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Zeitschriftenartikel zum Thema „Signed Distance Functions“

Autor: Grafiati

Veröffentlicht am 29. Juni 2021

Zuletzt aktualisiert am 7. Februar 2022

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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 functions.

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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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3

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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4

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 defining function for the shape, helps to avoid undesirable singularities in the material distribution, like stress or concentrations. We illustrate application of the SARDF operations by two- and three-dimensional heterogeneous object modeling case studies.

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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

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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7

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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8

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 usually applied to express a geometrical object. Thus, a signed distance function based on R-functions is created to represent whether two objects intervene and their level of intervention or separation. As the signed function is continuous and differentiable, the gradient information of the objective function guides a moving part to avoid its obstacles and to approach its target position rapidly. Therefore, a path planning approach with obstacle avoidance based on normalized R-functions is proposed in this paper. A discrete convex hull approach is adopted to solve the problem that R-function is inappropriate to represent a geometric object with some curves or surfaces, and pendent points and edges are generated in Boolean operations. Besides, a normalized approach ensures accuracy calculation of signed distance function. Experimental results have shown that the presented approach is a feasible way for path planning with obstacle avoidance.

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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 Hausdorff distance between two such sets. We recall fundamental properties of the Hausdorff distance, including a characterisation in terms of distance functions. In numerical applications, this result gives at least an exact lower bound on the Hausdorff distance. We also derive an upper bound, and consequently a precise error estimate. By giving an example, we show that our error estimate cannot be further improved for a general situation. On the other hand, we also show that much better accuracy can be expected for non-pathological situations that are more likely to occur in practice. The resulting error estimate can be improved even further if one assumes that the grid is rotated randomly with respect to the involved sets.

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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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11

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 n and h are the numbers of sites and non-empty Voronoi regions, respectively. The all nearest neighbors problem for skew distances, which has certain features different from its Euclidean counterpart, is solved in O(n log n) time.

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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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13

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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14

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 simulations show the performance from both control laws.

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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. This paper explores: operators and functionals which provide natural links between the metric structure of (X,d), the semi-inner product space structure of ℳ0(X) and the Banach space C(X) of continuous real-valued functions on X; conditions equivalent to the quasihypermetric property; the topological properties of ℳ0(X) with the topology induced by the semi-inner product, and especially the relation of this topology to the weak-* topology and the measure-norm topology on ℳ0(X); and the functional-analytic properties of ℳ0(X) as a semi-inner product space, including the question of its completeness. A later paper [P. Nickolas and R. Wolf, Distance geometry in quasihypermetric spaces. II, Math. Nachr., accepted] will apply the work of this paper to a detailed analysis of the constant M(X).

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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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17

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 cone structure, compact spacelike hypersurfaces with boundary can be extended to Cauchy spacelike hypersurfaces of the same regularity. We end the work with a separation result and a density result.

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18

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 segmented region (like Dice or cross-entropy). Unfortunately, the number of foreground and background voxels is usually highly imbalanced in liver and tumor segmentation tasks. This greatly varies the value of regional loss between various segmentation classes, and affects the training stability and effect. In the present study, an improved V-net algorithm was applied for 3D liver and tumor segmentation based on region and distance metrics. The distance metric-based loss function utilized a distance metric of the contour (or shape) space rather than the area. The model was jointly trained by the original regional loss and the three distance-based loss functions (including Boundary (BD) loss, Hausdorff (HD) loss, and Signed Distance Map (SDM) loss) to solve the problem of the highly unbalanced liver and tumor segmentation. Besides, the algorithm was tested in two databases LiTS 2017 (Technical University of Munich, Munich, Germany, 2017) and 3D-IRCADb (Research Institute against Digestive Cancer, Strasbourg Cedex, France, 2009), and the results proved the effectiveness of improvement.

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19

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 130 000 grains in three dimensions, is presented and analysed. It is shown that the average grain radius grows as the square root of time and the grain-size distribution is self-similar. Good agreement with other theoretical predictions, experimental results and simulation results via other techniques is also demonstrated.

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20

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 benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as a Rayleigh–Taylor instability, post glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

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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 benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh–Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

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22

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 defuzzification is applied to determine the average total cost (ATC) in fuzzy environment. The objective is to optimize the ATC and the order quantity. One solved example is provided in order to show the applicability of the proposed model. The convexity of the cost function is verified with the help of 3D-graph.

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23

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 derivatives. The most important advantage of this method is that the domain can be partitioned as nonmatching grid without considering the presence of fractures. Arbitrarily multiple, kinking, branching, and intersecting fractures can be treated with the new approach. In particular, for propagating fractures, such as hydraulic fracturing or network volume fracturing in fissured reservoirs, this method can process the complex fluid leak-off behavior without remeshing. Numerical examples are presented to demonstrate the capability of the proposed method in saturated fractured porous media.

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Jaafari, Abolfazl, Davood Mafi-Gholami, Binh Thai Pham, and Dieu Tien Bui. "Wildfire Probability Mapping: Bivariate vs. Multivariate Statistics." Remote Sensing 11, no. 6 (2019): 618. http://dx.doi.org/10.3390/rs11060618.

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Wildfires are one of the most common natural hazards worldwide. Here, we compared the capability of bivariate and multivariate models for the prediction of spatially explicit wildfire probability across a fire-prone landscape in the Zagros ecoregion, Iran. Dempster–Shafer-based evidential belief function (EBF) and the multivariate logistic regression (LR) were applied to a spatial dataset that represents 132 fire events from the period of 2007–2014 and twelve explanatory variables (altitude, aspect, slope degree, topographic wetness index (TWI), annual temperature, and rainfall, wind effect, land use, normalized difference vegetation index (NDVI), and distance to roads, rivers, and residential areas). While the EBF model successfully characterized each variable class by four probability mass functions in terms of wildfire probabilities, the LR model identified the variables that have a major impact on the probability of fire occurrence. Two distribution maps of wildfire probability were developed based upon the results of each model. In an ensemble modeling perspective, we combined the two probability maps. The results were verified and compared by the receiver operating characteristic (ROC) and the Wilcoxon Signed-Rank Test. The results showed that although an improved predictive accuracy (AUC = 0.864) can be achieved via an ensemble modeling of bivariate and multivariate statistics, the models fail to individually provide a satisfactory prediction of wildfire probability (EBFAUC = 0.701; LRAUC = 0.728). From these results, we recommend the employment of ensemble modeling approaches for different wildfire-prone landscapes.

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Krawczyk, Maciej, Małgorzata Syczewska, and Ewa Szczerbik. "Gait kinematics and clinical test changes in post-stroke patients during rehabilitation. Preliminary results of 12 patients of randomized clinical trial." Advances in Rehabilitation 26, no. 1 (2012): 13–18. http://dx.doi.org/10.2478/rehab-2013-0025.

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Abstract More precise knowledge concerning gait patterns of movement in stroke patients incorporating modern diagnostic tools is necessary. Exact information about qualitative and quantitative changes during the process of rehabilitation based on reeducation of functions and relating it to possible changes of motor deficit will possibly lead to better physiotherapy planning. Goal of this study is to assess some components and changes of gait pattern and motor deficit after stroke to develop better physiotherapy this group of patients Materials and methods Consecutively admitting to rehabilitation unit first stroke patients who met inclusion criteria ( time from the onset of stroke between 1st and 3th month, independent walking skills on the distance of 10m, motor deficit, self awareness of disease, signed inform consent form) were enrolled to the study. Patients were participating in physiotherapy five days a week for 12 weeks. Rivermead Motor Assessment (Lower Extremity Section), Fugl-Meyer Motor Deficit Scale, Nottingham Extended Activities of Daily Living Scale and three-dimension motion analysis system Vicon 460 (amplitude of hip joint range of motion, walking speed, cadence, steps length) were used. All measurement procedures were carried out three times: before therapy, after 6 weeks and after 12 weeks of treatment. Results: Twelve patients were enrolled to the study (4 female, 8 man, mean age 58 years old, 5 persons suffering from right side paresis). All patients improved after 6 and 12 weeks. Alterations were related both to clinical assessment and to objective movement analysis and they were positively correlated. Mean motor deficit (FM) stated 140,148, 161p, ADL -30, 42, 47p., walking speed: 0,4m/s, 0,5m/s, 0,6m/s, cadence (steps/min):70, 81, 89. Conclusions: Results indicate relatively constant progress of motor abilities in this group of patients however it decreased during second period. Clinical improvements were accompanied by similar progress of walking speed and cadence. Further studies are necessary

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Luo, Chen, LiMin Zhu, and Han Ding. "A novel curvature-based method for analyzing the second-order immobility of frictionless grasp." Robotica 30, no. 4 (2011): 613–25. http://dx.doi.org/10.1017/s0263574711000853.

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SUMMARYThis paper presents a new method to analyze frictionless grasp immobility based on defined surface-to-surface signed distance function. Distance function's differential properties are analyzed and its second-order Taylor expansion with respect to differential motion is deduced. Based on the non-negative condition of the signed distance function, the first- and second-order free motions are defined and the corresponding conditions for immobility of frictionless grasp are derived. As one benefit of the proposed method, the second-order immobility check can be formulated as a nonlinear programming problem. Numerical examples are used to verify the proposed method.

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Paragios, Nikos, Mikael Rousson, and Visvanathan Ramesh. "Non-rigid registration using distance functions." Computer Vision and Image Understanding 89, no. 2-3 (2003): 142–65. http://dx.doi.org/10.1016/s1077-3142(03)00010-9.

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28

Di Gesù, Vito, and Valery Starovoitov. "Distance-based functions for image comparison." Pattern Recognition Letters 20, no. 2 (1999): 207–14. http://dx.doi.org/10.1016/s0167-8655(98)00115-9.

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29

Atallah, Mikhail J., Celso C. Ribeiro, and Sergio Lifschitz. "Computing some distance functions between polygons." Pattern Recognition 24, no. 8 (1991): 775–81. http://dx.doi.org/10.1016/0031-3203(91)90045-7.

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30

Gomes, José, and Olivier Faugeras. "Reconciling Distance Functions and Level Sets." Journal of Visual Communication and Image Representation 11, no. 2 (2000): 209–23. http://dx.doi.org/10.1006/jvci.1999.0439.

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31

McCane, Brendan, and Michael Albert. "Distance functions for categorical and mixed variables." Pattern Recognition Letters 29, no. 7 (2008): 986–93. http://dx.doi.org/10.1016/j.patrec.2008.01.021.

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Pavlov, A. V., and N. A. Kolomeec. "PROPERTIES OF BENT FUNCTIONS WITH MINIMAL DISTANCE." Prikladnaya diskretnaya matematika, no. 6 (December 1, 2009): 5–20. http://dx.doi.org/10.17223/20710410/6/1.

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Ong, Eng-Jon, and Richard Bowden. "Learning multi-kernel distance functions using relative comparisons." Pattern Recognition 38, no. 12 (2005): 2653–57. http://dx.doi.org/10.1016/j.patcog.2005.05.011.

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34

Cheng, Cuiping, and Fuyuan Xiao. "A distance for belief functions of orderable set." Pattern Recognition Letters 145 (May 2021): 165–70. http://dx.doi.org/10.1016/j.patrec.2021.02.010.

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35

Georgiou, T. T. "Distances and Riemannian Metrics for Spectral Density Functions." IEEE Transactions on Signal Processing 55, no. 8 (2007): 3995–4003. http://dx.doi.org/10.1109/tsp.2007.896119.

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Ikonomakis, Emmanouil K., George M. Spyrou, and Michael N. Vrahatis. "Content driven clustering algorithm combining density and distance functions." Pattern Recognition 87 (March 2019): 190–202. http://dx.doi.org/10.1016/j.patcog.2018.10.007.

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Flemming, Jens, Bernd Hofmann, and Peter Mathé. "Sharp converse results for the regularization error using distance functions." Inverse Problems 27, no. 2 (2011): 025006. http://dx.doi.org/10.1088/0266-5611/27/2/025006.

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38

Frey, Hannes. "Lower and Upper Bounds for Multicasting under Distance Dependent Forwarding Cost Functions." IEEE Transactions on Parallel and Distributed Systems 24, no. 5 (2013): 963–76. http://dx.doi.org/10.1109/tpds.2012.145.

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39

Mayer, Johannes. "A TIME-OPTIMAL ALGORITHM FOR THE ESTIMATION OF CONTACT DISTRIBUTION FUNCTIONS OF RANDOM SETS." Image Analysis & Stereology 23, no. 3 (2011): 177. http://dx.doi.org/10.5566/ias.v23.p177-183.

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This paper presents a linear-time and therefore time-optimal algorithm for the estimation of distance distribution functions and contact distribution functions of random sets. The distance distribution function is the area fraction of a dilated set, where this function depends on the size of the structuring element used for the dilation. Furthermore, contact distribution functions are related to distance distribution functions. Minussampling estimators are used for the estimation.

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Burlando, Laura. "Computing the Distance to the Functions with Range in a Given Set in Lebesgue Spaces of Vector-Valued Functions." Numerical Functional Analysis and Optimization 26, no. 6 (2005): 641–58. http://dx.doi.org/10.1080/nfa-01630560500248298.

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41

Biasotti, Silvia, Andrea Cerri, Patrizio Frosini, and Daniela Giorgi. "A new algorithm for computing the 2-dimensional matching distance between size functions." Pattern Recognition Letters 32, no. 14 (2011): 1735–46. http://dx.doi.org/10.1016/j.patrec.2011.07.014.

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42

Nienkötter, Andreas, and Xiaoyi Jiang. "A lower bound for generalized median based consensus learning using kernel-induced distance functions." Pattern Recognition Letters 140 (December 2020): 339–47. http://dx.doi.org/10.1016/j.patrec.2020.11.003.

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43

Ahmed, Mahmoud, and Deok Ryong Kim. "target: an R package to predict combined function of transcription factors." F1000Research 10 (May 5, 2021): 344. http://dx.doi.org/10.12688/f1000research.52173.1.

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Researchers use ChIP binding data to identify potential transcription factor binding sites. Similarly, they use gene expression data from sequencing or microarrays to quantify the effect of the factor overexpression or knockdown on its targets. Therefore, the integration of the binding and expression data can be used to improve the understanding of a transcription factor function. Here, we implemented the binding and expression target analysis (BETA) in an R/Bioconductor package. This algorithm ranks the targets based on the distances of their assigned peaks from the factor ChIP experiment and the signed statistics from gene expression profiling with factor perturbation. We further extend BETA to integrate two sets of data from two factors to predict their targets and their combined functions. In this article, we briefly describe the workings of the algorithm and provide a workflow with a real dataset for using it. The gene targets and the aggregate functions of transcription factors YY1 and YY2 in HeLa cells were identified. Using the same datasets, we identified the shared targets of the two factors, which were found to be, on average, more cooperatively regulated.

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Stoyan, Dietrich, Helga Stoyan, André Tscheschel, and Torsten Mattfeldt. "ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS." Image Analysis & Stereology 20, no. 1 (2011): 65. http://dx.doi.org/10.5566/ias.v20.p65-69.

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This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.

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Battaglini, Luca, Carolina Maria Oletto, Giulio Contemori, Michele Barollo, Ambra Ciavarelli, and Clara Casco. "Perceptual learning improves visual functions in patients with albinistic bilateral amblyopia: A pilot study." Restorative Neurology and Neuroscience 39, no. 1 (2021): 45–59. http://dx.doi.org/10.3233/rnn-201043.

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Background: Several visual functions are impaired in patients with oculocutaneous albinism (OCA) associated to albinistic bilateral amblyopia (ABA). Objective: In this study, we aimed at exploring whether perceptual learning (PL) can improve visual functions in albinism. Method: Six patients and six normal sighted controls, were trained in a contrast detection task with lateral masking. Participants were asked to choose which of the two intervals contained a foveally presented low-contrast Gabor patch. Targets were presented between higher contrast collinear flankers with equal spatial frequency. When increasing target-to-flanker distance, lateral interactions effect normally switches from inhibition to facilitation, up to no effect. Results: Our findings showed that before PL, only controls showed facilitation. After PL, results suggest that facilitatory lateral interactions are found both in controls as well as in albino patients. These results suggest that PL could induce higher processing efficiency at early cortical level. Moreover, PL positive effect seems to transfer to higher-level visual functions, but results were not very consistent among tasks (visual acuity, contrast sensitivity function, hyperacuity and foveal crowding). Conclusions: Although a small sample size was tested, our findings suggest a rehabilitative potential of PL in improving visual functions in albinism.

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Shayesteh, Farid, and Reihaneh Kardehi Moghaddam. "Improving firefly-based multi-objective optimization based on attraction law and crowding distance." Statistics, Optimization & Information Computing 8, no. 1 (2020): 229–41. http://dx.doi.org/10.19139/soic-2310-5070-382.

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Multi-objective optimization problems are so designed that they simultaneously minimize several objectives functions (which are sometimes contradictory). In most cases, the objectives are in conflict with each other such that optimization of one objective does not lead to the optimization of another ones. Therefore, we should achieve a certain balance of goals to solve these problems, which usually requires the application of an intelligent method. In this regard, use of meta-heuristic algorithms will be associated with resolved problems. In this paper, we propose a new multi-objective firefly optimization method which is designed based on the law of attraction and crowding distance. The proposed methods efficiency has been evaluated by three valid test functions containing convex, nonconvex and multi discontinuous convex Pareto fronts. Simulation results confirm the significant accuracy of proposed method in defining the Pareto front for all three test functions. In addition, the simulation results indicates that proposed algorithm has higher accuracy and greater convergence speed, compared to other well known multi-objective algorithms such as non-dominated sorting genetic algorithm, Bees algorithm, Differential Evolution algorithm and Strong Pareto Evolutionary Algorithm.

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Dunai, Larisa, Ismael Lengua, Guillermo Peris-Fajarnés, and Fernando Brusola. "Virtual Sound Localization by Blind People." Archives of Acoustics 40, no. 4 (2015): 561–67. http://dx.doi.org/10.1515/aoa-2015-0055.

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AbstractThe paper demonstrates that blind people localize sounds more accurately than sighted people by using monaural and/or binaural cues.In the experiment, blind people participated in two tests; the first one took place in the laboratory and the second one in the real environment under different noise conditions. A simple click sound was employed and processed with non-individual head related transfer functions. The sounds were delivered by a system with a maximum azimuth of 32° to the left side and 32° to the right side of the participant’s head at a distance ranging from 0.3 m up to 5 m.The present paper describes the experimental methods and results of virtual sound localization by blind people through the use of a simple electronic travel aid based on an infrared laser pulse and the time of flight distance measurement principle. The lack of vision is often compensated by other perceptual abilities, such as the tactile or hearing ability.The results show that blind people easily perceive and localize binaural sounds and assimilate them with sounds from the environment.

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Mayhew, Terry M. "CROSS-CORRELATION ANALYSIS OF THE SPATIAL INTERACTIONS BETWEEN TISSUE COMPARTMENTS OF THE RENAL CORPUSCLE." Image Analysis & Stereology 21, no. 3 (2011): 151. http://dx.doi.org/10.5566/ias.v21.p151-155.

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The renal corpuscle is a multi-compartment unit of kidney morphology which is important for normal ultrafiltration of blood. Its structure is perturbed during ontogeny, disease and experimental manipulation. Transmission electron microscopy and second-order stereological tools (cross covariance and cross correlation functions) were used to examine 3-D spatial interactions between the main tissue compartments (glomerular capillaries, podocytes, mesangium, urinary space) of the renal corpuscle in normal adult rats. Volume densities, covariance and correlation functions were estimated by counting test points (randomly positioned) and linear dipole probes (randomly positioned and orientated) superimposed on random samples of photomontages prepared from ultrathin resin sections. Differences in clustering exist between compartments (at distances < 8 Î¼m, mesangium is the most tightly-clustered and capillaries the least tightly-clustered compartment; > 8 Î¼m, compartments are neither hypodisperse nor hyperdisperse). Despite this, cross correlation functions for linked sets of compartments (capillary-mesangium, capillary-podocytes, capillary-urinary space, mesangium-podocytes, mesangium-urinary space and podocytes-urinary space) did not vary with dipole distance. This indicates that the spatial relations between linked compartments do not favour attraction or repulsion. In addition, inter-individual variation is greater for some linked compartments than others. Variation is less for compartments (capillary-podocyte and capillary-urinary space) which contribute to the ultrafiltration barrier and this probably reflects the structural and functional integration evident at this site as well as the higher volume densities (and smaller inter-subject variation) for capillaries.

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Kolomeec, N. A. "An upper bound for the number of bent functions at the distance 2 k from an arbitrary bent function in 2k variables." Prikladnaya diskretnaya matematika, no. 25 (September 1, 2014): 28–39. http://dx.doi.org/10.17223/20710410/25/3.

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50

Zhang, Hui, Yongfei Zhu, Xuefei Liu, and Xiangrong Xu. "Analysis of Obstacle Avoidance Strategy for Dual-Arm Robot Based on Speed Field with Improved Artificial Potential Field Algorithm." Electronics 10, no. 15 (2021): 1850. http://dx.doi.org/10.3390/electronics10151850.

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In recent years, dual-arm robots have been favored in various industries due to their excellent coordinated operability. One of the focused areas of study on dual-arm robots is obstacle avoidance, namely path planning. Among the existing path planning methods, the artificial potential field (APF) algorithm is widely applied in obstacle avoidance for its simplicity, practicability, and good real-time performance over other planning methods. However, APF is firstly proposed to solve the obstacle avoidance problem of mobile robot in plane, and thus has some limitations such as being prone to fall into local minimum, not being applicable when dynamic obstacles are encountered. Therefore, an obstacle avoidance strategy for a dual-arm robot based on speed field with improved artificial potential field algorithm is proposed. In our method, the APF algorithm is used to establish the attraction and repulsion functions of the robotic manipulator, and then the concepts of attraction and repulsion speed are introduced. The attraction and repulsion functions are converted into the attraction and repulsion speed functions, which mapped to the joint space. By using the Jacobian matrix and its inverse to establish the differential velocity function of joint motion, as well as comparing it with the set collision distance threshold between two robotic manipulators of robot, the collision avoidance can be solved. Meanwhile, after introducing a new repulsion function and adding virtual constraint points to eliminate existing limitations, APF is also improved. The correctness and effectiveness of the proposed method in the self-collision avoidance problem of a dual-arm robot are validated in MATLAB and Adams simulation environment.

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