News about Mesh_3

_posts/2024-12-01-mesh3-improvements.md

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+---
+layout: post
+title: "Tetrahedral Mesh Generation improvements"
+description: "Tetrahedral Mesh Generation improvements in CGAL-6.0.1"
+category:
+tags: [""]
+---
+{% include JB/setup %}
+
+<h3><a href="https://geometryfactory.com/who-we-are/">Jane Tournois</a></h3>
+<h4><a href="http://www.geometryfactory.com" target="_blank">GeometryFactory</a></h4>
+
+
+<p>Introduced in CGAL 3.5, the package
+<a href="https://doc.cgal.org/latest/Manual/packages.html#PkgMesh3" text="3D Mesh Generation">3D Mesh Generation</a>
+is designed to generate a isotropic simplicial meshes discretizing 3D domains.
+Since then, multiple improvements in mesh quality, performances, and versatility have been made available in CGAL.
+Lately, CGAL authors have focused more on the quality of the output mesh, the ability of the
+mesh generation algorithm to represent the input surface in a more accurate way, for a wider range of input data types.
+</p>
+
+<br>
+<p>Recent releases of CGAL have introduced improvements to the 3D Tetrahedral Mesh Generation package:
+detection and protection of triple lines from labeled images,
+generation and use of weighted labeled images,
+and a new approximation error criterion for polyline features.</p>
+
+
+<br>
+<h3>Triple lines from labeled images</h3>
+
+<p>CGAL's tetrahedral mesh generation algorithm is able to compute tetrahedral meshes from 3D segmented images.
+For all types of inputs, detection and construction of one-dimensional features must be done a priori for the
+feature protection algorithm to be able to represent them properly in the generated mesh.
+In 3D segmented images, such features correspond to the intersections of the bounding box of the image with the surfaces
+defined by the image, as well as polylines that lie at the intersection of three or more subdomains (including the outside).</p>
+
+<p>The article
+<a href="https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/274"><i>Hege, H. C., Seebass, M., Stalling, D., & Zöckler, M. (1997),
+A generalized marching cubes algorithm based on non-binary classifications</i></a>, provides a list of possible voxel configurations.
+This description has been generalized for tetrahedral mesh generation needs, and
+implemented in CGAL.</p>
+
+<p>After feature lines detection, similarly to what is done for polyhedral surfaces, the polyline features
+are added to the feature graph of the domain for feature protection.</p>
+
+<p>Two detection functors are provided :
+<ul>
+  <li><i>CGAL::Detect_features_in_image()</i> detects and constructs all
+    polylines lying at the intersection of three or more subdomains, and</li>
+  <li><i>CGAL::Detect_features_on_image_bbox()</i> detects and constructs the polylines
+    that lie at the intersection of two or more subdomains and the bounding box of the input labeled image.</li>
+</ul>
+</p>
+
+<div style="text-align:center;">
+  <a href="../../../../images/mesh3_triple_lines_protection.png"><img src="../../../../images/mesh3_triple_lines_protection.png" style="max-width:80%"/></a><br>
+  <br><small>Mesh generation from labeled image without (left)
+   and with triple lines detection and protection (right).
+   The polylines lying at the intersection of three or more subdomains are
+   a lot more precise with a lot fewer vertices.</small>
+</div>
+
+
+<br>
+<h3>Weighted Labeled Images</h3>
+
+<p>When a segmented image is given as input for tetrahedral mesh generation,
+the generated mesh surface sometimes sticks too closely to the voxels surface, causing an aliasing effect. A solution to generate
+a smooth and accurate output surface was described by Stalling et al in
+<a href="https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/382"><i>Stalling, D., Zöckler, M., Sander, O., & Hege, H. C. (1998),
+Weighted labels for 3D image segmentation</i></a>.
+It consists in generating a second input image, made of integer coefficients called weights, and use those weights to define
+smoother domain boundaries. The 3D image of weights can be generated by <i>CGAL::Mesh_3::generate_label_weights()</i>.</p>
+
+<div style="text-align:center;">
+  <a href="../../../../images/mesh3_weighted_images.png"><img src="../../../../images/mesh3_weighted_images.png" style="max-width:100%"/></a><br>
+  <br><small>Mesh generation from labeled image without weights (left, 88,000 vertices)
+   and with weights (right, 67,000 vertices).</small>
+</div>
+
+<br>
+<p>The following example shows how to use weighted labeled images: <a href="https://doc.cgal.org/6.0.1/Mesh_3/Mesh_3_2mesh_3D_weighted_image_8cpp-example.html">mesh_3D_weighted_image.cpp</a>.</p>
+
+<p>Utilizing tetrahedral mesh generation from labeled images, incorporating both feature detection and weighted labels,
+presents challenges. A new method that combines feature detection and weighted labels has been
+designed and implemented in CGAL, achieving smooth and feature preserving output meshes.
+This method leverages the best of these two new functionalities.</p>
+
+
+<br>
+<h3>Approximation Criterion on Feature Edges</h3>
+
+<p>A Delaunay refinement algorithm is guided by meshing criteria that trigger Steiner vertices insertions,
+until they are satisfied.
+The list of CGAL meshing criteria has been enriched with a new criterion that enables the user to
+define an upper bound on the distance between the input feature graph and the output feature edges.</p>
+
+<p>The following example shows how to use this new criterion, called <i>edge_distance</i>:
+<a href="https://doc.cgal.org/6.0.1/Mesh_3/Mesh_3_2mesh_polyhedral_domain_with_edge_distance_8cpp-example.html">
+mesh_polyhedral_domain_with_edge_distance.cpp</a>.</p>
+
+<div style="text-align:center;">
+  <a href="../../../../images/mesh3_edge_distance_stool.png"><img src="../../../../images/mesh3_edge_distance_stool.png" style="max-width:65%"/></a><br>
+  <br><small>Mesh generation from polyhedral surface with varying <i>edge_distance</i> meshing criterion.
+  The quality improvement is important on the lower end of stool feet.</small>
+</div>
+
+
+<h3>Status</h3>
+
+<p>All these new improvements have been integrated in CGAL-6.0.1, which has just been officially released.</p>
+
+<i class="bi bi-book"></i>
+<a href="https://www.cgal.org/2024/10/22/cgal601/">CGAL-6.0.1 announcement</a>
+<br>
+<i class="bi bi-book"></i>
+<a href="https://doc.cgal.org/latest/Manual/packages.html#PkgMesh3">Documentation of the Tetrahedral Mesh Generation package</a>
+<br>
+<i class="bi bi-arrow-down-circle"></i>
+<a href="https://github.com/CGAL/cgal/tree/master">CGAL master branch on GitHub</a>