2D Points Curve Reconstruction Survey and Benchmark

Ohrhallinger, Stefan; Peethambaran, Jiju; Parakkat, Amal Dev; Dey, Tamal K.; Muthuganapathy, Ramanathan

doi:10.1111/cgf.142659

Cited by 12 publications

(5 citation statements)

References 100 publications

(179 reference statements)

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“…We compare the global variant of our algorithm in 2D to various state‐of‐the‐art reconstruction algorithms, using a recent benchmark [OPP*21]. Fig.…”

Section: Resultsmentioning

confidence: 99%

BallMerge: High‐quality Fast Surface Reconstruction via Voronoi Balls

Parakkat,

Ohrhallinger,

Eisemann

et al. 2024

Computer Graphics Forum

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We introduce a Delaunay‐based algorithm for reconstructing the underlying surface of a given set of unstructured points in 3D. The implementation is very simple, and it is designed to work in a parameter‐free manner. The solution builds upon the fact that in the continuous case, a closed surface separates the set of maximal empty balls (medial balls) into an interior and exterior. Based on discrete input samples, our reconstructed surface consists of the interface between Voronoi balls, which approximate the interior and exterior medial balls. An initial set of Voronoi balls is iteratively processed, merging Voronoi‐ball pairs if they fulfil an overlapping error criterion. Our complete open‐source reconstruction pipeline performs up to two quick linear‐time passes on the Delaunay complex to output the surface, making it an order of magnitude faster than the state of the art while being competitive in memory usage and often superior in quality. We propose two variants (local and global), which are carefully designed to target two different reconstruction scenarios for watertight surfaces from accurate or noisy samples, as well as real‐world scanned data sets, exhibiting noise, outliers, and large areas of missing data. The results of the global variant are, by definition, watertight, suitable for numerical analysis and various applications (e.g., 3D printing). Compared to classical Delaunay‐based reconstruction techniques, our method is highly stable and robust to noise and outliers, evidenced via various experiments, including on real‐world data with challenges such as scan shadows, outliers, and noise, even without additional preprocessing.

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“…We compare the global variant of our algorithm in 2D to various state‐of‐the‐art reconstruction algorithms, using a recent benchmark [OPP*21]. Fig.…”

Section: Resultsmentioning

confidence: 99%

BallMerge: High‐quality Fast Surface Reconstruction via Voronoi Balls

Parakkat,

Ohrhallinger,

Eisemann

et al. 2024

Computer Graphics Forum

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“…In the context of comparing our algorithm with existing state-of-the-art methods for contour reconstruction from 2D point sets, we primarily focused on analyzing two algorithms: HNN-Crust [28] and Vicur [24]. Our selection of these two was informed by a thorough review paper [11], where they particularly distinguished themselves from other methods in an experimental study. We also selected these two algorithms because, as highlighted in Section 2, they represent cutting-edge techniques within their respective algorithm categories.…”

Section: Resultsmentioning

confidence: 99%

“…During the last several decades, numerous methods dedicated to line reconstruction from a set of unstructured points have been presented [11]. In general, these techniques can be classified based on their ability to handle lines, as well as sets of points, of different properties.…”

Section: Related Workmentioning

confidence: 99%

Reconstructing Nerve Structures from Unorganized Points

Kljajić,

Kvaščev,

Đurović

2023

Applied Sciences

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Realistic sensory feedback is paramount for amputees as it improves prosthetic limb control and boosts functionality, safety, and overall quality of life. This sensory restoration relies on the direct electrostimulation of residual peripheral nerves. Computational models are instrumental in simulating these neurostimulation effects, offering solutions to the complexities tied to extensive animal/human trials and costly materials. Central to these models is the detailed mapping of nerve geometry, necessitating the delineation of internal nerve structures, such as fascicles, across various cross-sections. In our modeling process, we faced the challenge of organizing an originally unstructured set of points into coherent contours. We introduced a parameter-free curve-reconstruction algorithm that combines valley-seeking clustering, an adaptive Kalman filter, and the nearest neighbor classification technique. While intuitively simple for humans, the task of reconstructing multiple open and/or closed lines with pronounced corners from a nonuniform point set is daunting for many algorithms. Additionally, the precise differentiation of adjacent curves, commonly encountered in realistic nerve models, remains a formidable challenge even for top-tier algorithms. Our proposed method adeptly navigates the complexities inherent to nerve structure reconstruction. While our algorithm is chiefly designed for closed curves, as dictated by nerve geometry, we believe it can be reconfigured with appropriate code adjustments to handle open curves. Beyond neuroprosthetics, our proposed model has the potential to be applied and spark innovations in biomedicine and a variety of other fields.

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“…In this experiment, we test our parameterization model on point sequences sampled by the benchmark presented in [15]. By considering B-spline approximation of degree 4 with at most 15 adaptive interior knots, Fig.…”

Section: Spline Curve Approximation Of Benchmark Datasetsmentioning

confidence: 99%

Parameterization Learning with Convolutional Neural Networks for Gridded Data Fitting

De Vita,

Giannelli,

Imperatore

et al. 2024

Lecture Notes in Networks and Systems

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The approximation of point clouds in terms of parametric representations is a fundamental task for geometric modeling and processing applications to properly analyze the (re-)constructed model in its full complexity. A necessary and key step in this process requires the identification of a suitable data parameterization. If the data connectivity is determined by a rectilinear grid, standard closed-form methods are available for general multivariate configurations. Existing data-driven parameterization methods instead are limited to the univariate case and require pre/post-processing steps of the input data to handle point sequences without fixed length. In this paper we propose a dimension independent method based on convolutional neural networks to assign parameter values to gridded point clouds of arbitrary size, without the need for additional data processing steps. We train the proposed networks by considering polynomial least squares approximations and demonstrate, both in the univariate and bivariate settings, that the accuracy of the final model properly scales when uniform and adaptive spline refinement is considered. A selection of numerical experiments on point clouds of different sizes highlights the performance of our parameterization scheme. Noisy data sets which simulate measurement errors are also considered.

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2D Points Curve Reconstruction Survey and Benchmark

Abstract: Figure 1: We survey 36 curve reconstruction algorithms and compare 14 of these with quantitative and qualitative analysis. As inputs, we take unorganized points, samples on the boundary of binary images or smooth curves, and evaluate with ground truth.

Cited by 12 publications

References 100 publications

BallMerge: High‐quality Fast Surface Reconstruction via Voronoi Balls

BallMerge: High‐quality Fast Surface Reconstruction via Voronoi Balls

Reconstructing Nerve Structures from Unorganized Points

Parameterization Learning with Convolutional Neural Networks for Gridded Data Fitting

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