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We propose a framework to generate customized summarizations of visual data collections, such as collections of images, materials, 3D shapes, and 3D scenes. We assume that the elements in the visual data collections can be mapped to a set of vectors in a feature space, in which a fitness score for each element can be defined, and we pose the problem of customized summarizations as selecting a subset of these elements. We first describe the design choices a user should be able to specify for modeling customized summarizations and propose a corresponding user interface. We then formulate the problem as a constrained optimization problem with binary variables and propose a practical and fast algorithm based on the alternating direction method of multipliers (ADMM). Our results show that our problem formulation enables a wide variety of customized summarizations, and that our solver is both significantly faster than state‐of‐the‐art commercial integer programming solvers and produces better solutions than fast relaxation‐based solvers. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm for isotropic surface remeshing which progressively eliminates obtuse triangles and improves small angles. The main novelty of the proposed approach is a simple vertex insertion scheme that facilitates the removal of large angles, and a vertex removal operation that improves the distribution of small angles. In combination with other standard local mesh operators, e.g., connectivity optimization and local tangential smoothing, our algorithm is able to remesh efficiently a low-quality mesh surface. Our approach can be applied directly or used as a post-processing step following other remeshing approaches. Our method has a similar computational efficiency to the fastest approach available, i.e., real-time adaptive remeshing [1]. In comparison with state-of-the-art approaches, our method consistently generates better results based on evaluations using different metrics. [ABSTRACT FROM AUTHOR]

We introduce an algorithmic framework for tuning the spatial density of disks in a maximal random packing, without changing the sizing function or radii of disks. Starting from any maximal random packing such as a Maximal Poisson-disk Sampling (MPS), we iteratively relocate, inject (add), or eject (remove) disks, using a set of three successively more-aggressive local operations. We may achieve a user-defined density, either more dense or more sparse, almost up to the theoretical structured limits. The tuned samples are conflict-free, retain coverage maximality, and, except in the extremes, retain the blue noise randomness properties of the input. We change the density of the packing one disk at a time, maintaining the minimum disk separation distance and the maximum domain coverage distance required of any maximal packing. These properties are local, and we can handle spatially-varying sizing functions. Using fewer points to satisfy a sizing function improves the efficiency of some applications. We apply the framework to improve the quality of meshes, removing non-obtuse angles; and to more accurately model fiber reinforced polymers for elastic and failure simulations. [ABSTRACT FROM AUTHOR]

Connectivity and layout of underlying networks largely determine agent behavior and usage in many environments. For example, transportation networks determine the flow of traffic in a neighborhood, whereas building floorplans determine the flow of people in a workspace. Designing such networks from scratch is challenging as even local network changes can have large global effects. We investigate how to computationally create networks starting from only high-level functional specifications. Such specifications can be in the form of network density, travel time versus network length, traffic type, destination location, etc. We propose an integer programming-based approach that guarantees that the resultant networks are valid by fulfilling all the specified hard constraints and that they score favorably in terms of the objective function. We evaluate our algorithm in two different design settings, street layout and floorplans to demonstrate that diverse networks can emerge purely from high-level functional specifications. [ABSTRACT FROM AUTHOR]

In this paper, we present a simple yet efficient algorithm for triangulating a 2D input domain containing a Poisson-disk sampled point set. The proposed algorithm combines a regular grid and a discrete clustering approach to speedup the triangulation. Moreover, our triangulation algorithm is flexible and performs well on more general point sets such as adaptive, non-maximal Poisson-disk sets. The experimental results demonstrate that our algorithm is robust for a wide range of input domains and achieves significant performance improvement compared to the current state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Abstract: We present a framework for the automatic disassembly of 3D man-made models and the illustration of the disassembly process. Given an assembled 3D model, we first analyze the individual parts using sharp edge loops and extract the contact faces between each pair of neighboring parts. The contact faces are then used to compute the possible moving directions of each part. We then present a simple algorithm for clustering the sets of the individual parts into meaningful sub-assemblies, which can be used for a hierarchical decomposition. We take the stability of sub-assemblies into account during the decomposition process by considering the upright orientation of the input models. Our framework also provides a user-friendly interface to enable the superimposition of the constraints for the decomposition. Finally, we visualize the disassembly process by generating an animated sequence. The experiments demonstrate that our framework works well for a variety of complex models. [Copyright &y& Elsevier]

Volumetric PolyCube-Map-based methods offer automatic ways to construct all-hexahedral meshes for closed 3D polyhedral domains, but their meshing quality is limited by the lack of interior singularities and feature alignment. In the presented work, we propose cut-enhanced PolyCube-Maps, to introduce essential interior singularities and preserve most input features. Our main idea is simple and intuitive: by inserting proper parameterization seams into the initial PolyCube-Map via novel PolyCube cutting operations, the mapping distortion can be reduced significantly. The cut-enhanced PolyCube-Map computation includes feature-aware PolyCube-Map construction and cut-enhanced PolyCube deformation. The former aims to preserve input feature edges during the initial PolyCube-Map construction. The latter introduces seams into the volumetric PolyCube shape by cutting it through selective PolyCube edges and deforms the modified PolyCube under the seamless constraints to compute a low-distortion PolyCube-Map. The hexahedral mesh induced by the final PolyCube-Map can be further enhanced by our mesh improvement algorithm. We validate the efficacy of our method on a collection of more than one hundred CAD models and demonstrate its advantages over other automatic all-hex meshing methods and padding strategies. The limitations of cut-enhanced PolyCube-Maps are also discussed thoroughly. [ABSTRACT FROM AUTHOR]

• A novel circle detection method based on inscribed triangles, which is resistant to occlusion and robust to noise. • A new arc grouping strategy using the relative position constraint and the inscibed triangle constraint.. • A total geometry-based parameter estimation method by inscribed triangles without the dependence of least-square fitting but with the equivalent accuracy. • A new collected real-world dataset with the sufficient examination for circle detection methods. • Extensive experiments compared with representative state-of-the-art methods and better results have been obtained both in F-measure and execution speed. Circle detection is a critical issue in pattern recognition and image analysis. Conventional geometry-based methods such as tangent or symmetry are sensitive to noise or occlusion. Area computation is more robust against noise, because it avoids differential calculations. Inspired by this characteristic, we present a novel method for fast circle detection using inscribed triangles. The proposed algorithm, which is robust to noise and resistant to occlusion, first extracts circular arcs by approximating line segments and identifying inflection points and sharp corners. To speed up the computation, irrelevant segments are filtered out through the triangle inequality. Arcs that belong to the same circle are then combined according to the position constraint and the inscribed triangle constraint. The circle parameters are further estimated by inscribed triangles based upon the Theil-Sen estimator and linear error refinement without the dependence of least-square fitting but still with the equivalent accuracy. Finally, candidate circles are verified to prune false positives through an inlier ratio rule, which jointly considers both distance and angle deviations. Extensive experiments are conducted on synthetic images including overlapping circles, and real images from four diverse datasets (three publicly available and one we built). Results are compared with those of representative state-of-the-art methods, and the proposed method is demonstrated to embraces several advantages: resistant to occlusion, more robust to noise, and better performance and efficiency. [ABSTRACT FROM AUTHOR]

We introduce a new method to interpolate scattered 3D data points with a single B-spline surface patch which is globally smooth. Given a set of scattered 3D data points and their corresponding parametrization, our method first constructs a set α of B-spline bases using a weighted strategy, and inserts knots to the knot vectors based on α. Then, the knot insertion procedure is iterated until a set β of B-spline bases exists, which indicates the existence of the interpolation surface. Finally, by applying the fairing energy minimizing with interpolation constraints, a globally smooth B-spline surface which interpolates the data points can be produced. Experimental results demonstrate that the generated B-spline surfaces often have fewer control points than those of traditional methods, while keeping the scattered data points interpolated accurately. The implementation of our algorithm and the scripts to reproduce all the results are available at https://github.com/wangbolun300/sparse_data. • An iterative knot insertion algorithm is introduced to guarantee the existence of B-spline interpolation surfaces when fitting scattered 3D data points. • The generated B-spline surfaces often use fewer control points than those of tranditional interpolation methods. • A novel parameter δ is introduced to improve the stability of control point solving. • The control points can be solved by a global fairing energy minimization procedure with strict interpolation constraints. Thus, the generated B-spline surface is globally smooth. [ABSTRACT FROM AUTHOR]

Abstract: Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy. [Copyright &y& Elsevier]

Meaningful feature curves provide high-level shape representation of the geometrical shapes and are useful in various applications. In this paper, we propose an automatic method on the basis of the quadric surface fitting technique to extract complete feature curve networks (FCNs) from 3D surface meshes, as well as finding cycles and generating a high-quality segmentation. In the initial collection of noisy and fragmented feature curves, we first fit the quadric surfaces of each curve and the corresponding neighbor vertices to filter out non-salient or noisy feature curves. Then we conduct a feature extension step to address the curve intersections and form a closed FCN. Finally, we regard circle curves as cycles in the complete FCN and segment the mesh into patches to reveal a highly structured representation of the input geometry. Experimental results demonstrate that our algorithm is more robust for FCN extraction from complex input meshes and achieves higher quality patch layouts compared with the state-of-the-art approaches. We also verify the validity of extracted feature curve cycles by applying them to surface reconstruction. • We provide an efficient method to preserve meaningful feature curves and extract complete FCNs from 3D models. • We simultaneously find the curve cycles in the network and generate high-quality patch layouts. • We obtain a compact high-level representation of 3D models that can be used for surface reconstruction. [ABSTRACT FROM AUTHOR]