International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
adopted to create TRI, TR2 and TR5 from the original grid is
optimized to build a TIN model and not to apply a multi-
resolution interpolation. At present, an optimized criterion for
the automatic activation of the splines is under study.
Moreover, new decimation algorithms will be applied.
To honestly compare the storage size required by different
models, they should have the same accuracy. Except for the
POL interpolation, all the final DTMggp's interpolated from
TRI are more accurate than DTMyg(TRI1). In the storage
comparison, coarser DTMorp have been chosen, with
accuracies similar to that provided by our approach. Even the
final DTMgnrp's interpolated from TR2 have better accuracies
than DTMyr(TR2) but, in this case, the coarser grids are
worse. Therefore, for DTMyg&(TR2) and DTMyg(TRS5) the
storage requirements are compared with the grids of Table 3,
for DTMyr(TRI) with the grids reported in Table 5. The
comparisons, in term of storage saving, are reported in Table 6.
At the end, our approach has been compared also with the
Multilevel B Spline Approximation, that represents a different
multi-resolution interpolation approach by bicubic splines (Lee
et al., 1997). To make the comparisons (Tab. 7), the lower level
of MBA whose accuracies are similar to our approach has been
chosen: also the storage requirements of MBA are significantly
bigger than those of our approach.
IR [S(DTMyr) / S(DTMorm)] (%) [S(DTMyr) /
IDW | POL | CRS | SWT | TPS |S(DTMin)] (%)
Im | 1,9% | 0,2% | 3,4% | 3,4% | 1,9% 6,9%
2m | 1,7% | 0,1% | 1,7% | 1,7% | 1,1% 5,2%
Sm | 1,3% | 0,8% | 1,3% | 1,0% | 1,3% 3,1%
Table 6. Storage size comparisons between DTMyr and
DTMcrıp, DTMyın
TR |ResObs(m) ResCheck(m) |TotCff |S (KB) |R (%)
M |RMSE| M | RMSE
Im | 00 | 090 | 001] 1.50 .[ 1.510°| 11019 | 0.5
2m | -0.0 1.22 | -0.0 176. | 3.910. | 2779 | 0.6
5m | 0.0 3.66 | 0.1 299 ]23]0* | 183 1.6
Table 7. Analysis of MBA. TR: interpolated dataset. ResObs,
ResCheck: MBA statistics of the residuals on the used
Observations and the check points. M: mean. RMSE: root mean
square error. TotCff: total number of coefficients of MBA. S:
MBA storage size. R: ratio between the storage requirements of
our algorithm and MBA.
4. CONCLUSIONS
In this paper a new approach has been presented to interpolate
and store a DTM, aimed at saving storing size without losing in
accuracy with respect to classical models. Multi-resolution
bilinear splines are adopted to interpolate the observations and
their coefficients are stored, instead of the interpolated heights.
The coefficients can then be used to reconstruct the height at
any point. The model is defined analytical instead of data
based.
The classical models have been compared with our approach,
considering accuracy and storage requirements. An original
grid has been sampled to produce three TINs with tolerances of
one, two and five meters respectively. Then, the TINs vertices
have been interpolated by different deterministic techniques to
produce grids at different spatial resolutions and the grids have
been compared with the original data. Synthetically, different
interpolation techniques provide similar results and the
accuracy of the grids increases with their resolution: in
particular, accuracies of one, two and five meters are obtained
12
respectively with one, five and ten meters of spatial resolution.
At present, our approach reaches an accuracy slightly worse
than the accuracies provided by the finest grids: this problem is
probably due to a particular interpolation choice that still needs
to be deeply analyzed and optimized. However, for similar
accuracies, our approach allows a significant storage saving
with respect to the classical models: indeed, its storage size is
about 2% of the grids size and 5% of the TINs.
The results are quite satisfactory and justify further studies
finalized to define a complete scheme for the managing of the
data in the server, for their transmission and for their use by the
clients.
ACKNOWLEDGEMENTS
The research has been funded by the INTERREG HELI-DEM
(Helvetia Italy Digital Elevation Model) project.
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