Implicit Meshes for Modeling and Reconstruction

Explicit surfaces, such as triangulations or wireframe models, have been extensively used to represent the deformable 3–D models that are used to fit 3–D point and 2–D silhouette data. The resulting approaches, however, suffer from the fact that fitting typically involves finding the facets that are closest to the 3–D data points or most likely to be silhouette facets. This requires searching, which is slow, and dealing with the non-differentiability of the distance function. By contrast, implicit surface representations allow fitting without search, since one can simply evaluate a differentiable field function at every data point. However, implicit representations are not necessarily the most intuitive ones and users, such as graphics designers, tend to prefer explicit models.