1,721,022 research outputs found
Sparse Iterative Closest Point
No full textRigid registration of two geometric data sets is essential in many applications, including robot navigation, surface reconstruction, and shape matching. Most commonly, variants of the Iterative Closest Point (ICP) algorithm are employed for this task. These methods alternate between closest point computations to establish correspondences between two data sets, and solving for the optimal transformation that brings these correspondences into alignment. A major difficulty for this approach is the sensitivity to outliers and missing data often observed in 3D scans. Most practical implementations of the ICP algorithm address this issue with a number of heuristics to prune or reweight correspondences. However, these heuristics can be unreliable and difficult to tune, which often requires substantial manual assistance. We propose a new formulation of the ICP algorithm that avoids these difficulties by formulating the registration optimization using sparsity inducing norms. Our new algorithm retains the simple structure of the ICP algorithm, while achieving superior registration results when dealing with outliers and incomplete data. The complete source code of our implementation is provided at http://lgg.epfl.ch/sparseicp.Computer Graphics Foru
Approximating Functions on a Mesh with Restricted Voronoï Diagrams
No full textWe propose a method that computes a piecewise constant approximation of a function defined on a mesh. The approximation is associated with the cells of a restricted Voronoï diagram. Our method optimizes an objective function measuring the quality of the approximation. This objective function depends on the placement of the samples that define the restricted Voronoï diagram and their associated function values. We study the continuity of the objective function, derive the closed-form expression of its derivatives and use them to design a numerical solution mechanism. The method can be applied to a function that has discontinuities, and the result aligns the boundaries of the Voronoï cells with the discontinuities. Some examples are shown, suggesting potential applications in image vectorization and compact representation of lighting.Computer Graphics Foru
Consolidation of Low-quality Point Clouds from Outdoor Scenes
No full textThe emergence of laser/LiDAR sensors, reliable multi-view stereo techniques and more recently consumer depth cameras have brought point clouds to the forefront as a data format useful for a number of applications. Unfortunately, the point data from those channels often incur imperfection, frequently contaminated with severe outliers and noise. This paper presents a robust consolidation algorithm for low-quality point data from outdoor scenes, which essentially consists of two steps: 1) outliers filtering and 2) noise smoothing. We first design a connectivitybased scheme to evaluate outlierness and thereby detect sparse outliers. Meanwhile, a clustering method is used to further remove small dense outliers. Both outlier removal methods are insensitive to the choice of the neighborhood size and the levels of outliers. Subsequently, we propose a novel approach to estimate normals for noisy points based on robust partial rankings, which is the basis of noise smoothing. Accordingly, a fast approach is exploited to smooth noise, while preserving sharp features. We evaluate the effectiveness of the proposed method on the point clouds from a variety of outdoor scenes.Computer Graphics Foru
Consistent Volumetric Discretizations Inside Self-Intersecting Surfaces
No full textDecades of research have culminated in a robust geometry processing pipeline for surfaces. Most steps in this pipeline, like deformation, smoothing, subdivision and decimation, may create self-intersections. Volumetric processing of solid shapes then becomes difficult, because obtaining a correct volumetric discretization is impossible: existing tet-meshing methods require watertight input. We propose an algorithm that produces a tetrahedral mesh that overlaps itself consistently with the self-intersections in the input surface. This enables volumetric processing on self-intersecting models. We leverage conformalized mean-curvature flow, which removes self-intersections, and define an intrinsically similar reverse flow, which prevents them. We tetrahedralize the resulting surface and map the mesh inside the original surface. We demonstrate the effectiveness of our method with applications to automatic skinning weight computation, physically based simulation and geodesic distance computation.Computer Graphics Foru
Animation-Aware Quadrangulation
No full textGeometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point-to-point correspondence, and we automatically produce a quadrangular mesh that fits well the input animation. We first analyze the local deformation that the surface undergoes at each point, and we initialize a cross field that remains as aligned as possible to the principal directions of deformation throughout the sequence. We then smooth this cross field based on an energy that uses a weighted combination of the initial field and the local amount of stretch. Finally, we compute a field-aligned quadrangulation with an off-the-shelf method. Our technique is fast and very simple to implement, and it significantly improves the quality of the output quad mesh and its suitability for character animation, compared to creating the quad mesh based on a single pose. We present experimental results and comparisons with a state-of-the-art quadrangulation method, on both sequences from 3D scanning and synthetic sequences obtained by a rough animation of a triangulated model.Computer Graphics Foru
Consistent Shape Maps via Semidefinite Programming
No full textRecent advances in shape matching have shown that jointly optimizing the maps among the shapes in a collection can lead to significant improvements when compared to estimating maps between pairs of shapes in isolation. These methods typically invoke a cycle-consistency criterion - the fact that compositions of maps along a cycle of shapes should approximate the identity map. This condition regularizes the network and allows for the correction of errors and imperfections in individual maps. In particular, it encourages the estimation of maps between dissimilar shapes by compositions of maps along a path of more similar shapes. In this paper, we introduce a novel approach for obtaining consistent shape maps in a collection that formulates the cycle-consistency constraint as the solution to a semidefinite program (SDP). The proposed approach is based on the observation that, if the ground truth maps between the shapes are cycle-consistent, then the matrix that stores all pair-wise maps in blocks is low-rank and positive semidefinite. Motivated by recent advances in techniques for low-rank matrix recovery via semidefinite programming, we formulate the problem of estimating cycle-consistent maps as finding the closest positive semidefinite matrix to an input matrix that stores all the initial maps. By analyzing the Karush-Kuhn-Tucker (KKT) optimality condition of this program, we derive theoretical guarantees for the proposed algorithm, ensuring the correctness of the recovery when the errors in the inputs maps do not exceed certain thresholds. Besides this theoretical guarantee, experimental results on benchmark datasets show that the proposed approach outperforms state-of-the-art multiple shape matching methods.Computer Graphics Foru
Weak Convex Decomposition by Lines-of-sight
No full textWe define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all-pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches.Computer Graphics Foru
Fast and Robust Approximation of Smallest Enclosing Balls in Arbitrary Dimensions
No full textIn this paper, an algorithm is introduced that computes an arbitrarily fine approximation of the smallest enclosing ball of a point set in any dimension. This operation is important in, for example, classification, clustering, and data mining. The algorithm is very simple to implement, gives reliable results, and gracefully handles large problem instances in low and high dimensions, as confirmed by both theoretical arguments and empirical evaluation. For example, using a CPU with eight cores, it takes less than two seconds to compute a 1:001-approximation of the smallest enclosing ball of one million points uniformly distributed in a hypercube in dimension 200. Furthermore, the presented approach extends to a more general class of input objects, such as ball sets.Computer Graphics Foru
Connectivity Editing for Quad-Dominant Meshes
No full textWe propose a connectivity editing framework for quad-dominant meshes. In our framework, the user can edit the mesh connectivity to control the location, type, and number of irregular vertices (with more or fewer than four neighbors) and irregular faces (non-quads). We provide a theoretical analysis of the problem, discuss what edits are possible and impossible, and describe how to implement an editing framework that realizes all possible editing operations. In the results, we show example edits and illustrate the advantages and disadvantages of different strategies for quad-dominant mesh design.Computer Graphics Foru
Locally Injective Mappings
No full textMappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise-linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion-free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.Computer Graphics Foru
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