Hermite Radial Basis Functions Implicits

Macêdo, Ives; Góis, João Paulo; Velho, Luiz

doi:10.1111/j.1467-8659.2010.01785.x

Cited by 83 publications

(61 citation statements)

References 34 publications

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“…Because of the importance of vector data, such as geological attitudes, Hermite Radial Basis Function (HRBF, as formula 1) surface (Macedo, I., 2011) was preferred and adopted to complete 3D geological mapping, ore body simulation and subsurface stratum modelling in our study.…”

Section: Methodsmentioning

confidence: 99%

Implicit Three-Dimensional Geo-Modelling Based on HRBF Surface

Gou

Zhou

2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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ABSTRACT:Three-dimensional (3D) geological models are important representations of the results of regional geological surveys. However, the process of constructing 3D geological models from two-dimensional (2D) geological elements remains difficult and time-consuming. This paper proposes a method of migrating from 2D elements to 3D models. First, the geological interfaces were constructed using the Hermite Radial Basis Function (HRBF) to interpolate the boundaries and attitude data. Then, the subsurface geological bodies were extracted from the spatial map area using the Boolean method between the HRBF surface and the fundamental body. Finally, the top surfaces of the geological bodies were constructed by coupling the geological boundaries to digital elevation models. Based on this workflow, a prototype system was developed, and typical geological structures (e.g., folds, faults, and strata) were simulated. Geological modes were constructed through this workflow based on realistic regional geological survey data. For extended applications in 3D modelling of other kinds of geo-objects, mining ore body models and urban geotechnical engineering stratum models were constructed by this method from drill-hole data. The model construction process was rapid, and the resulting models accorded with the constraints of the original data.

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Section: Methodsmentioning

confidence: 99%

Implicit Three-Dimensional Geo-Modelling Based on HRBF Surface

Gou

Zhou

2016

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…To address this issue, Hermite data is incorporated into the RBF, which directly use derivatives. This method ensures the existence of a non-null implicit surface without the need of additional information [18]. Using the first order Hermite interpolation in combination with RBF, the scalar field can be formulated as follows:…”

Section: D Interpolationmentioning

confidence: 99%

“…The linear systems of equations can be also written as DX = B, with D ∈ R M+N×M+N , X ∈ R M+N and B ∈ R M+N . The blue block describes the constraints on the 3D variables α 3D i , β 3D i derived from the 3D constraints and orthogonality conditions Equations (12), (14), (16) and (18). Thus, the matrices K i,j , S i and the vectors s, w i , and c i are defined as:…”

Section: Dmentioning

confidence: 99%

Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation

et al. 2017

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Segmentation is one of the most important parts of medical image analysis. Manual segmentation is very cumbersome, time-consuming, and prone to inter-observer variability. Fully automatic segmentation approaches require a large amount of labeled training data and may fail in difficult or abnormal cases. In this work, we propose a new method for 2D segmentation of individual slices and 3D interpolation of the segmented slices. The Smart Brush functionality quickly segments the region of interest in a few 2D slices. Given these annotated slices, our adapted formulation of Hermite radial basis functions reconstructs the 3D surface. Effective interactions with less number of equations accelerate the performance and, therefore, a real-time and an intuitive, interactive segmentation of 3D objects can be supported effectively. The proposed method is evaluated on 12 clinical 3D magnetic resonance imaging data sets and are compared to gold standard annotations of the left ventricle from a clinical expert. The automatic evaluation of the 2D Smart Brush resulted in an average Dice coefficient of 0.88 ± 0.09 for the individual slices. For the 3D interpolation using Hermite radial basis functions, an average Dice coefficient of 0.94 ± 0.02 is achieved.

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“…Carr et al interpolated sparse points using a radial basis function to obtain an implicit surface using hand-tuned offset points to find a non-trivial interpolant [22]. To avoid offset points, Macedo et al [23] proposed using the HRBF to directly interpolate the values and the normal. These surfaces have been widely used in CAD/CAM and have made surface modeling much simpler.…”

Section: Related Workmentioning

confidence: 99%

Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes

Guo

Zhou

et al. 2016

IJGI

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Three-dimensional (3D) geological models are important representations of the results of regional geological surveys. However, the process of constructing 3D geological models from two-dimensional (2D) geological elements remains difficult and is not necessarily robust. This paper proposes a method of migrating from 2D elements to 3D models. First, the geological interfaces were constructed using the Hermite Radial Basis Function (HRBF) to interpolate the boundaries and attitude data. Then, the subsurface geological bodies were extracted from the spatial map area using the Boolean method between the HRBF surface and the fundamental body. Finally, the top surfaces of the geological bodies were constructed by coupling the geological boundaries to digital elevation models. Based on this workflow, a prototype system was developed, and typical geological structures (e.g., folds, faults, and strata) were simulated. Geological modes were constructed through this workflow based on realistic regional geological survey data. The model construction process was rapid, and the resulting models accorded with the constraints of the original data. This method could also be used in other fields of study, including mining geology and urban geotechnical investigations.

show abstract

Hermite Radial Basis Functions Implicits

Cited by 83 publications

References 34 publications

Implicit Three-Dimensional Geo-Modelling Based on HRBF Surface

Implicit Three-Dimensional Geo-Modelling Based on HRBF Surface

Rapid Interactive and Intuitive Segmentation of 3D Medical Images Using Radial Basis Function Interpolation

Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes

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