Abstract: Understanding when a cloud of points in three-dimensional space can be, semantically, interpreted as a surface, and then being able to describe the surface, is an interesting problem in itself and an important task to tackle in several application fields. Finding a possible solution to the problem implies to answer to many typical questions about surface acquisition and mesh reconstruction: how one can build a metric telling whether a point in space belongs to the surface? Given data from 3D scanning devices, how can we tell apart (and eventually discard) points representing noise from signal? Can the reached insight be used to align point clouds coming from different acquisitions? Inside this framework, the present paper investigates the features of a new dimensional clustering algorithm. Unless standard clustering methods, the peculiarity of this algorithm is, using the local fractal dimension, to select subsets of lower dimensionality inside the global of dimension N. When applied to the study of discrete surfaces embedded in three dimensional space, the algorithm results to be robust and able to discriminate the surface as a subset of fractal dimension two, differentiating it from the background, even in the presence of an intense noise. The preliminary tests we performed, on points clouds generated from known surfaces, show that the recognition error is lower than 3 percent and does not affect the visual quality of the final result.
Authors: M. Porcu, R. Scateni.
Dimensional Induced Clustering for Surface Recognition.
WSCG 2007, 257-264.
Plzen, Rep. Ceca, Gennaio-Febbraio 2007.
Abstract: A triangular mesh is the piecewise linear approximation of a sampled or analytical surface, when each patch is a triangle. The connectivity of the mesh can be easily represented using its dual graph. Each node of such a graph has at most three incident edges; if the surface is homeomorphic to a sphere, each node has exactly three incident edges. Several triangular meshes, representing the same surface, with an increasing number of triangles are a representation of the surface at different levels of detail (LOD). When the number of triangles from one LOD to another varies continuously we call such a structure a continuous level of detail (CLOD) approximation of the surface. Given a CLOD data structure we can extract, at each level, the mesh representing the surface and derive its dual graph. If we group the triangles forming each mesh in strips, to accelerate their rendering, we should use two colors for the dual graph’s edges to distinguish between the edges linking nodes belonging to the same strip or not. The main goal of this paper is to present a set of rules to recolor the dual graph of the mesh when passing from one LOD to the next and back. The operations used to change the mesh are a Vertex Split (VS) when the resolution increases, and an Edge Collapse (EC) when the resolution decreases. We can, then, use a local topological analysis to derive the rules allowing to recolor the graph, and to show that, under certain conditions, the recoloring is optimal. This allows to keep effectively an optimal triangle strip structure over the mesh, while changing its resolution.