Efficient Hausdorff Distance computation for freeform geometric models in close proximity

Kim, Yong-Joon; Oh, Young‐Taek; Yoon, Seung‐Hyun; Kim, Myung-Soo; Elber, Gershon

doi:10.1016/j.cad.2012.10.010

Cited by 21 publications

(10 citation statements)

References 14 publications

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“…choice of the distance [25]. The distance chosen has to fulfil certain conditions, such as being robust against noise and outliers to ensure its trustworthiness, particularly when the objects are close to each other [26]. Furthermore, it should correspond to the problem under consideration, that is, shape recognition or image comparisons may require another definition than object matching applications [27].…”

Section: Introductionmentioning

confidence: 99%

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Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

2020

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The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.

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Section: Introductionmentioning

confidence: 99%

“…Unfortunately, the traditional HD only provides a global measure of the distance and is known to be sensitive to outliers. Alternatives were proposed, including the Hausdorff quantile [32], for close objects [26], for the specific case of B-spline curves [33], spatially coherent matching [34] or the averaged Hausdorff distance (AHD; [27]).…”

Section: Introductionmentioning

confidence: 99%

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

2020

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“…Based on the methods in [34,35], they have extended to compute the Hausdorff distance between two B-spline curves. Based on matching a surface patch from one model to the other model which is the corresponding nearby surface patch, an algorithm for solving the Hausdorff distance between two freeform surfaces is presented in Kim et al [36], where a hierarchy of Coons patches and bilinear surfaces that approximate the NURBS surfaces with bounding volume is adopted. Of course, the common feature of geometric methods is that the ultimate solution accuracy is not very high.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space

Liang

Hou

et al. 2018

Mathematics

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Orthogonal projection a point onto a parametric curve, three classic first order algorithms have been presented by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, H-H-H method). In this research, we give a proof of the approach’s first order convergence and its non-dependence on the initial value. For some special cases of divergence for the H-H-H method, we combine it with Newton’s second order method (hereafter, Newton’s method) to create the hybrid second order method for orthogonal projection onto parametric curve in an n-dimensional Euclidean space (hereafter, our method). Our method essentially utilizes hybrid iteration, so it converges faster than current methods with a second order convergence and remains independent from the initial value. We provide some numerical examples to confirm robustness and high efficiency of the method.

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“…For the design of efficient geometric algorithms for freeform NURBS surfaces, the Coons BVH construction (based on Coons patch approximation [6]) is highly effective, often demonstrating interactive-speed performance in computing minimum and Hausdorff distances and convex hulls [12,14,15]. Coons patches approximate NURBS surfaces considerably more tightly and thus have a higher approximation order than other regular shapes such as spheres and boxes.…”

Section: Introductionmentioning

confidence: 99%

Comparison of three bounding regions with cubic convergence to planar freeform curves

Lee

Kim

et al. 2015

Vis Comput

Self Cite

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We compare the relative performance of bounding regions generated by three different curve-bounding methods with cubic convergence to planar freeform curves: spiral fat arcs (SFA) (Barton and Elber in Graph Models 73(2):50-57, 2011), bilens (Kumosenko in Comput Aided Geom Des 30(3):310-330, 2013), and bounding circular arcs (BCA) (Meek and Walton in J Comput Appl Math 59 (2): [221][222][223][224][225][226][227][228][229][230][231] 1995). For quantitative comparison, we consider three different criteria: geometric complexity (the number of circular arcs and line segments), construction time, and numerical stability. The BCA construction after one-step refinement (producing four circular arcs) is almost comparable to the other two methods in geometric complexity: the SFA with two circular arcs and two line segments, and the bilens with four circular arcs. In other comparison criteria, the BCA approach is more efficient and stable than the other two methods in producing a hierarchy of bounding regions that approximate a family of freeform planar curves within a given error bound.

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Efficient Hausdorff Distance computation for freeform geometric models in close proximity

Cited by 21 publications

References 14 publications

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space

Comparison of three bounding regions with cubic convergence to planar freeform curves

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