi-fusion attention feature aggregation for efficient pose estimation, a residual subnet for decoding rotation information from input face images, and a gating subnet to learn rotation magnitude for controlling the strength of the residual component that contributes to the feature learning process. Finally, we conduct a large number of ablation experiments, and our quantitative and visualization results both corroborate the credibility of our theory and corresponding network designs. Our comprehensive experimental evaluations on frontal-profile face datasets, general unconstrained face recognition datasets, and industrial-grade tasks demonstrate that our method consistently outperforms the state-of-the-art ones.

Singularity computation is a fundamental problem in Computer Graphics and Computer Aided Geometric Design, since it is closely related to topology determination, intersection, mesh generation, rendering, simulation, and modeling of curves and surfaces. In this article, we present an efficient and robust algorithm for computing all the singularities (including their orders) of rational parametric surfaces using the technique of moving planes. The main approach is first to construct a representation matrix whose columns correspond to moving planes following the parametric surface. Then, by substituting the parametric equation of the rational surface into this representation matrix, one can extract the singularity information from the corresponding matrix and return all the singular loci including self-intersection curves, cusp curves, and isolated singular points of the rational surface, together with the order of each singular locus. We present some examples to compare our algorithm with state-of-the-art methods from different perspectives including robustness, efficiency, order computation, and numerical stability, and the experimental results show that our method outperforms existing methods in all these aspects. Furthermore, applications of our algorithm in surface rendering, mesh generation and surface/surface intersections are provided to demonstrate that correctly computing the self-intersection curves of a surface is essential to generate high quality results for these applications.

The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.

Ellipses are important elements in projective geometry. Accurate extraction of ellipse information is the first step in many computer vision applications, such as ellipse-based camera calibration and camera pose estimation. At present, most ellipse detection algorithms rely on the edge features extracted by Canny, which leads to a number of wrong detection results since non-ellipse edges features are also involved. To address this problem, this paper proposes a novel ellipse marker detection neural network, called EllipseNet. Notably, we propose a new loss function to enhance the rotation perception ability of EllipseNet. Furthermore, a novel ellipse marker data enhancement method is proposed for saving the time cost of labelling ellipse parameters. Experiments show that EllipseNet can improve the detection precision of ellipse regions by more than 3% improvement compared with other SOTA general object detectors.

This study presents a high-accuracy, efficient, and physically induced method for 3D point cloud registration, which is the core of many important 3D vision problems. In contrast to existing physics-based methods that merely consider spatial point information and ignore surface geometry, we explore geometry aware rigid-body dynamics to regulate the particle (point) motion, which results in more precise and robust registration. Our proposed method consists of four major modules. First, we leverage the graph signal processing (GSP) framework to define a new signature, i.e., point response intensity for each point, by which we succeed in describing the local surface variation, resampling keypoints, and distinguishing different particles. Then, to address the shortcomings of current physics-based approaches that are sensitive to outliers, we accommodate the defined point response intensity to median absolute deviation (MAD) in robust statistics and adopt the X84 principle for adaptive outlier depression, ensuring a robust and stable registration. Subsequently, we propose a novel geometric invariant under rigid transformations to incorporate higher-order features of point clouds, which is further embedded for force modeling to guide the correspondence between pairwise scans credibly. Finally, we introduce an adaptive simulated annealing (ASA) method to search for the global optimum and substantially accelerate the registration process. We perform comprehensive experiments to evaluate the proposed method on various datasets captured from range scanners to LiDAR. Results demonstrate that our proposed method outperforms representative state-of-the-art approaches in terms of accuracy and is more suitable for registering large-scale point clouds. Furthermore, it is considerably faster and more robust than most competitors. Our implementation is publicly available at https://github.com/zikai1/GraphReg.

Face recognition is an important yet challenging problem in computer vision. A major challenge in practical face recognition applications lies in significant variations between profile and frontal faces. Traditional techniques address this challenge either by synthesizing frontal faces or by pose invariant learning. In this paper, we propose a novel method with Lie algebra theory to explore how face rotation in the 3D space affects the deep feature generation process of convolutional neural networks (CNNs). We prove that face rotation in the image space is equivalent to an additive residual component in the feature space of CNNs, which is determined solely by the rotation. Based on this theoretical finding, we further design a Lie Algebraic Residual Network (LARNet) for tackling pose robust face recognition. Our LARNet consists of a residual subnet for decoding rotation information from input face images, and a gating subnet to learn rotation magnitude for controlling the strength of the residual component contributing to the feature learning process. Comprehensive experimental evaluations on both frontal-profile face datasets and general face recognition datasets convincingly demonstrate that our method consistently outperforms the state-of-the-art ones.

Fitting ellipses from unrecognized data is a fundamental problem in computer vision and pattern recognition. Classic least-squares based methods are sensitive to outliers. To address this problem, in this paper, we present a novel and effective method called hierarchical Gaussian mixture models (HGMM) for ellipse fitting in noisy, outliers-contained, and occluded settings on the basis of Gaussian mixture models (GMM). This method is crafted into two layers to significantly improve its fitting accuracy and robustness for data containing outliers/noise and has been proven to effectively narrow down the iterative interval of the kernel bandwidth, thereby speeding up ellipse fitting. Extensive experiments are conducted on synthetic data including substantial outliers (up to 60%) and strong noise (up to 200%) as well as on real images including complex benchmark images with heavy occlusion and images from versatile applications. We compare our results with those of representative state-of-the-art methods and demonstrate that our proposed method has several salient advantages, such as its high robustness against outliers and noise, high fitting accuracy, and improved performance.

We present a simple yet efficient algorithm for recognizing simple quadric primitives (plane, sphere, cylinder, cone) from triangular meshes. Our approach is an improved version of a previous hierarchical clustering algorithm, which performs pairwise clustering of triangle patches from bottom to top. The key contributions of our approach include a strategy for priority and fidelity consideration of the detected primitives, and a scheme for boundary smoothness between adjacent clusters. Experimental results demonstrate that the proposed method produces qualitatively and quantitatively better results than representative state-of-the-art methods on a wide range of test data.

Arrangements of geometric objects refer to the spatial partitions formed by the objects, and they serve as an underlining structure of motion design, analysis, and planning in CAD/CAM, robotics, molecular modeling, manufacturing, and computer-assisted radio-surgery. Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation, virtual reality, computer games, robotics, CAD/CAM, and computational physics. Ellipsoids are commonly used as bounding volumes in approximating complex geometric objects in collision detection. In this article, we present an in-depth study on the arrangements formed by two ellipsoids. Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids. A stratification diagram is also established to show the connections among all the arrangements formed by two ellipsoids. Our results, for the first time, elucidate all possible relative positions between two arbitrary ellipsoids and provide an efficient and robust algorithm for determining the relative position of any two given ellipsoids, therefore providing the necessary foundation for developing practical and trustworthy methods for processing ellipsoids for collision analysis or simulation in various applications.

Abstract In this paper, we present a novel method for surface sampling and remeshing with good blue‐noise properties. Our approach is based on the farthest point optimization (FPO), a relaxation technique that generates high quality blue‐noise point sets in 2D. We propose two important generalizations of the original FPO framework: adaptive sampling and sampling on surfaces. A simple and efficient algorithm for accelerating the FPO framework is also proposed. Experimental results show that the generalized FPO generates point sets with excellent blue‐noise properties for adaptive and surface sampling. Furthermore, we demonstrate that our remeshing quality is superior to the current state‐of‐theߚart approaches.

Color transfer is a practical image editing technology which is useful in various applications. An ideal color transfer algorithm should keep the scene in the source image and apply the color styles of the reference image. All the dominant color styles of the reference image should be presented in the result especially when there are similar contents in the source and reference images.