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Journal articles on the topic 'Signed Distance Functions'

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Published: 29 June 2021

Last updated: 29 July 2025

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1

Bálint, Csaba, Gábor Valasek, and Lajos Gergó. "Operations on Signed Distance Functions." Acta Cybernetica 24, no. 1 (2019): 17–28. http://dx.doi.org/10.14232/actacyb.24.1.2019.3.

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We present a theoretical overview of signed distance functions and analyze how this representation changes when applying an offset transformation. First, we analyze the properties of signed distance and the sets they describe. Second, we introduce our main theorem regarding the distance to an offset set in (X,||.||) strictly normed Banach spaces. An offset set of D in X is the set of points equidistant to D. We show when such a set can be represented by f(x)-c=0, where c denotes the radius of the offset. Finally, we explain these results for applications that offset signed distance funct

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Esedog¯lu, Selim, Steven Ruuth, and Richard Tsai. "Diffusion generated motion using signed distance functions." Journal of Computational Physics 229, no. 4 (2010): 1017–42. http://dx.doi.org/10.1016/j.jcp.2009.10.002.

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3

Luo, Honglin, Xianfu Wang, and Brett Lukens. "Variational Analysis on the Signed Distance Functions." Journal of Optimization Theory and Applications 180, no. 3 (2018): 751–74. http://dx.doi.org/10.1007/s10957-018-1414-2.

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Fayolle, Pierre-Alain, Alexander Pasko, Benjamin Schmitt, and Nikolay Mirenkov. "Constructive Heterogeneous Object Modeling Using Signed Approximate Real Distance Functions." Journal of Computing and Information Science in Engineering 6, no. 3 (2005): 221–29. http://dx.doi.org/10.1115/1.2218366.

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We introduce a smooth approximation of the min∕max operations, called signed approximate real distance function (SARDF), for maintaining an approximate signed distance function in constructive shape modeling. We apply constructive distance-based shape modeling to design objects with heterogeneous material distribution in the constructive hypervolume model framework. The introduced distance approximation helps intuitively model material distributions parametrized by distances to so-called material features. The smoothness of the material functions, provided here by the smoothness of the definin

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Zollhöfer, Michael, Angela Dai, Matthias Innmann, et al. "Shading-based refinement on volumetric signed distance functions." ACM Transactions on Graphics 34, no. 4 (2015): 1–14. http://dx.doi.org/10.1145/2766887.

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6

Vicini, Delio, Sébastien Speierer, and Wenzel Jakob. "Differentiable signed distance function rendering." ACM Transactions on Graphics 41, no. 4 (2022): 1–18. http://dx.doi.org/10.1145/3528223.3530139.

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Physically-based differentiable rendering has recently emerged as an attractive new technique for solving inverse problems that recover complete 3D scene representations from images. The inversion of shape parameters is of particular interest but also poses severe challenges: shapes are intertwined with visibility, whose discontinuous nature introduces severe bias in computed derivatives unless costly precautions are taken. Shape representations like triangle meshes suffer from additional difficulties, since the continuous optimization of mesh parameters cannot introduce topological changes. O

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Jiang, Sijia, Tong Wu, Jing Hua, and Zhizhong Han. "Sensing Surface Patches in Volume Rendering for Inferring Signed Distance Functions." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 4 (2025): 4066–74. https://doi.org/10.1609/aaai.v39i4.32426.

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It is vital to recover 3D geometry from multi-view RGB images in many 3D computer vision tasks. The latest methods infer the geometry represented as a signed distance field by minimizing the rendering error on the field through volume rendering. However, it is still challenging to explicitly impose constraints on surfaces for inferring more geometry details due to the limited ability of sensing surfaces in volume rendering. To resolve this problem, we introduce a method to infer signed distance functions (SDFs) with a better sense of surfaces through volume rendering. Using the gradients and s

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Wegen, Ole, Jürgen Döllner, and Matthias Trapp. "Interactive Editing of Voxel-Based Signed Distance Fields." Journal of WSCG 30, no. 1-2 (2022): 72–81. http://dx.doi.org/10.24132/jwscg.2022.9.

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Signed distance functions computed in discrete form from given RGB-D data as regular voxel grids can represent manifold shapes as the zero crossing of a trivariate function; the corresponding meshes can be derived by the Marching Cubes algorithm. However, 3D models automatically reconstructed in this way often contain irrelevant objects or artifacts, such as holes or noise, due to erroneous scan data and error-prone reconstruction processes. This paper presents an approach for interactive editing of signed distance functions, derived from RGB-D data in the form of regular voxel grids, that ena

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9

Koch, Philipp, Stefan May, Michael Schmidpeter, et al. "Multi-Robot Localization and Mapping Based on Signed Distance Functions." Journal of Intelligent & Robotic Systems 83, no. 3-4 (2016): 409–28. http://dx.doi.org/10.1007/s10846-016-0375-7.

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10

Park, Sangkun. "Infinite Generation of 3D Voxel Terrain using Signed Distance Functions." Korean Journal of Computational Design and Engineering 28, no. 4 (2023): 357–65. http://dx.doi.org/10.7315/cde.2023.357.

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11

Garifullin, A. R., V. A. Frolov, A. S. Budak, and V. A. Galaktionov. "Study of Surface Representation Methods Based on Signed Distance Functions." Programming and Computer Software 51, no. 3 (2025): 131–39. https://doi.org/10.1134/s036176882570001x.

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12

Deutsch, Clayton V., and Brandon J. Wilde. "Modeling multiple coal seams using signed distance functions and global kriging." International Journal of Coal Geology 112 (June 2013): 87–93. http://dx.doi.org/10.1016/j.coal.2012.11.013.

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13

Tao, Songqiao, and Juan Tan. "Path Planning with Obstacle Avoidance Based on Normalized R-Functions." Journal of Robotics 2018 (October 4, 2018): 1–10. http://dx.doi.org/10.1155/2018/5868915.

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Existing methods for path planning with obstacle avoidance need to check having the interference between a moving part and an obstacle at iteration and even to calculate their shortest distance in the case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance calculating themselves are complicated and time-consuming. Rigorous mathematical analysis might be a practical way for dealing with the above-mentioned problems. An R-function is a real-valued function whose properties are fully determined by corresponding attributes of their parameters, which is usua

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14

Kim, Ho-Jun, and Hak-Gu Kim. "Meta-learning integrated with Signed Distance Functions to Enhance Scene Text Segmentation." TECHART: Journal of Arts and Imaging Science 11, no. 2 (2024): 50–57. http://dx.doi.org/10.15323/techart.2024.5.11.2.50.

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15

Marić, Ante, Yiming Li, and Sylvain CALINON. "Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials." Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials 9, no. 6 (2024): 6020–26. https://doi.org/10.1109/LRA.2024.3397085.

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Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis functions. Starting from an arbitrary prior shape, our method incrementally constructs a continuous and smooth distance representation from incoming surface points, with analytical access to gradient information. The underlying model does not store training data for prediction, and its performance can be balanced through interpretable hyperparameters such as poly

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16

Kraft, Daniel. "Computing the Hausdorff Distance of Two Sets from Their Distance Functions." International Journal of Computational Geometry & Applications 30, no. 01 (2020): 19–49. http://dx.doi.org/10.1142/s0218195920500028.

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The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has applications, for instance, in image processing. However, we would like to apply the Hausdorff distance to control and evaluate optimisation methods in level-set based shape optimisation. In this context, the involved sets are not finite point sets but characterised by level-set or signed distance functions. This paper discusses the computation of the Hausdor

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Molchanov, Vladimir, Paul Rosenthal, and Lars Linsen. "Non-iterative Second-order Approximation of Signed Distance Functions for Any Isosurface Representation." Computer Graphics Forum 29, no. 3 (2010): 1211–20. http://dx.doi.org/10.1111/j.1467-8659.2009.01699.x.

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18

Chen, Gengxiang, Yingguang Li, Charyar Mehdi-Souzani, Wenjun Yang, and Xu Liu. "Implicit multi-sensor reconstruction based on neural signed distance functions for reverse engineering." Procedia CIRP 119 (2023): 552–57. http://dx.doi.org/10.1016/j.procir.2023.01.012.

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19

AICHHOLZER, OSWIN, FRANZ AURENHAMMER, DANNY Z. CHEN, D. T. LEE, and EVANTHIA PAPADOPOULOU. "SKEW VORONOI DIAGRAMS." International Journal of Computational Geometry & Applications 09, no. 03 (1999): 235–47. http://dx.doi.org/10.1142/s0218195999000169.

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On a tilted plane T in three-space, skew distances are defined as the Euclidean distance plus a multiple of the signed difference in height. Skew distances may model realistic environments more closely than the Euclidean distance. Voronoi diagrams and related problems under this kind of distances are investigated. A relationship to convex distance functions and to Euclidean Voronoi diagrams for planar circles is shown, and is exploited for a geometric analysisis and a plane-sweep construction of Voronoi diagrams on T. An output-sensitive algorithm running in time O(n log h) is developed, where

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Shigeto, Yusuke, and Mikio Sakai. "Arbitrary-shaped wall boundary modeling based on signed distance functions for granular flow simulations." Chemical Engineering Journal 231 (September 2013): 464–76. http://dx.doi.org/10.1016/j.cej.2013.07.073.

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21

Reiner, Tim, Gregor Mückl, and Carsten Dachsbacher. "Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions." Computers & Graphics 35, no. 3 (2011): 596–603. http://dx.doi.org/10.1016/j.cag.2011.03.010.

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22

Chen, Chao, Yu-Shen Liu, and Zhizhong Han. "Sharpening Neural Implicit Functions with Frequency Consolidation Priors." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 2 (2025): 2025–33. https://doi.org/10.1609/aaai.v39i2.32199.

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Signed Distance Functions (SDFs) are vital implicit representations to represent high fidelity 3D surfaces. Current methods mainly leverage a neural network to learn an SDF from various supervisions including signed distances, 3D point clouds, or multi-view images. However, due to various reasons including the bias of neural network on low frequency content, 3D unaware sampling, sparsity in point clouds, or low resolutions of images, neural implicit representations still struggle to represent geometries with high frequency components like sharp structures, especially for the ones learned from

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23

Levin, David. "Set-Valued Approximation—Revisited and Improved." Mathematics 13, no. 7 (2025): 1194. https://doi.org/10.3390/math13071194.

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We address the problem of approximating a set-valued function F, where F:[a,b]→K(Rd) given its samples {F(a+ih)}i=0N, with h=(b−a)/N. We revisit an existing method that approximates set-valued functions by interpolating signed-distance functions. This method provides a high-order approximation for general topologies but loses accuracy near points where F undergoes topological changes. To address this, we introduce new techniques that enhance efficiency and maintain high-order accuracy across [a,b]. Building on the foundation of previous publication, we introduce new techniques to improve the m

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24

Hernandez-Martinez, E. G., E. D. Ferreira-Vazquez, G. Fernandez-Anaya, and J. J. Flores-Godoy. "Formation Tracking of Heterogeneous Mobile Agents Using Distance and Area Constraints." Complexity 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/9404193.

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This paper presents two formation tracking control strategies for a combined set of single and double integrator agents with an arbitrary undirected communication topology. The first approach is based on the design of distance-based potential functions with interagent collision avoidance using local information about the distance and orientation between agents and the desired trajectory. The second approach adds signed area constraints to the desired formation specification and a control strategy that uses distance as well as area terms is designed to achieve tracking convergence. Numerical si

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Zhang, Mengfan, Zuoqi Hu, Tiange Zhang, et al. "Learning neural implicit surfaces from sonar image based on signed distance functions combined with occupancy representation." Expert Systems with Applications 270 (April 2025): 126505. https://doi.org/10.1016/j.eswa.2025.126505.

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26

NICKOLAS, PETER, and REINHARD WOLF. "DISTANCE GEOMETRY IN QUASIHYPERMETRIC SPACES. I." Bulletin of the Australian Mathematical Society 80, no. 1 (2009): 1–25. http://dx.doi.org/10.1017/s0004972708000932.

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AbstractLet (X,d) be a compact metric space and let ℳ(X) denote the space of all finite signed Borel measures on X. Define I:ℳ(X)→ℝ by and set M(X)=sup I(μ), where μ ranges over the collection of signed measures in ℳ(X) of total mass 1. The metric space (X,d) is quasihypermetric if for all n∈ℕ, all α1,…,αn∈ℝ satisfying ∑ i=1nαi=0 and all x1,…,xn∈X, the inequality ∑ i,j=1nαiαjd(xi,xj)≤0 holds. Without the quasihypermetric property M(X) is infinite, while with the property a natural semi-inner product structure becomes available on ℳ0(X), the subspace of ℳ(X) of all measures of total mass 0. Thi

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Grosso, Tamara. "Methodological Issues in Constructing a Typology of Pointing in Signed Languages." Sign Language Studies 25, no. 1 (2024): 132–76. https://doi.org/10.1353/sls.2024.a950730.

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Abstract: Pointing serves many functions both syntactically and communicatively across signed languages. This study seeks to clarify the use of pointing by surveying signed language descriptions of thirty-one languages. Languages are coded for various attributes of pointing such as anaphoric and deictic use, distance marking, eye gaze patterns, and other attributes commonly associated with pointing. The study finds that all but three signed languages in the sample utilize pointing in sign space for anaphoric reference. Methodological issues with constructing a sample as well as a lack of avail

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Ren, C. Y., V. A. Prisacariu, O. Kähler, I. D. Reid, and D. W. Murray. "Real-Time Tracking of Single and Multiple Objects from Depth-Colour Imagery Using 3D Signed Distance Functions." International Journal of Computer Vision 124, no. 1 (2017): 80–95. http://dx.doi.org/10.1007/s11263-016-0978-2.

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Gillespie, Mark, Denise Yang, Mario Botsch, and Keenan Crane. "Ray Tracing Harmonic Functions." ACM Transactions on Graphics 43, no. 4 (2024): 1–18. http://dx.doi.org/10.1145/3658201.

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Sphere tracing is a fast and high-quality method for visualizing surfaces encoded by signed distance functions (SDFs). We introduce a similar method for a completely different class of surfaces encoded by harmonic functions , opening up rich new possibilities for visual computing. Our starting point is similar in spirit to sphere tracing: using conservative Harnack bounds on the growth of harmonic functions, we develop a Harnack tracing algorithm for visualizing level sets of harmonic functions, including those that are angle-valued and exhibit singularities. The method takes much larger steps

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30

Minguzzi, Ettore. "On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures." Reviews in Mathematical Physics 32, no. 10 (2020): 2050033. http://dx.doi.org/10.1142/s0129055x20500336.

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We complement our work on the causality of upper semi-continuous distributions of cones with some results on Cauchy hypersurfaces. We prove that every locally stably acausal Cauchy hypersurface is stable. Then we prove that the signed distance [Formula: see text] from a spacelike hypersurface [Formula: see text] is, in a neighborhood of it, as regular as the hypersurface, and by using this fact we give a proof that every Cauchy hypersurface is the level set of a Cauchy temporal (and steep) function of the same regularity as the hypersurface. We also show that in a globally hyperbolic closed co

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Zhang, Yi, Xiwen Pan, Congsheng Li, and Tongning Wu. "3D Liver and Tumor Segmentation with CNNs Based on Region and Distance Metrics." Applied Sciences 10, no. 11 (2020): 3794. http://dx.doi.org/10.3390/app10113794.

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Liver and liver tumor segmentation based on abdomen computed tomography (CT) images is an essential step in computer-assisted clinical interventions. However, liver and tumor segmentation remains the difficult issue in the medical image processing field, which is ascribed to the anatomical complexity of the liver and the poor demarcation between the liver and other nearby organs on the image. The existing 3D automatic liver and tumor segmentation algorithms based on full convolutional networks, such as V-net, have utilized the loss functions on the basis of integration (summing) over a segment

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Pandey, Atharva, Vishal Yadav, Rajendra Nagar, and Santanu Chaudhury. "LISR: Learning Linear 3D Implicit Surface Representation Using Compactly Supported Radial Basis Functions." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 5 (2024): 4415–23. http://dx.doi.org/10.1609/aaai.v38i5.28239.

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Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed, differing in memory efficiency and shape retrieval effectiveness, such as volumetric, parametric, and implicit surfaces. Radial basis functions provide memory-efficient parameterization of the implicit surface. However, we show that training a neural network using the mean squared error between the ground-truth implicit surface and the linear basis-based implic

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Guo, Hao-Xiang, Yang Liu, Hao Pan, and Baining Guo. "Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation." ACM Transactions on Graphics 41, no. 6 (2022): 1–15. http://dx.doi.org/10.1145/3550454.3555502.

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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 alg

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Neroev, V. V., M. D. Sengaeva, E. P. Tarutta, et al. "Subjective assessment of vision quality by patients over 35 after excimer laser and orthokeratological correction of myopia according to a survey." Russian Ophthalmological Journal 15, no. 2 (2022): 56–59. http://dx.doi.org/10.21516/2072-0076-2022-15-2-56-59.

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Purpose: to analyze the results of a survey aimed at assessing the patients’satisfaction with the results of excimer laser or orthokeratological correction of myopia. Materials and methods. 135 patients aged 35 to 50 took part in a satisfaction survey: 105 after excimer laser and 30 after orthokeratological correction of myopia. Excimer laser surgery was performed with planned binocular hypocorrection within -0.75 — 1.5 D depending on age. To participate in the survey, the patients signed a preliminary consent. The questionnaire asked for age, gender, occupation, self-assessment of visual func

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Wang, Angtian, Yuanlu Xu, Nikolaos Sarafianos, et al. "HISR: Hybrid Implicit Surface Representation for Photorealistic 3D Human Reconstruction." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 6 (2024): 5298–308. http://dx.doi.org/10.1609/aaai.v38i6.28337.

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Neural reconstruction and rendering strategies have demonstrated state-of-the-art performances due, in part, to their ability to preserve high level shape details. Existing approaches, however, either represent objects as implicit surface functions or neural volumes and still struggle to recover shapes with heterogeneous materials, in particular human skin, hair or clothes. To this aim, we present a new hybrid implicit surface representation to model human shapes. This representation is composed of two surface layers that represent opaque and translucent regions on the clothed human body. We s

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Elsey, Matt, Selim Esedoḡlu, and Peter Smereka. "Large-scale simulation of normal grain growth via diffusion-generated motion." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2126 (2010): 381–401. http://dx.doi.org/10.1098/rspa.2010.0194.

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Diffusion-generated motion is used to perform a very large-scale simulation of normal grain growth in three dimensions with high accuracy. The method is based on the diffusion of signed distance functions and shares similarities with level-set methods. The Herring-angle condition at junctions and topological transitions are naturally captured with this formulation. This approach offers significant advantages over existing numerical methods and allows for accurate computations on scales not previously possible. A fully resolved simulation of normal grain growth, initially containing over 130 00

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Zhu, Xiaoqiang, Yanhua Zhao, and Lihua You. "Neuronal Mesh Reconstruction from Image Stacks Using Implicit Neural Representations." Mathematics 13, no. 8 (2025): 1276. https://doi.org/10.3390/math13081276.

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Reconstructing neuronal morphology from microscopy image stacks is essential for understanding brain function and behavior. While existing methods are capable of tracking neuronal tree structures and creating membrane surface meshes, they often lack seamless processing pipelines and suffer from stitching artifacts and reconstruction inconsistencies. In this study, we propose a new approach utilizing implicit neural representation to directly extract neuronal isosurfaces from raw image stacks by modeling signed distance functions (SDFs) with multi-layer perceptrons (MLPs). Our method accurately

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38

Hillebrand, B., C. Thieulot, T. Geenen, A. P. van den Berg, and W. Spakman. "Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface." Solid Earth Discussions 6, no. 2 (2014): 1523–54. http://dx.doi.org/10.5194/sed-6-1523-2014.

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Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface and on which side it is located. In this paper we present four benchmar

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Hillebrand, B., C. Thieulot, T. Geenen, A. P. van den Berg, and W. Spakman. "Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface." Solid Earth 5, no. 2 (2014): 1087–98. http://dx.doi.org/10.5194/se-5-1087-2014.

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Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four b

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40

Kumar, Pavan. "Optimal policies for inventory model with shortages, time-varying holding and ordering costs in trapezoidal fuzzy environment." Independent Journal of Management & Production 12, no. 2 (2021): 557–74. http://dx.doi.org/10.14807/ijmp.v12i2.1212.

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This paper proposes the optimal policies for a fuzzy inventory model considering the holding cost and ordering cost as continuous functions of time. Shortages are allowed and partially backlogged. The demand rate is assumed in such to be linearly dependent on time during on-hand inventory, while during the shortage period, it remains constant. The inventory problem is formulated in crisp environment. Considering the demand rate, holding cost and ordering cost as trapezoidal fuzzy numbers, the proposed problem is transformed into fuzzy model. For this fuzzy model, the signed distance method of

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Chen, Anpei, Zexiang Xu, Xinyue Wei, Siyu Tang, Hao Su, and Andreas Geiger. "Dictionary Fields: Learning a Neural Basis Decomposition." ACM Transactions on Graphics 42, no. 4 (2023): 1–12. http://dx.doi.org/10.1145/3592135.

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We present Dictionary Fields, a novel neural representation which decomposes a signal into a product of factors, each represented by a classical or neural field representation, operating on transformed input coordinates. More specifically, we factorize a signal into a coefficient field and a basis field, and exploit periodic coordinate transformations to apply the same basis functions across multiple locations and scales. Our experiments show that Dictionary Fields lead to improvements in approximation quality, compactness, and training time when compared to previous fast reconstruction method

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Guo, Yuhao, Yan Wang, Qiqi Hao, and Tongguang Wang. "An Interface-Corrected Diffuse Interface Model for Incompressible Multiphase Flows with Large Density Ratios." Applied Sciences 12, no. 18 (2022): 9337. http://dx.doi.org/10.3390/app12189337.

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An interface-corrected diffuse interface method is presented in this work for the simulation of incompressible multiphase flows with large density ratios. In this method, an interface correction term together with a mass correction term is introduced into the diffuse-interface Cahn–Hilliard model to maintain both mass conservation and interface shapes between binary fluids simultaneously. The interface correction term is obtained by connecting the signed distance functions in the Hamilton–Jacobian equation with the order parameter of the Cahn–Hilliard model. In addition, an improved multiphase

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Cai, Yuxiang, Jiaxiong Qiu, Zhong Li, and Bo Ren. "NeuralTO: Neural Reconstruction and View Synthesis of Translucent Objects." ACM Transactions on Graphics 43, no. 4 (2024): 1–14. http://dx.doi.org/10.1145/3658186.

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Learning from multi-view images using neural implicit signed distance functions shows impressive performance on 3D Reconstruction of opaque objects. However, existing methods struggle to reconstruct accurate geometry when applied to translucent objects due to the non-negligible bias in their rendering function. To address the inaccuracies in the existing model, we have reparameterized the density function of the neural radiance field by incorporating an estimated constant extinction coefficient. This modification forms the basis of our innovative framework, which is geared towards highfidelity

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Liu, Fei, Li-qiang Zhao, Ping-li Liu, Zhi-feng Luo, Nian-yin Li, and Pei-shan Wang. "An Extended Finite Element Model for Fluid Flow in Fractured Porous Media." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/604212.

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This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method. The governing equations account for the fluid flow in the porous medium and the discrete natural fractures, as well as the fluid exchange between the fracture and the porous medium surrounding the fracture. The pore fluid pressure is continuous, while its derivatives are discontinuous on both sides of these high conductivity fractures. The pressure field is enriched by the absolute signed distance and appropriate asymptotic functions to capture the discontinuities in deri

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Sharp, Nicholas, and Alec Jacobson. "Spelunking the deep." ACM Transactions on Graphics 41, no. 4 (2022): 1–16. http://dx.doi.org/10.1145/3528223.3530155.

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Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these representations are easy to fit, it is not clear how to best evaluate geometric queries on the shape, such as intersecting against a ray or finding a closest point. The predominant approach is to encourage the network to have a signed distance property. However, this property typically holds only approximately, leading to robustness issues, and holds only at the

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Chen, Zhiqin, Andrea Tagliasacchi, Thomas Funkhouser, and Hao Zhang. "Neural dual contouring." ACM Transactions on Graphics 41, no. 4 (2022): 1–13. http://dx.doi.org/10.1145/3528223.3530108.

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We introduce neural dual contouring (NDC), a new data-driven approach to mesh reconstruction based on dual contouring (DC). Like traditional DC, it produces exactly one vertex per grid cell and one quad for each grid edge intersection, a natural and efficient structure for reproducing sharp features. However, rather than computing vertex locations and edge crossings with hand-crafted functions that depend directly on difficult-to-obtain surface gradients, NDC uses a neural network to predict them. As a result, NDC can be trained to produce meshes from signed or unsigned distance fields, binary

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Vizzo, Ignacio, Tiziano Guadagnino, Jens Behley, and Cyrill Stachniss. "VDBFusion: Flexible and Efficient TSDF Integration of Range Sensor Data." Sensors 22, no. 3 (2022): 1296. http://dx.doi.org/10.3390/s22031296.

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Mapping is a crucial task in robotics and a fundamental building block of most mobile systems deployed in the real world. Robots use different environment representations depending on their task and sensor setup. This paper showcases a practical approach to volumetric surface reconstruction based on truncated signed distance functions, also called TSDFs. We revisit the basics of this mapping technique and offer an approach for building effective and efficient real-world mapping systems. In contrast to most state-of-the-art SLAM and mapping approaches, we are making no assumptions on the size o

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Cui, Mingtao, Wennan Cui, Wang Li, and Xiaobo Wang. "A polygonal topology optimization method based on the alternating active-phase algorithm." Electronic Research Archive 32, no. 2 (2024): 1191–226. http://dx.doi.org/10.3934/era.2024057.

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<abstract> <p>We propose a polygonal topology optimization method combined with the alternating active-phase algorithm to address the multi-material problems. During the process of topology optimization, the polygonal elements generated by signed distance functions are utilized to discretize the structural design domain. The volume fraction of each material is considered as a design variable and mapped to its corresponding element variable through a filtering matrix. This method is used to solve a multi-material structural topology optimization problem of minimizing compliance, in

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Modi, Vismay, Nicholas Sharp, Or Perel, Shinjiro Sueda, and David I. W. Levin. "Simplicits: Mesh-Free, Geometry-Agnostic Elastic Simulation." ACM Transactions on Graphics 43, no. 4 (2024): 1–11. http://dx.doi.org/10.1145/3658184.

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The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act

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Hackstein, Vincent, Paul Fauth-Mayer, Mathias Rothermel, and Norbert Haala. "Depth Supervised Neural Surface Reconstruction from Airborne Imagery." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences X-2-2024 (June 10, 2024): 89–96. http://dx.doi.org/10.5194/isprs-annals-x-2-2024-89-2024.

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Abstract. While originally developed for novel view synthesis, Neural Radiance Fields (NeRFs) have recently emerged as an alternative to multi-view stereo (MVS). Triggered by a manifold of research activities, promising results have been gained especially for textureless, transparent, and reflecting surfaces, while such scenarios remain challenging for traditional MVS-based approaches. However, most of these investigations focus on close-range scenarios, with studies for airborne scenarios still missing. For this task, NeRFs face potential difficulties at areas of low image redundancy and weak

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