Semi-Automatic Generation of Transfer FunctionsDirect Volume RenderingExampleWhat are we looking for?Getting a good transfer functionPrevious workSlide 7The Boundary ModelThe Boundary Model (2)Directional DerivativesDirectional Derivatives (2)Relations between f, f’, f’’Histogram VolumeHistogram CreationImplementationImplementation (2)Implementation (3)Histogram Volume InspectionMore examplesBoundary AnalysisWhere is the boundary?Opacity functionUsing both data value and gradient magnitudeResultsSemi-Automatic Generation of Transfer FunctionsG. Kindlmann, J. DurkinCornell UniversityPresented by Jian Huang, CS594, Spring 2002Direct Volume Rendering•Render the volume by computing the volume integration – Direct Volume Rendering•Iso-surfacing: extract the iso-surfaces from the dataset, and render as surface geometry primitives•Pros and cons: ? depend on who you talk toExampleWhat are we looking for?•look for boundary regions between relatively homogeneous material in the scalar volume•The boundary might be associated with a range of values•Use an opacity function to modulate the parameters corresponding to this rangeGetting a good transfer function•Transfer function: assign renderable optical properties to the numerical values•This paper focuses on the opacity functions•Getting a good transfer function is trickyPrevious work•He et al.,use genetic algorithm to breed a good transfer function•Marks et al., design gallery•Both only look at good-looking renderings, driven by images.•But, good transfer function should come from an analysis of the data set•Work also exists in the iso-surfacing domainExampleThe Boundary Model•Assumption–There exist a sharp, discontinuous change in the physical property of the entity–The data/signal has been low-pass filtered, (band-limited, or, blurred)–The blur is isotropic–The blurring function (low-pass filter) is GaussianThe Boundary Model (2)Directional DerivativesDirectional Derivatives (2)Relations between f, f’, f’’Histogram Volume•Measure the relationship between the data value and its derivatives.Histogram Creation•Measure f and its directional derivatives exactly once per voxel, at the original sample points of the data setImplementation•First directional derivative•Three ways to compute the gradientsImplementation (2)•Use central difference•Use method 1 to compute 2nd derivative–Need the 1st directional derivative computed and stored as a volumeImplementation (3)Histogram Volume InspectionMore examplesBoundary Analysis•Based on the assumption of Gaussian profileWhere is the boundary?•Average 1st directional derivative of f over all the positions x at which f(x) equals v,–g(v)•Average 2nd directional derivative of f over all the positions x at which f(x) equals v,–h(v)Opacity functionUsing both data value and gradient magnitude•Extend h(v) to h(v,g).•Benefit: –distinguish between boundaries that have overlapping ranges of values–Capture surface of a material which attains a wide range of values
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