Sharp Feature Preservation Research Articles

Surface remeshing with preservation of sharp features through iterative identification and optimization of sample points

High-quality triangular meshes with sharp features are necessary for geometric processing applications, e.g., CAD models. Existing approaches either directly utilize the original sharp features as outputs, or predetermine feature sample points and reconstruct feature edges after an optimization process. However, these may result in poor-quality triangular facets close to feature edges or even feature preservation failure. With this regard, we present a feature-preservation surface remeshing method to generate high-quality triangular meshes with sharp feature preservation from raw manifold meshes. Unlike existing predetermination strategy, we introduce a heuristic strategy to dynamically determine feature sample points in each iteration. Based on the projection distance, each feature sample point is identified and projected onto the original feature edges, achieving the preservation of feature sample points. Besides, to eliminate the large gaps between two adjacent feature sample points and edge-close sample points, a feature edge continuity preservation strategy is proposed. Some additional sample points are further projected onto the large gaps and the edge-close sample points are deviated from the feature edges, achieving the preservation of reconstructed feature edges. Experimental results on several models demonstrate the effectiveness and efficiency of our method in generating high-quality triangular meshes with sharp feature preservation.

Feature-preserving shrink wrapping with adaptive alpha

Recent advancements in shrink-wrapping-based mesh approximation have shown tremendous advantages for non-manifold defective meshes. However, these methods perform unsatisfactorily when maintaining the regions with sharp features and rich details of the input mesh. We propose an adaptive shrink-wrapping method based on the recent Alpha Wrapping technique, offering improved feature preservation while handling defective inputs. The proposed approach comprises three main steps. First, we compute a new sizing field with the capability to assess the discretization density of non-manifold defective meshes. Then, we generate a mesh feature skeleton by projecting input feature lines onto the offset surface, ensuring the preservation of sharp features. Finally, an adaptive wrapping approach based on normal projection is applied to preserve the regions with sharp features and rich details simultaneously. By conducting experimental tests on various datasets including Thingi10k, ABC, and GrabCAD, we demonstrate that our method exhibits significant improvements in mesh fidelity compared to the Alpha Wrapping method, while maintaining the advantage of manifold property inherited from shrink-wrapping methods.

Learning Implicit Fields for Point Cloud Filtering.

Since point clouds acquired by scanners inevitably contain noise, recovering a clean version from a noisy point cloud is essential for further 3D geometry processing applications. Several data-driven approaches have been recently introduced to overcome the drawbacks of traditional filtering algorithms, such as less robust preservation of sharp features and tedious tuning for multiple parameters. Most of these methods achieve filtering by directly regressing the position/displacement of each point, which may blur detailed features and is prone to uneven distribution. In this paper, we propose a novel data-driven method that explores the implicit fields. Our assumption is that the given noisy points implicitly define a surface, and we attempt to obtain a point's movement direction and distance separately based on the predicted signed distance fields (SDFs). Taking a noisy point cloud as input, we first obtain a consistent alignment by incorporating the global points into local patches. We then feed them into an encoder-decoder structure and predict a 7D vector consisting of SDFs. Subsequently, the distance can be obtained directly from the first element in the vector, and the movement direction can be obtained by computing the gradient descent from the last six elements (i.e., six surrounding SDFs). We finally obtain the filtered results by moving each point with its predicted distance along its movement direction. Our method can produce feature-preserving results without requiring explicit normals. Experiments demonstrate that our method visually outperforms state-of-the-art methods and generally produces better quantitative results than position-based methods (both learning and non-learning).

Deep Shape Representation with Sharp Feature Preservation

Deep Shape Representation with Sharp Feature Preservation

Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation

We present a novel implicit representation --- neural halfspace representation (NH-Rep), to convert manifold B-Rep solids to implicit representations. NH-Rep is a Boolean tree built on a set of implicit functions represented by the neural network, and the composite Boolean function is capable of representing solid geometry while preserving sharp features. We propose an efficient algorithm to extract the Boolean tree from a manifold B-Rep solid and devise a neural network-based optimization approach to compute the implicit functions. We demonstrate the high quality offered by our conversion algorithm on ten thousand manifold B-Rep CAD models that contain various curved patches including NURBS, and the superiority of our learning approach over other representative implicit conversion algorithms in terms of surface reconstruction, sharp feature preservation, signed distance field approximation, and robustness to various surface geometry, as well as a set of applications supported by NH-Rep.

Deep Shape Representation with Sharp Feature Preservation

Deep Shape Representation with Sharp Feature Preservation

Computational paradigms for direct triangular surface remeshing

Direct triangular surface remeshing algorithms work directly on the surface meshes without involving any complex parameterization techniques. The typical goal of surface remeshing is to find a mesh that is a faithful approximation of the input mesh that maintains the geometric fidelity between input and output meshes, achieve a lower bound on the minimal angles to enhance high element quality while maintaining vertex regularity and sharp feature preservation of the input mesh. The goal of each surface remeshing algorithm varies as per the requirement of the end application and thus achieving a balance between all common goals is a challenging task in remeshing. In this paper, a survey of numerous direct surface remeshing algorithms that have been developed over the past decade is presented. A framework of direct surface remeshing is defined and various phases of the framework are discussed in detail to give new insights into both existing methods and issues. A detailed analysis of how significant challenges have already been overcome and promising perspectives of various methods are presented.

Sharp Feature Detection as a Useful Tool in Smart Manufacturing

Industry 4.0 comprises a wide spectrum of developmental processes within the management of manufacturing and chain production. Presently, there is a huge effort to automate manufacturing and have automatic control of the production. This intention leads to the increased need for high-quality methods for digitization and object reconstruction, especially in the area of reverse engineering. Commonly used scanning software based on well-known algorithms can correctly process smooth objects. Nevertheless, they are usually not applicable for complex-shaped models with sharp features. The number of the points on the edges is extremely limited due to the principle of laser scanning and sometimes also low scanning resolution. Therefore, a correct edge reconstruction problem occurs. The same problem appears in many other laser scanning applications, i.e., in the representation of the buildings from airborne laser scans for 3D city models. We focus on a method for preservation and reconstruction of sharp features. We provide a detailed description of all three key steps: point cloud segmentation, edge detection, and correct B-spline edge representation. The feature detection algorithm is based on the conventional region-growing method and we derive the optimal input value of curvature threshold using logarithmic least square regression. Subsequent edge representation stands on the iterative algorithm of B-spline approximation where we compute the weighted asymmetric error using the golden ratio. The series of examples indicates that our method gives better or comparable results to other methods.

Shape Reconstruction Using Boolean Operations in Electrical Impedance Tomography.

In this work, we propose a new shape reconstruction framework rooted in the concept of Boolean operations for electrical impedance tomography (EIT). Within the framework, the evolution of inclusion shapes and topologies are simultaneously estimated through an explicit boundary description. For this, we use B-spline curves as basic shape primitives for shape reconstruction and topology optimization. The effectiveness of the proposed approach is demonstrated using simulated and experimentally-obtained data (testing EIT lung imaging). In the study, improved preservation of sharp features is observed when employing the proposed approach relative to the recently developed moving morphable components-based approach. In addition, robustness studies of the proposed approach considering background inhomogeneity and differing numbers of B-spline curve control points are performed. It is found that the proposed approach is tolerant to modeling errors caused by background inhomogeneity and is also quite robust to the selection of control points.

Surface reconstruction based on CAD model driven priori templates.

In this paper, a method of reconstructing 3D (three dimensional) models from the original scanned point cloud using priori templates is proposed. Different from previous reconstruction methods that triangulate and fit the original scanning point cloud directly, we construct a priori template based on the CAD (computer aided design) model and guide the reconstruction of the original scanning point cloud with the priori template. Given a CAD model, the basic geometric elements are used as the basic units to extract the set elements of 3D shapes. Then the geometric elements are meshed, and the normal vectors at the mesh nodes are extracted. The corresponding point cloud data of each basic element are extracted from the original point cloud. The point cloud data near the normal of the guide point are searched, and the Gaussian weighted average value of the searched point represents the actual geometric parameters of the part at the guide point. Finally, the geometric elements of the basic unit are reconstructed locally by Non-Uniform Rational B-Splines surface fitting, and the complete reconstruction model is obtained by integrating the local reconstruction. Experiments show that our method can solve the problems of high quality reconstruction, sharp feature preservation, and detail recovery in surface reconstruction.

Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

AbstractThe combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12, CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all‐hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.

Deep Learning-Based Classification and Reconstruction of Residential Scenes From Large-Scale Point Clouds

The reconstruction of urban buildings from large-scale airborne laser scanning point clouds is an important research topic in the geoscience field. Large-scale urban scenes usually contain a large number of object categories and many overlapped or closely neighboring objects, which poses great challenges for classifying and modeling buildings from these data sets. In this paper, we propose a deep reinforcement learning framework that integrates a 3-D convolutional neural network, a deep Q-network, and a residual recurrent neural network for the efficient semantic parsing of large-scale 3-D point clouds. The proposed framework provides an end-to-end automatic processing method that maps the raw point cloud to the classification results of the given categories. After obtaining the building classes, we utilize an edge-aware resampling algorithm to consolidate the point set with noise-free normals and clean preservation of sharp features. Finally, 2.5-D dual contouring, which is a data-driven approach, is introduced to generate urban building models from the consolidated point clouds. Our method can generate lightweight building models with arbitrarily shaped roofs while preserving the verticality of connecting walls.

Super-Resolution of Multi-Observed RGB-D Images Based on Nonlocal Regression and Total Variation.

There is growing demand for accuracy in image processing and visualization, and the super-resolution (SR) technique for multi-observed RGB-D images has become popular, because it provides space-redundant information and produces a detailed reconstruction even with a large magnification factor. This technique has been thoroughly investigated in recent years. Nevertheless, technical challenges remain, such as finding sub-pixel correspondences with low-resolution (LR) observations, exploiting space-redundant information, formulating space homogeneity constraints, and leveraging cross-image similarities in structures. To address these challenges, this paper proposes a unified optimization framework to estimate both the super-resolved RGB image and the super-resolved depth image from the multi-observed LR RGB-D images using their correlations. Using depth-assisted cross-image correspondences, the RGB image SR problem is formulated as an effective regularization function by incorporating the normalized bilateral total variation regularizer, and it is efficiently solved by a first-order primal-dual algorithm. The depth image SR estimate can be obtained by minimizing a nonlocal regression-based energy, which integrates the structural cues of the super-resolved RGB image in a detail-preserving fashion. Essentially, our unified optimization framework uses the RGB image and depth image as a priori knowledge that the SR process uses for better accuracy. Our extensive experiments on public RGB-D benchmarks and real data and our quantitative comparison with several state-of-the-art methods demonstrate the superiority of our method in terms of accuracy, versatility, and reliability of details and sharp feature preservation.

LayTracks3D: A new approach for meshing general solids using medial axis transform

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.

Robust surface reconstruction via dictionary learning

Surface reconstruction from point cloud is of great practical importance in computer graphics. Existing methods often realize reconstruction via a few phases with respective goals, whose integration may not give an optimal solution. In this paper, to avoid the inherent limitations of multi-phase processing in the prior art, we propose a unified framework that treats geometry and connectivity construction as one joint optimization problem. The framework is based on dictionary learning in which the dictionary consists of the vertices of the reconstructed triangular mesh and the sparse coding matrix encodes the connectivity of the mesh. The dictionary learning is formulated as a constrained ℓ 2,q -optimization (0 < q < 1), aiming to find the vertex position and triangulation that minimize an energy function composed of point-to-mesh metric and regularization. Our formulation takes many factors into account within the same framework, including distance metric, noise/outlier resilience, sharp feature preservation, no need to estimate normal, etc., thus providing a global and robust algorithm that is able to efficiently recover a piecewise smooth surface from dense data points with imperfections. Extensive experiments using synthetic models, real world models, and publicly available benchmark show that our method outperforms the state-of-the-art in terms of accuracy, robustness to noise and outliers, geometric feature and detail preservation, and mesh connectivity.

Robust statistical approaches for local planar surface fitting in 3D laser scanning data

This paper proposes robust methods for local planar surface fitting in 3D laser scanning data. Searching through the literature revealed that many authors frequently used Least Squares (LS) and Principal Component Analysis (PCA) for point cloud processing without any treatment of outliers. It is known that LS and PCA are sensitive to outliers and can give inconsistent and misleading estimates. RANdom SAmple Consensus (RANSAC) is one of the most well-known robust methods used for model fitting when noise and/or outliers are present. We concentrate on the recently introduced Deterministic Minimum Covariance Determinant estimator and robust PCA, and propose two variants of statistically robust algorithms for fitting planar surfaces to 3D laser scanning point cloud data. The performance of the proposed robust methods is demonstrated by qualitative and quantitative analysis through several synthetic and mobile laser scanning 3D data sets for different applications. Using simulated data, and comparisons with LS, PCA, RANSAC, variants of RANSAC and other robust statistical methods, we demonstrate that the new algorithms are significantly more efficient, faster, and produce more accurate fits and robust local statistics (e.g. surface normals), necessary for many point cloud processing tasks. Consider one example data set used consisting of 100 points with 20% outliers representing a plane. The proposed methods called DetRD-PCA and DetRPCA, produce bias angles (angle between the fitted planes with and without outliers) of 0.20° and 0.24° respectively, whereas LS, PCA and RANSAC produce worse bias angles of 52.49°, 39.55° and 0.79° respectively. In terms of speed, DetRD-PCA takes 0.033s on average for fitting a plane, which is approximately 6.5, 25.4 and 25.8 times faster than RANSAC, and two other robust statistical methods, respectively. The estimated robust surface normals and curvatures from the new methods have been used for plane fitting, sharp feature preservation and segmentation in 3D point clouds obtained from laser scanners. The results are significantly better and more efficiently computed than those obtained by existing methods.

LayTracks3D: A New Approach to Meshing General Solids using Medial Axis Transform

This paper presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex and hex- dominant meshes of 3D assembly models. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D are similar to tunnels with no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to the MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the result section. The paper also describes how this algorithm can be extended to produce all-hex meshes in general geometries.

Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets

We introduce a robust and feature-capturing surface reconstruction and simplification method that turns an input point set into a low triangle-count simplicial complex. Our approach starts with a (possibly non-manifold) simplicial complex filtered from a 3D Delaunay triangulation of the input points. This initial approximation is iteratively simplified based on an error metric that measures, through optimal transport, the distance between the input points and the current simplicial complex--both seen as mass distributions. Our approach is shown to exhibit both robustness to noise and outliers, as well as preservation of sharp features and boundaries. Our new feature-sensitive metric between point sets and triangle meshes can also be used as a post-processing tool that, from the smooth output of a reconstruction method, recovers sharp features and boundaries present in the initial point set.

Edge-aware point set resampling

Points acquired by laser scanners are not intrinsically equipped with normals, which are essential to surface reconstruction and point set rendering using surfels. Normal estimation is notoriously sensitive to noise. Near sharp features, the computation of noise-free normals becomes even more challenging due to the inherent undersampling problem at edge singularities. As a result, common edge-aware consolidation techniques such as bilateral smoothing may still produce erroneous normals near the edges. We propose a resampling approach to process a noisy and possibly outlier-ridden point set in an edge-aware manner. Our key idea is to first resample away from the edges so that reliable normals can be computed at the samples, and then based on reliable data, we progressively resample the point set while approaching the edge singularities. We demonstrate that our Edge-Aware Resampling (EAR) algorithm is capable of producing consolidated point sets with noise-free normals and clean preservation of sharp features. We also show that EAR leads to improved performance of edge-aware reconstruction methods and point set rendering techniques.

Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C 2-continuity everywhere except the local region around irregular nodes. Finally, a Bezier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.