GEOMETRIC PROCESSING OF VOLUMETRIC OBJECTS
Romildo José da Silva, Jonas Gomes, Cícero Mota · International Conference in Central Europe on Computer Graphics and Visualization · 2001
Instituto de Ciencias Exatas – Universidade do Amazonas, 69077-000, Brazil.ˆfrjs, jonas, [email protected] paper introduces techniques of Riemannian geometry for processing and visualising volumetric graph-ical objects. A family of non-linear high-pass filters, based on the curvature tensor, is introduced and usedto study the local redundancy on objects. It is shown how to reconstruct an object from geometric non-redundant regions and applications are presented and discussed.Keywords: Volumetric objects, processing, coding1 INTRODUCTIONThe output data for a great number of processes arevolumetric. Computer tomography, magnetic reso-nance, seismic data and movies are important exam-ples of this class of data. Nevertheless, most tech-niques from computer graphics are related to two-dimensional objects. This is in part, due to limitationsimposed by the hardware. Today, technical advancesin memory and processing capabilities of computersare favouring the appearance of new methods of visu-alisation and processing of volumetric objects.In this work we introduce techniques from Rieman-nian geometry in the analysis of volumetric objects.This technique allows one to construct a family ofnonlinear filters which are scale invariant and allowfor reconstruction. Although some of the results inthis paper could be obtained by linear filtering, the useof geometry is motivated by recent advances in humanvision, [Koend87, Barth98]. The physical propertiesof our environment are related to strong geometric re-strictions in volumetric objects. Motion, e.g., is re-lated to zero Gaussian curvature. Differential geom-etry can be regarded as a strong tool for analysis ofredundancy in such objects.2 VOLUMETRIC OBJECTSA volumetric graphical object is a pair (U;f), whereUis a tridimensional subset of R