Dimensional Induced Clustering for Surface Recognition

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 elds. 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 di erent 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 a ffect the visual quality of the final result.