Image Processing Reference
In-Depth Information
can be used to indicate the most likely value, and a transparent volume rendering
surrounding the isosurface can indicate the range of possible values [ 43 ]. Uncer-
tainty information for large collections of aggregated data can be presented using
hierarchical parallel coordinates [ 29 ]. Lee et al. [ 52 ] visualize differences in loca-
tion and sub-tree structure between two hierarchies through color and transparency.
Finally, bounded uncertainty, while not effectively visualized in 3D, can be expressed
through the ambiguation of boundaries and edges of pie charts, error bars, and other
2D abstract graphs [ 70 ] or as modifications to line charts [ 96 ].
1.5.2.2 Attribute Modification
Another standard method to visualize uncertainty involves mapping it to free vari-
ables in the rendering equation or modifying the visual attributes of the data. Such
methods include modifying the bidirectional reflectance function (BRDF) to change
surface reflectance, mapping uncertainty to color or opacity [ 65 , 91 , 97 ], or pseudo-
coloring using a look-up table [ 75 ]. This technique has been used as a means for
conveying uncertainty in the areas of volume rendering [ 22 , 51 , 89 ], point cloud
surface data [ 77 ], isosurfacing [ 45 , 79 , 80 , 86 ] and flow fields [ 8 ], and is often com-
binedwith other uncertainty visualizationmethods. An example technique colormaps
flowline curvature onto volume rendered surfaces, highlighting areas in which small
changes in isovalue lead to large changes in isosurface orientation and thus indicat-
ing areas where the isosurface is a poor representation of material boundary [ 49 ].
Another example uses height as a free parameter to display uncertainty in 2D vector
fields [ 72 ]. Texture can be used similarly to convey uncertainty and is also often
modified by opacity, hue, or texture irregularities [ 18 , 40 , 74 ]. Sound has also been
used as another channel for expressing uncertainty [ 58 ].
1.5.2.3 Glyphs
Glyphs are symbols used in visualization to signify data through parameters such
as location, size, shape, orientation, and color. Because of the multivariate nature
of glyphs, they can be used in visualization to map uncertainty to a free parameter.
One such approach uses glyphs to present the distribution of multivariate aggregated
data over a range of values [ 15 ]. These glyphs show the average, standard deviation,
and distribution of three attributes of the data set. Conical glyphs have also been
used to portray fiber tracks from DTI, leveraging the radius of the cone to encode
uncertainty in the orientation of bundles [ 44 ]. An approach that modifies attributes
of glyphs already present in the visualization is presented as a procedural generation
algorithm [ 13 ]. In this work, the data is sampled on a regular grid and the size, color,
and placement of glyphs are taken directly from the data samples. The uncertainty
is then used to distort the glyphs so that glyphs with low uncertainty are very sharp,
with the sharpness level decreasing as the uncertainty level increases. This distortion
provides a clear indication of uncertainty and error while not placing heavy emphasis
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