Parametric Blending of Hole Patches Based on Shape Difference
"> Figure 1
<p>Accessibility limitation of an oral 3D scanner results in (<b>a</b>) a hole in the scanned model. (<b>b</b>) The artifact is repaired by a hole-filling technique.</p> "> Figure 2
<p>Overview of the proposed algorithm. (<b>a</b>) a hole is detected in a triangular mesh by searching closed boundary edges, (<b>b</b>) simple triangulation fills the hole without additional vertices, (<b>c</b>) refinement and remeshing are applied iteratively to produce an initial hole patch, (<b>d</b>) two different patches are constructed by Laplacian smoothing and minimizing curvature variation, (<b>e</b>) the result of the hole patch generated by using our method.</p> "> Figure 3
<p>Process of incremental remeshing: (<b>a</b>) initial triangulation, (<b>b</b>) first iteration, (<b>c</b>) third iteration, (<b>d</b>) fifth iteration.</p> "> Figure 4
<p>Hole patches generated by (<b>a</b>) minimizing membrane energy (<math display="inline"><semantics> <mrow> <mi>L</mi> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>), (<b>b</b>) minimizing thin-plate energy (<math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>), and (<b>c</b>) minimizing curvature variation energy (<math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>3</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>).</p> "> Figure 5
<p>Two hole patches to be blended: (<b>a</b>) Source patch <math display="inline"><semantics> <msub> <mi>P</mi> <mi>S</mi> </msub> </semantics></math>, and (<b>b</b>) target patch <math display="inline"><semantics> <msub> <mi>P</mi> <mi>T</mi> </msub> </semantics></math>.</p> "> Figure 6
<p>Cotangent weight <math display="inline"><semantics> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </semantics></math> for Laplacian smoothing.</p> "> Figure 7
<p>Color-coded shape difference between <math display="inline"><semantics> <msub> <mi>P</mi> <mi>S</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>P</mi> <mi>T</mi> </msub> </semantics></math> for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p> "> Figure 8
<p>Per-vertex blending weight <math display="inline"><semantics> <msub> <mover accent="true"> <mi>w</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> </semantics></math> is determined by a user-specified blending parameter <span class="html-italic">w</span> and a shape difference <math display="inline"><semantics> <msub> <mi>σ</mi> <mi>i</mi> </msub> </semantics></math>.</p> "> Figure 9
<p>Four examples with complex holes. (<b>a</b>) Left: a bunny model; middle: minimizing curvature variation(<math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>3</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>), right: shape-difference-based blending(our method), <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mi>w</mi> <mo>=</mo> <mn>1.2</mn> </mrow> </semantics></math>. (<b>b</b>) Left: a bunny model; middle: <math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>3</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>; right: our method, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.9</mn> <mo>,</mo> <mi>w</mi> <mo>=</mo> <mn>3.3</mn> </mrow> </semantics></math>. (<b>c</b>) Left: a molar model; middle: <math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>3</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>, right: our method, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mi>w</mi> <mo>=</mo> <mn>1.55</mn> </mrow> </semantics></math>. (<b>d</b>): Left: an armadillo model; middle: <math display="inline"><semantics> <mrow> <msup> <mi>L</mi> <mn>3</mn> </msup> <mi mathvariant="bold">x</mi> <mo>=</mo> <mn mathvariant="bold">0</mn> </mrow> </semantics></math>; right: our method, <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mi>w</mi> <mo>=</mo> <mn>1.4</mn> </mrow> </semantics></math>.</p> "> Figure 10
<p>Computational time for creating a hole patch for different hole sizes.</p> "> Figure 11
<p>Limitation of our method caused by small shape differences in the center of a large hole.</p> ">
Abstract
:1. Introduction
- Robustness: Our method is based on the remeshing followed by fairing technique, which guarantees the robust solutions to symmetric Laplacian system without self-intersections. Therefore, our method can robustly be used for filling holes with arbitrary sizes and shapes.
- Effectiveness: By analyzing the shape difference between the source and the target patches, salient features, such as convexity and concavity, can be exaggerated or reduced in the resulting patch.
- Controllability: Our system provides the user with a shape control parameter. The user can interactively modify the hole patch until the desired shape is obtained.
2. Related Work
3. Construction of Hole Patches
3.1. Triangulation of Hole Boundary
3.2. Incremental Remeshing
Algorithm 1 Incremental remeshing |
|
3.3. Source and Target Patches
4. Parametric Blending of Hole Patches
4.1. Shape Difference
4.2. Blending Hole Patches
5. Experimental Results
6. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
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Park, J.-H.; Park, S.; Yoon, S.-H. Parametric Blending of Hole Patches Based on Shape Difference. Symmetry 2020, 12, 1759. https://doi.org/10.3390/sym12111759
Park J-H, Park S, Yoon S-H. Parametric Blending of Hole Patches Based on Shape Difference. Symmetry. 2020; 12(11):1759. https://doi.org/10.3390/sym12111759
Chicago/Turabian StylePark, Jung-Ho, Sanghun Park, and Seung-Hyun Yoon. 2020. "Parametric Blending of Hole Patches Based on Shape Difference" Symmetry 12, no. 11: 1759. https://doi.org/10.3390/sym12111759