Constrained Remeshing Using Evolutionary Vertex Optimization

Zhang, Wen‐Xiang; Wang, Qi; Guo, Jia‐Peng; Chai, Shuangming; Liu, Ligang; Fu, Xiao‐Ming

doi:10.1111/cgf.14471

Cited by 9 publications

(13 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For our unconstrained optimization problem (13), it is used to find the optimal positions of control points for minimizing the color error. Since the problem (13) is similar to the problem (2) in [ZWG*22], we use the same differential evolution (DE) algorithm as [ZWG*22]. The DE algorithm contains three important parameters, i.e., population size N p , mutation scale F , and crossover rate C r , and we test them in Figs.…”

Section: Methodsmentioning

confidence: 99%

“…We primarily concentrate on constrained remeshing problems and explore various objectives and constraints that are comparable to those we use. Typical constraints include bounding the two‐sided Hausdorff distance between the input and output meshes [HYB*17,CFZC19,YZL*20,ZWG*22], guaranteeing the local Delaunay condition [ZWG*22], and preventing any intersections [GZYF23]. Since these constraints are non‐differentiable, explicit checks are used to ensure that they are satisfied.…”

Section: Related Workmentioning

confidence: 99%

“…When conducting local operations, we apply explicit checks to avoid violating the hard constraints, including error‐bounded and quality constraints. For each local operation, we decompose it into topological and geometric changes, similar to [ZWG*22]. To adapt to combinatorial, discontinuous functions and produce various visual effects, we use the differential evolution algorithm to update geometry.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Error‐bounded Image Triangulation

Fang,

Guo,

Xiao

et al. 2023

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

We propose a novel image triangulation method to reduce the complexity of image triangulation under the color error‐bounded constraint and the triangle quality constraint. Meanwhile, we realize a variety of visual effects by supporting different types of triangles (e.g., linear or curved) and color approximation functions (e.g., constant, linear, or quadratic). To adapt to these discontinuous and combinatorial objectives and constraints, we formulate it as a constrained optimization problem that is solved by a series of tailored local remeshing operations. The feasibility and practicability of our method are demonstrated over various types of images, such as organisms, landscapes, portraits and cartoons. Compared to state‐of‐the‐art methods, our method generates far fewer triangles for the same color error or much smaller color errors using the same number of triangles.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Error‐bounded Image Triangulation

Fang,

Guo,

Xiao

et al. 2023

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

show abstract

“…Incremental remeshing algorithms on single shapes typically generate approximating surface meshes via a series of local mesh connectivity modifications and geometric update steps. While classical methods are driven solely by a target edge length criterion [BK04, DVBB13], a different approach is to formulate the task as an energy minimization problem [ZWG*22]. Besides soft optimization goals, many methods are able to achieve hard quality bounds, e.g., in terms of surface approximation error [MCSA15, HYB*16, CFZC19, JSZP20, ZWG*22] or mesh quality [YW15, YLH18, ZWG*22].…”

Section: Related Workmentioning

confidence: 99%

Surface Maps via Adaptive Triangulations

Schmidt

Pieper

Kobbelt

2023

Computer Graphics Forum

View full text Add to dashboard Cite

We present a new method to compute continuous and bijective maps (surface homeomorphisms) between two or more genus‐0 triangle meshes. In contrast to previous approaches, we decouple the resolution at which a map is represented from the resolution of the input meshes. We discretize maps via common triangulations that approximate the input meshes while remaining in bijective correspondence to them. Both the geometry and the connectivity of these triangulations are optimized with respect to a single objective function that simultaneously controls mapping distortion, triangulation quality, and approximation error. A discrete‐continuous optimization algorithm performs both energy‐based remeshing as well as global second‐order optimization of vertex positions, parametrized via the sphere. With this, we combine the disciplines of compatible remeshing and surface map optimization in a unified formulation and make a contribution in both fields. While existing compatible remeshing algorithms often operate on a fixed pre‐computed surface map, we can now globally update this correspondence during remeshing. On the other hand, bijective surface‐to‐surface map optimization previously required computing costly overlay meshes that are inherently tied to the input mesh resolution. We achieve significant complexity reduction by instead assessing distortion between the approximating triangulations. This new map representation is inherently more robust than previous overlay‐based approaches, is less intricate to implement, and naturally supports mapping between more than two surfaces. Moreover, it enables adaptive multi‐resolution schemes that, e.g., first align corresponding surface regions at coarse resolutions before refining the map where needed. We demonstrate significant speedups and increased flexibility over state‐of‐the art mapping algorithms at similar map quality, and also provide a reference implementation of the method.

show abstract

“…We evaluated our proposed method by comparing it with two state-of-the-art approaches: Liu's method [4] and Zhang's method [10]. Liu's method aims to minimise error for a given mesh size, while Zhang's method focuses on reducing size within a specified error threshold.…”

Section: Experimental Settingmentioning

confidence: 99%

Delaunay meshes simplification with multi‐objective optimisation and fine tuning

Fan,

Wu,

et al. 2023

IET Collab Intel Manufact

View full text Add to dashboard Cite

Abstract3D meshes simplification plays an important role in many industrial domains. The two goals of Delaunay mesh simplification are maintaining high geometric fidelity and reducing mesh complexity. However, they are conflicting and cannot solved by gradient. Such limitation prevents existing Delaunay mesh simplification to obtain a small enough number of vertices and promising fidelity at the same time. To address these issues, this paper proposes an evolutionary multi‐objective approach for Delaunay mesh simplification. Firstly, the authors replace the previous fixed error‐bound threshold by the designed adaptive segment‐specific thresholds. Secondly, a constrained simplification is performed through a series of edge collapses that satisfy both Delaunay and error constraints. Next, the non‐dominated sorting genetic algorithm II (NSGA‐II) is employed to solve the multi‐objective problem to search for the optimal trade‐off threshold sequences. Finally, a fine‐tuning method is designed to further enhance the geometric fidelity of the simplified mesh. Experimental results demonstrate that the authors’ method consistently achieves a satisfactory balance between the approximation error and number of vertices, outperforming existing state‐of‐the‐art methods.

show abstract

Constrained Remeshing Using Evolutionary Vertex Optimization

Cited by 9 publications

References 40 publications

Error‐bounded Image Triangulation

Error‐bounded Image Triangulation

Surface Maps via Adaptive Triangulations

Delaunay meshes simplification with multi‐objective optimisation and fine tuning

Contact Info

Product

Resources

About