Derivatives and Eigensystems for Volume-Data Analysis and Visualization
Jiřı́ Hladůvka · reposiTUm (TU Wien) · 2001
Volume data refer to sampled three-dimensional spatial signals.The tools which handle them can broadly be divided into two categories: visual tools which aim at an output interpretable by a human user and analytic tools which prepare the data for further machine processing.Although it would be natural that the two related disciplines, i.e., volume visualization and volume processing closely collaborate, they are still rather separated.The work presented here contributes to bridge the gap in between.This thesis addresses classification of volume samples based on observations of how the scalar values vary in their vicinity.We investigate the first three terms of a Taylor series expansion of the corresponding scalar field at the inspected points.An important issue arising with such an analysis in higher dimensions are the directions to be examined.In order to find an answer to this problem we study the eigensystems of algebraic structures composed of the first-and second-order partial derivatives.After a survey on derivative-based classification in volume visualization and processing we present new contributions which apply to three distinct problems: specification of transfer functions, content-based retrieval of volume-data features, and shape-based interpolation.. . . in 10 years all rendering will be volume rendering Jim Kajiya at SIGGRAPH '91 [9] Why is real-time volume rendering no longer a year away?Because it is more than two years away!Bill Lorensen at IEEE Visualization '98 [36] Why is real-time volume rendering no longer a year away?Because it is a half a year away!Hanspeter Pfister at IEEE Visualization '98 [36] . . .full screen volume rendering may arrive in 25 years, not 5 years.And full eye in 70 years!