SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
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New quadric metric for simplifiying meshes with appearance attributes
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Optimal triangulation and quadric-based surface simplification
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Neural Networks: A Comprehensive Foundation
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A Developer's Survey of Polygonal Simplification Algorithms
IEEE Computer Graphics and Applications
Using Growing Cell Structures for Surface Reconstruction
SMI '03 Proceedings of the Shape Modeling International 2003
Mesh Simplification with Hierarchical Shape Analysis and Iterative Edge Contraction
IEEE Transactions on Visualization and Computer Graphics
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Quadric-based simplification in any dimension
ACM Transactions on Graphics (TOG)
A Bayesian method for probable surface reconstruction and decimation
ACM Transactions on Graphics (TOG)
A comparison of two optimization methods for mesh quality improvement
Engineering with Computers
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Viewpoint-based simplification using f-divergences
Information Sciences: an International Journal
Tumble tree: reducing complexity of the growing cells approach
ICANN'10 Proceedings of the 20th international conference on Artificial neural networks: Part III
A neural network model to develop urban acupuncture
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
Geometric bone modeling: from macro to micro structures
Journal of Computer Science and Technology
A neural network algorithm to simplify 2D meshes
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We have developed a mesh simplification method called GNG3D which is able to produce high quality approximations of polygonal models. This method consists of two distinct phases: an optimization phase and a reconstruction phase. The optimization phase is developed by applying an extension algorithm of the growing neural gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces obtaining the optimized mesh as a result. We study the model theoretically, analyzing its main components, and experimentally, using for this purpose some 3D objects with different topologies. To evaluate the quality of approximations produced by the method proposed in this paper, three existing error measurements are used. The ability of the model to establish the number of vertices of the final simplified mesh is demonstrated in the examples.