Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
On the normal vector estimation for point cloud data from smooth surfaces
Computer-Aided Design
A survey of point-based techniques in computer graphics
Computers and Graphics
Gabriel Graphs in Arbitrary Metric Space and their Cellular Automaton for Many Grids
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
Probabilistic auto-tuning for architectures with complex constraints
Proceedings of the 1st International Workshop on Adaptive Self-Tuning Computing Systems for the Exaflop Era
Neighborhood random classification
PAKDD'12 Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
Topological comparisons of proximity measures
PAKDD'12 Proceedings of the 16th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part I
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Point-based shape representation has received increased attention in recent years, mainly due to its simplicity. One of the most fundamental operations for point set processing is to find the neighbors of each point. Mesh structures and neighborhood graphs are commonly used for this purpose. However, though meshes are very popular in the field of computer graphics, neighbor relations encoded in a mesh are often distorted. Likewise, neighborhood graphs, such as the minimum spanning tree (MST), relative neighborhood graph (RNG), and Gabriel graph (GG), are also imperfect as they usually give too few neighbors for a given point. In this paper, we introduce a generalization of Gabriel graph, named elliptic Gabriel graph (EGG), which takes an elliptic influence region instead of the circular region in GG. In order to determine the appropriate aspect ratio of the elliptic influence region of EGG, this paper also presents the analysis between the aspect ratio of the elliptic influence region and the average valence of the resulting neighborhood. Analytic and empirical test results are included.