Topology-preserving scan-based immersed isogeometric analysis

Sai C. Divi; Clemens V. Verhoosel; Ferdinando Auricchio; Alessandro Reali; E. Harald van Brummelen

doi:10.1016/j.cma.2022.114648

Topology-preserving scan-based immersed isogeometric analysis

Sai C. Divi (Corresponding author), Clemens V. Verhoosel, Ferdinando Auricchio, Alessandro Reali, E. Harald van Brummelen

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting.

Original language	English
Article number	114648
Number of pages	34
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	392
DOIs	https://doi.org/10.1016/j.cma.2022.114648
Publication status	Published - 15 Mar 2022

Funding

We acknowledge the support from the European Commission EACEA Agency, Framework Partnership Agreement 2013–0043 Erasmus Mundus Action 1b , as a part of the EM Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED). A.R. acknowledges the partial support of the MIUR-PRIN project XFAST-SIMS, Italy (no. 20173C478N ). All the simulations in this work were performed based on the open source software package Nutils ( www.nutils.org ) [113] . We acknowledge the support of the Nutils team, Netherlands . We acknowledge Michele Conti for providing the CT-scan data of the stenotic carotid and Alice Finotello for the help in understanding the data. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: E.H. van Brummelen reports financial support was provided by European Commission. A Reali reports financial support.

Keywords

Finite Cell Method (FCM)
Image filtering
Isogeometric analysis (IGA)
Scan-based analysis
Topology detection

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title = "Topology-preserving scan-based immersed isogeometric analysis",

abstract = "To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting.",

keywords = "Finite Cell Method (FCM), Image filtering, Isogeometric analysis (IGA), Scan-based analysis, Topology detection",

author = "Divi, {Sai C.} and Verhoosel, {Clemens V.} and Ferdinando Auricchio and Alessandro Reali and {van Brummelen}, {E. Harald}",

note = "Funding Information: We acknowledge the support from the European Commission EACEA Agency, Framework Partnership Agreement 2013–0043 Erasmus Mundus Action 1b , as a part of the EM Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED). A.R. acknowledges the partial support of the MIUR-PRIN project XFAST-SIMS, Italy (no. 20173C478N ). All the simulations in this work were performed based on the open source software package Nutils ( www.nutils.org ) [113] . We acknowledge the support of the Nutils team, Netherlands . We acknowledge Michele Conti for providing the CT-scan data of the stenotic carotid and Alice Finotello for the help in understanding the data. Funding Information: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: E.H. van Brummelen reports financial support was provided by European Commission. A Reali reports financial support. Publisher Copyright: {\textcopyright} 2022 The Author(s)",

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doi = "10.1016/j.cma.2022.114648",

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AU - Verhoosel, Clemens V.

AU - Auricchio, Ferdinando

AU - Reali, Alessandro

AU - van Brummelen, E. Harald

N1 - Funding Information: We acknowledge the support from the European Commission EACEA Agency, Framework Partnership Agreement 2013–0043 Erasmus Mundus Action 1b , as a part of the EM Joint Doctorate Simulation in Engineering and Entrepreneurship Development (SEED). A.R. acknowledges the partial support of the MIUR-PRIN project XFAST-SIMS, Italy (no. 20173C478N ). All the simulations in this work were performed based on the open source software package Nutils ( www.nutils.org ) [113] . We acknowledge the support of the Nutils team, Netherlands . We acknowledge Michele Conti for providing the CT-scan data of the stenotic carotid and Alice Finotello for the help in understanding the data. Funding Information: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: E.H. van Brummelen reports financial support was provided by European Commission. A Reali reports financial support. Publisher Copyright: © 2022 The Author(s)

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N2 - To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting.

AB - To exploit the advantageous properties of isogeometric analysis (IGA) in a scan-based setting, it is important to extract a smooth geometric domain from the scan data (e.g., voxel data). IGA-suitable domains can be constructed by convoluting the grayscale data using B-splines. A negative side-effect of this convolution technique is, however, that it can induce topological changes in the process of smoothing when features with a size similar to that of the voxels are encountered. This manuscript presents an enhanced B-spline-based segmentation procedure using a refinement strategy based on truncated hierarchical (TH)B-splines. A Fourier analysis is presented to explain the effectiveness of local grayscale function refinement in repairing topological anomalies. A moving-window-based topological anomaly detection algorithm is proposed to identify regions in which the grayscale function refinements must be performed. The criterion to identify topological anomalies is based on the Euler characteristic, giving it the capability to distinguish between topological and shape changes. The proposed topology-preserving THB-spline image segmentation strategy is studied using a range of test cases. These tests pertain to both the segmentation procedure itself, and its application in an immersed IGA setting.

KW - Finite Cell Method (FCM)

KW - Image filtering

KW - Isogeometric analysis (IGA)

KW - Scan-based analysis

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JO - Computer Methods in Applied Mechanics and Engineering

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M1 - 114648

ER -

Topology-preserving scan-based immersed isogeometric analysis

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Keywords

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