News about Mesh_3

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

@@ -0,0 +1,123 @@
+---
+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>
+<br>
+
+<p>The CGAL component
+<a href="https://doc.cgal.org/latest/Manual/packages.html#PkgMesh3" text="3D Mesh Generation">3D Mesh Generation</a>
+is the primary component to generate isotropic simplicial meshes discretizing 3D domains with CGAL.
+First introduced in CGAL-3.5 (2009!), this component has been constantly updated through the years
+to improve its performance, its versatility, and the quality of the meshes it produces.</p>
+
+<p>Recent releases of CGAL have once again introduced new enhancements that enable more accurate
+representations of input surfaces, for a wider range of input data types. It is now possible to:
+<ul>
+<li>detect and recover sharp features in labeled images,</li>
+<li>generate meshes of <i>weighted</i> labeled images,</li>
+<li>control the maximum error on the approximation error of polyline features.</li>
+</ul></p>
+
+
+<br>
+<h3>Recovery of Sharp Features in Labeled Images</h3>
+
+<p>CGAL's tetrahedral mesh generation algorithm is able to generate tetrahedral meshes from 3D segmented images.
+Regardless of input type, one-dimensional feature detection and construction must be performed before
+the generation of the mesh.
+In 3D segmented images, these 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 classification
+of possible voxel configurations.
+This description has been generalized for tetrahedral mesh generation needs, and implemented in CGAL.</p>
+
+<p>Following feature lines detection, polyline features are added to the feature graph of the domain
+for feature protection, similarly to what is done for polyhedral surfaces.</p>
+
+<p>Two new detection functors are introduced to support the protection of triple lines:
+<ul>
+  <li><code>CGAL::Detect_features_in_image()</code>: detect and construct all
+    polylines lying at the intersection of three or more subdomains, and</li>
+  <li><code>CGAL::Detect_features_on_image_bbox()</code>: detect and construct 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).
+   Protection of the feature lines at the intersection of the three subdomains (pink, blue, outside)
+   enables a much more faithful mesh, with 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>.
+The approach consists in generating a second input image made of integer coefficients called <i>weights</i>,
+and to use those weights to define smoother domain boundaries.
+
+This addition has been added to CGAL, and the 3D image of weights can be generated using the new function
+<code>CGAL::Mesh_3::generate_label_weights()</code>.</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>A new method combining triple line protection and weighted labels has been
+designed and implemented in CGAL, achieving smooth and feature preserving meshes.
+This method leverages the best of these two new functionalities.</p>
+
+<br>
+<h3>Approximation Criterion for Feature Edges</h3>
+
+<p>Our Delaunay refinement algorithm is guided by meshing criteria (size, shape, etc.).
+When these criteria are not honored, new vertices are inserted until the criteria are satisfied,
+a process guaranteed to terminate.
+The list of CGAL meshing criteria has been enriched with a new criterion that enables users to
+define an upper bound on the distance between the input feature graph and the output feature edges,
+providing finer control over the mesh features.</p>
+
+<p>The example <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> shows how to use this new criterion, called <code>edge_distance</code>.</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 a varying <code>edge_distance</code> meshing criterion.
+  The quality improvement is noticeable at the extremities of the stool legs.</small>
+</div>
+
+
+<h3>Status</h3>
+
+<p>All these new improvements are part of 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>