Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
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
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Optimizing triangle strips for fast rendering
Proceedings of the 7th conference on Visualization '96
Geometric compression through topological surgery
ACM Transactions on Graphics (TOG)
Real time compression of triangle mesh connectivity
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Surface Approximation and Geometric Partitions
SIAM Journal on Computing
Smooth view-dependent level-of-detail control and its application to terrain rendering
Proceedings of the conference on Visualization '98
Adaptive Split-and-Merge Segmentation Based on Piecewise Least-Square Approximation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image compression using plane fitting with inter-block prediction
Image and Vision Computing
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The provably NP-hard problem of finding optimal piecewise linear approximation for images is extended from 1D curve fitting to 2D surface fitting by a dual-agent algorithm. The results not only yield a storage-efficient codec for range, or intensity, images but also a surface triangulation technique to generate succinct, accurate and visually pleasant 3D visualization model. Comparing with the traditional piecewise linear image coding (PLIC) algorithms, triangulation of a range image is more adaptive due to conformity of the shape, orientation and size of triangles with the image contents. The triangularization algorithm presented here differs from previous approaches in that it strives to minimize the total number of triangles (or vertices) needed to approximate the image surface while keeping the deviation of any intensity value to within a prescribed error tolerance. Unlike most methods of bottom-up triangularization, which could bog down before any mesh simplification even begins, this algorithm fits the surface in a top-down manner, avoiding the generation of most unnecessary triangles. When combined with an efficient 3D triangulation-encoding scheme, the algorithm achieves compact code length with guaranteed error bound, thus providing a more faithful representation of all image features. A variety of benchmark test images have been experimented and compared.