A method for local approximation of a planar deformation field

Marcin Ligas; Marek Banaś; Anna Szafarczyk

doi:10.2478/rgg-2019-0007

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A method for local approximation of a planar deformation field

Reports on Geodesy and Geoinformatics

Volume 108 (2019): Issue 1 (December 2019)

By: Marcin Ligas, Marek Banaś and Anna Szafarczyk

Open Access

|Oct 2019

Figures & Tables

The effect of swirl-like deformation model

The effect of pincusion deformation model

Table 1

Comparison of statistical measures for true and estimated strain components for regular grid (first rows) and irregular grid (second rows) in a central swirl-like deformation model

	E^B₁₁		E^B₂₂		E^B₁₂ = E^B₂₁

	True	Estimated	True	Estimated	True	Estimated
Minimum	-0.01979	-0.01712	-0.02272	-0.01787	-0.02262	-0.02093
	-0.02251	-0.02352	-0.02288	-0.02230	-0.02288	-0.02330
1st quartile	-0.00208	-0.00171	-0.00245	-0.00208	-0.00189	-0.00224
	-0.00209	-0.00326	-0.00283	-0.00359	-0.00202	-0.00196
Median	0.00001	-0.00002	-0.00001	-0.00005	0.00000	0.00001
	0.00000	-0.00018	0.00003	-0.00018	0.00000	0.00000
3rd quartile	0.00246	0.00194	0.00227	0.00209	0.00188	0.00226
	0.00288	0.00324	0.00210	0.00273	0.00334	0.00371
	0.02325	0.01808	0.02025	0.01713	0.02238	0.02075
Maximum	0.02261	0.02553	0.02303	0.02532	0.02285	0.02042
	0.00003		0.00002		-0.00001
ME	0.00010		0.00014		-0.00024
MAE	0.00110		0.00108		0.00122
	0.00285		0.00261		0.00218
Correlation	0.98327		0.98265		0.96365
coefficient	0.82977		0.86766		0.91781

Table 2

Comparison of statistical measures for true and estimated strain components for regular grid (first rows) and irregular grid (second rows) in a non-central barrel deformation model

	E^B₁₁		E^B₂₂		E^B₁₂ = E^B₂₁

	True	Estimated	True	Estimated	True	Estimated
	-0.00114	-0.00100	-0.00114	-0.00106	-0.00076	-0.00071
Minimum	-0.00091	-0.00092	-0.00089	-0.00090	-0.00055	-0.00062
	-0.00021	-0.00023	-0.00021	-0.00022	-0.00007	-0.00007
1st quartile	-0.00021	-0.00024	-0.00019	-0.00021	-0.00008	-0.00009
Median	-0.00005	-0.00006	-0.00005	-0.00006	0.00000	0.00000
	-0.00008	-0.00011	-0.00006	-0.00007	-0.00001	-0.00002
	-0.00001	-0.00001	-0.00001	-0.00001	0.00000	0.00000
3rd quartile	-0.00001	-0.00001	-0.00001	-0.00001	0.00000	0.00000
	0.00000	0.00000	0.00000	0.00000	0.00009	0.00009
Maximum	0.00000	0.00000	0.00000	0.00000	0.00011	0.00010
ME	0.00000		0.00000		0.00000
	0.00002		0.00002		0.00001
	0.00001		0.00001		0.00000
MAE	0.00003		0.00002		0.00001
Correlation	0.99427		0.99418		0.99925
coefficient	0.98163		0.98620		0.98415

Table 3

Comparison of statistical measures for true and estimated strain components for regular grid (first rows) and irregular grid (second rows) in a non-central pincushion deformation model

	E^B₁₁		E^B₂₂		E^B₁₂ = E^B₂₁

	True	Estimated	True	Estimated	True	Estimated
Minimum	0.00000	0.00000	0.00000	0.00000	-0.00010	-0.00010
	0.00000	0.00000	0.00000	0.00000	-0.00010	-0.00008
	0.00000	0.00001	0.00000	0.00001	-0.00001	-0.00001
1st quartile	0.00000	0.00000	0.00000	0.00000	-0.00001	-0.00001
	0.00002	0.00002	0.00002	0.00002	0.00000	0.00000
Median	0.00002	0.00002	0.00002	0.00003	0.00000	0.00000
3rd quartile	0.00007	0.00008	0.00007	0.00008	0.00001	0.00001
	0.00007	0.00007	0.00007	0.00007	0.00001	0.00001
Maximum	0.00046	0.00040	0.00046	0.00042	0.00031	0.00029
	0.00046	0.00042	0.00044	0.00046	0.00030	0.00029
ME	0.00000		0.00000		0.00000
	0.00000		0.00001		0.00000
	0.00001		0.00001		0.00000
MAE	0.00001		0.00001		0.00001
Correlation	0.99093		0.99057		0.99876
coefficient	0.98281		0.97792		0.98595

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/rgg-2019-0007 | Journal eISSN: 2391-8152 (formerly 0867-3179) | Journal ISSN: 0867-3179

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Language: English

Page range: 1 - 8

Submitted on: May 15, 2019

Accepted on: Aug 5, 2019

Published on: Oct 10, 2019

Published by: Warsaw University of Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

deformation analysis,

polar decomposition,

affine transformation,

rotation matrix,

stretch tensor

Related subjects:

Computer sciences,

Computer sciences, other,

Geosciences,

Geodesy,

Cartography and photogrammetry,

Geosciences, other

© 2019 Marcin Ligas, Marek Banaś, Anna Szafarczyk, published by Warsaw University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 108 (2019): Issue 1 (December 2019)

A method for local approximation of a planar deformation field

Figures & Tables

Figure 1

Figure 2

Figure 3

Table 1

Table 2

Table 3

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