Computer vision researchers have developed a method of using wavelets to construct triangular meshes in representing 3-D objects. This technique can be useful in analyzing 3-D data, in modeling 3-D objects, and in reducing storage requirements for large 3-D data sets.
A popular means of representing 3-D surfaces, triangular mesh approximations are used in activities ranging from mechanical engineering to computer games. Often, multi-resolution analysis (MRA) is used to obtain a compact representation of dense input data. multi-resolution approaches, particularly those moving from coarse to fine resolutions, can often improve the computational efficiency of mesh generation and provide easy control of level of details for approximations. Although they compact the input data, these approaches are still computationally intensive.
The new technique, developed by Sang-Mook Lee (Ph.D. 02) and Lynn Abbott, reduces a large grid of height (or distance) measurements to a relatively small set of triangles. They use a wavelet-based MRA method to get a fast surface approximation of height data. At a given scale, the wavelet coefficients indicate the locations of highly uneven regions. This information is used by the software to determine triangle placements that fit the data most accurately.
As depicted on this rendering of Hawaii, as the scale gets finer, the triangles get smaller and become dense only in the ridges and peaks of the volcanoes. The work was funded by the USDA Forest Service.