Image Processing Reference
In-Depth Information
(a)
(d)
∞
(b)
g
−∞
(c)
Fig. 3.8 a
-
c
Volume rendering of
g
field for Stag, as compared to down-sampling with the mean
and lower left corner of each block. The dataset is originally 832
×
×
494, and from
left-to-right
we shown hixel sizes of 4
3
to 64
3
, with all powers of 2 in between.
d
For hixel size 16
3
, we compare
the likelihood field
g
volume rendered to the isosurfaces computed for
832
580 for the mean and
lower-left down-sampling. ©IEEE reprinted, with permission, from Thompson et al. [
10
]
κ
=
3.3 Discussion
By unifying the representations of large scalar fields from various modalities, hixels
enable the analysis and visualization of data that would be otherwise be challenging
to process. While hixels have utility, they present a number of challenges and open
questions to explore. One important question regards information preserved by the
hixels vs. resolution loss. A study is required to explore the appropriate number
of bins per hixel as well as persistence thresholds for bucketing and mode seeking
algorithms. The performance of hixels was not currently emphasized in our work, but
the complexity of many techniques used here should allow for scaling to larger data.
Additional research is required to find a balance between data storage allotted for the
histograms versus feature preservation. Finally, further studies on what topological
features can and cannot be easily preserved by hixelation is required.
References
1. Bremer, P.T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A topological hierarchy for functions
on triangulated surfaces. IEEE Trans. Vis. Comp. Graph.
10
(4), 385-396 (2004)
2. Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse-Smale complexes for piece-
wise linear 2-manifolds. Discrete Comput. Geom.
30
(1), 87-107 (2003)
3. Feller, W.: An Introduction to Probability Theory and its Applications, vol. 1. Wiley, New York
(1968)
4. Forman, R.: A user's guide to discrete Morse theory. In: Proceedings of the 2001 Internat. Con-
ference on Formal Power Series and Algebraic Combinatorics. A Special Volume of Advances
in Applied Mathematics, p. 48 (2001)
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