Insight Journal - Surface Mesh Discrete Curvature Estimators

Surface Mesh Discrete Curvature Estimators

Department of System Biology, Harvard Medical School

Please use this identifier to cite or link to this publication: http://hdl.handle.net/1926/1494

Published in The Insight Journal - 2008 July - December.

Submitted by Arnaud Gelas on 09-07-2008.

Computing local curvatures of a given surface is important for applications, shape analysis, surface segmentation, meshing, and surface evolution. For a given smooth surface (with a given analytical expression which is sufficiently differentiable) curvatures can be analytically and directly computed. However in real applications, one often deals with a surface mesh which is an insufficiently differentiable approximation, and thus curvatures must be estimated. Based on a surface mesh data structure (code{itk::QuadEdgeMesh}~cite{itkQE}), we introduce and implement curvature estimators following the approach of Meyeretalcite{Meyer02}. We show on a sphere that this method results in more stable curvature approximations than the commonly used discrete estimators (as used in VTK: code{vtkCurvatures}).

Code

Automatic Testing Results by Insight-Journal Dashboard on Mon Sep 8 09:55:39 2008 for revision #1

expertise: 5 sensitivity: 5

Reviews

Very useful filters, clear and concise paper by Luis Ibanez on 2008-09-30 17:10:43 for revision #1

expertise: 5 sensitivity: 5

Summary:

This contribution provides filters for computing curvatures in a surface (2D manifold embedded in 3D) represented as a QuadEdgeMesh. The filters compute Gaussian, Minimum, Maximum and Mean curvatures.

The paper goes to the point and provides clear examples on the use of the filters.

Hypothesis:

N/A

Evidence:

The paper provides all the source code, data and parameters needed to replicate their work.

Open Science:

This is a fully compliant "OPEN SCIENCE" paper.

The authors provide all the material needed for rerproducing their work. This includes source code, data and parameters.

Reproducibility:

I downloaded the code and build it without any trouble. It compiled out of the box.

The example runs by simply invoking CTest.

The results produced by the example are consistent with the ones presented in the paper.

Word of warning: In order to build this contribution, the user must use an ITK build with ITK_USE_REVIEW enabled.

Use of Open Source Software:

The papers is based on ITK, and uses the VTK legacy format for polydata.

Open source Contributions:

The filters are in a well-presented format for being included in ITK.

Minor style issues: class naming convention and coding style formatting.

The code is readable, and the filters worked without any modifications.

It took just a couple of minutes to build the code and to run the examples.

Code Quality :

The classes have a nice hierarchical structure, with good code reuse.

I have tested the code in the following two platforms:

a) Debian Linux, gcc 4.1

b) Windows Vista, Visual Studio 9, 64bits,

In both cases the code build fine. ( just a couple of warnings, but nothing too serious).

Quality of the data :

The data was easy to use. It was the surface of a shpere.

It will be nice to complement this simple dataset with a more complex surface (e.g. a torous).

Interest:

These filters provide fundamental functionalities that ITK has been lacking for a long time.

They will help users to exploit the itk::Mesh (actually the itkQuadEdgeMesh) for many different applications.

In particular, the modelling of anatomical structures (bones and joints) comes to mind.

Free comment :

This paper provides the ideal size of a contribution to ITK. A clear and concise paper that goes to the point, and source code that works out of the box. The set of five to ten classes that are good candidates to be added to the ITK Code/Review directory.

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Paper Id:	302
Categories:	Filtering, Mathematics, Mesh
Keywords:	surface mesh, curvature
Toolkits:	ITK (moved into the toolkit), CMake
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Status:	Accepted for publication

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