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A Proposed Merging Methods of Digital Elevation Model Based on Artificial Neural Network and Interpolation Techniques for Improved Accuracy

Mustafa K. Alemam
Mustafa K. Alemam
, 
Bin YONG
Bin YONG
 y 
Abubakar Sani-Mohammed
Abubakar Sani-Mohammed
   | 10 oct 2023
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Publicado en línea: 10 oct 2023
Páginas: 122 - 170
Recibido: 06 feb 2023
Aceptado: 09 nov 2023
DOI: https://doi.org/10.2478/arsa-2023-0009
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© 2023 Mustafa K. Alemam et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

ANN architecture
ANN architecture

Figure 2.

First method
First method

Figure 3.

Last method
Last method

Figure 4.

Minimum method
Minimum method

Figure 5.

Maximum method
Maximum method

Figure 6.

Mean method
Mean method

Figure 7.

Blend method
Blend method

Figure 8.

Study area and the reference point R
Study area and the reference point R

Figure 9.

Methodology flow chart
Methodology flow chart

Figure 10.

The two cases of the study area border
The two cases of the study area border

Figure 11.

DEMGNSS for the study area
DEMGNSS for the study area

Figure 12.

SRTM DEM for the study area
SRTM DEM for the study area

Figure 13.

DEM of the overlap area
DEM of the overlap area

Figure 14.

The position of overlap area on SRTM DEM
The position of overlap area on SRTM DEM

Figure 15.

Algorithm steps of the ANN stage
Algorithm steps of the ANN stage

Figure 16.

Box and whisker plot elements
Box and whisker plot elements

Figure 17.

Elevation differences between DEMSRTM and DEMGNSS
Elevation differences between DEMSRTM and DEMGNSS

Figure 18.

Elevation differences between the conventional DEMs merging methods and DEMGNSS
Elevation differences between the conventional DEMs merging methods and DEMGNSS

Figure 19.

Root mean square error of the elevation’s differences between DEMGNSS and the merged DEMs in the case of conventional DEMs merging methods
Root mean square error of the elevation’s differences between DEMGNSS and the merged DEMs in the case of conventional DEMs merging methods

Figure 20.

Elevation differences according to DEMGNSS for the proposed DEM merging methods in the case of zero border and the ANN
Elevation differences according to DEMGNSS for the proposed DEM merging methods in the case of zero border and the ANN

Figure 21.

Errors in elevation between the DEMGNSS and the proposed DEM merging methods in the case of additional observations at the study area border
Errors in elevation between the DEMGNSS and the proposed DEM merging methods in the case of additional observations at the study area border

Figure 22.

Root mean square error of the elevations differences between DEMGNSS and the merged DEMs in the case of PDMMs
Root mean square error of the elevations differences between DEMGNSS and the merged DEMs in the case of PDMMs

Figure 23.

Classification of the difference between DEMGNSS and DEMSRTM into four categories of accuracy
Classification of the difference between DEMGNSS and DEMSRTM into four categories of accuracy

Figure 24.

Four categories of the merged DEMs accuracy resulting from the differences between DEMGNSS and the merged DEMs in the case of CDMMs
Four categories of the merged DEMs accuracy resulting from the differences between DEMGNSS and the merged DEMs in the case of CDMMs

Figure 25.

Classification of the elevations differences between DEMGNSS and the PDMMs in the case of zeros border and ANN
Classification of the elevations differences between DEMGNSS and the PDMMs in the case of zeros border and ANN

Figure 26.

Four categories of the merged DEMs accuracy resulting from the differences between DEMGNSS and merged DEMs by PDMMs in the case of additional observations at the border
Four categories of the merged DEMs accuracy resulting from the differences between DEMGNSS and merged DEMs by PDMMs in the case of additional observations at the border

Figure 27.

DEMs of the slopes and aspects for the GNSS points
DEMs of the slopes and aspects for the GNSS points

Figure 28.

DEMs of the slopes and aspects for the SRTM data
DEMs of the slopes and aspects for the SRTM data

Figure 29.

Slopes distribution of the conventional DEMs merging methods
Slopes distribution of the conventional DEMs merging methods

Figure 30.

Aspects distribution of the conventional DEMs merging methods
Aspects distribution of the conventional DEMs merging methods

Figure 31.

Root mean square error of the slope differences between DEMGNSS and the merged DEMs in the case of conventional DEMs merging methods
Root mean square error of the slope differences between DEMGNSS and the merged DEMs in the case of conventional DEMs merging methods

Figure 32.

Root mean square error of the aspects differences between DEMGNSS and the merged DEMs in the case of CDMMs
Root mean square error of the aspects differences between DEMGNSS and the merged DEMs in the case of CDMMs

Figure 33.

Slopes distribution of the proposed DEMs merging methods in the case of zeros border and the ANN
Slopes distribution of the proposed DEMs merging methods in the case of zeros border and the ANN

Figure 34.

Slopes distribution of the proposed DEMs merging methods in the case of additional observations at the study area border
Slopes distribution of the proposed DEMs merging methods in the case of additional observations at the study area border

Figure 35.

Aspects distribution of the proposed DEMs merging methods in the case of zeros border and the ANN
Aspects distribution of the proposed DEMs merging methods in the case of zeros border and the ANN

Figure 36.

Aspects distribution of the proposed DEMs merging methods in the case of additional observations at the study area border
Aspects distribution of the proposed DEMs merging methods in the case of additional observations at the study area border

Figure 37.

Root mean square error of the slope differences between DEMGNSS and the merged DEMs in the case of PDMMs
Root mean square error of the slope differences between DEMGNSS and the merged DEMs in the case of PDMMs

Figure 38.

Root mean square error of the aspects differences between DEMGNSS and the merged DEMs in the case of PDMMs
Root mean square error of the aspects differences between DEMGNSS and the merged DEMs in the case of PDMMs

Figure 39.

The improvement of elevations, slopes, and aspects by the conventional DEMs merging methods compared to DEMSRTM
The improvement of elevations, slopes, and aspects by the conventional DEMs merging methods compared to DEMSRTM

Figure 40.

The improvement of elevations, slopes, and aspects by the proposed DEMs merging methods in comparison with DEMSRTM
The improvement of elevations, slopes, and aspects by the proposed DEMs merging methods in comparison with DEMSRTM

The differences in elevations between the DEMSRTM and DEMGNSS

DEM type Absolute values statistics Box chart statistics
MAE Max. Min. RMSE Median Whisker (max.) Whisker (min.) 25th percentile 75th percentile
DEMSRTM 3.64 19.49 0.00 4.78 -2.47 3.37 -8.68 -4.16 -1.15

The elevation differences between the conventional DEMs merging methods and the DEMGNSS

Merged DEMs Absolute values statistics Box chart statistics
MAE Max. Min. RMSE Median Whisker (max.) Whisker (min.) 25th percentile 75th percentile
MDEMFirst 3.26 19.64 0.00 4.41 2.27 8.67 -4.07 0.71 3.89
MDEMLast 3.63 19.64 0.00 4.78 2.46 8.74 -3.44 1.13 4.17
MDEMMin 3.59 19.64 0.00 4.75 2.46 8.74 -3.44 1.13 4.17
MDEMMax 3.30 19.64 0.00 4.44 2.27 8.68 -4.08 0.71 3.89
MDEMMean 3.38 19.64 0.00 4.45 2.36 8.43 -3.47 0.99 3.97
MDEMBlend 3.26 19.64 0.00 4.41 2.27 8.67 -4.07 0.71 3.89

Four categories of the merged DEMs accuracy resulting from the differences between DEMGNSS and the merged DEMs in the case of CDMMs

Merged DEMs 1st category high accuracy 2nd category medium accuracy 3rd category low accuracy 4th category very low accuracy
diff. ≤ 1 m [%] 1 m < diff. ≤ 3 m [%] 3 m< diff. ≤ 5 m [%] diff. > 5 m [%]
MDEMFirst 21 38 23 18
MDEMLast 15 40 24 21
MDEMMm 15 40 24 21
MDEMMax 20 38 23 19
MDEMMean 16 41 24 19
MDEMBlend 21 38 23 18

The statistics of elevations differences between the proposed DEM merging methods and the DEMGNSS

Merged DEMs Absolute values statistics Box chart statistics
MAE Max. Min. RMSE Median Whisker (max.) Whisker (min.) 25th percentile 75th percentile
a. Zeros border
MDEM0Kriging 2.86 19.97 0.00 4.14 -1.71 5.01 -8.63 -3.52 -0.11
MDEM0IDW 2.98 22.17 0.00 4.30 -1.87 4.91 -8.75 -3.63 -0.22
MDEM0Spline 2.85 20.17 0.00 4.20 -1.60 5.12 -8.55 -3.43 -0.01
MDEMANN 2.19 22.01 0.00 3.71 0.37 5.53 -4.69 -0.86 1.70
b. H border
MDEMPKriging 1.99 19.54 0.00 3.23 -0.01 4.46 -4.79 -1.32 0.99
MDEMPIDW 2.12 21.93 0.00 3.51 -0.06 4.48 -5.11 -1.51 0.88
MDEMPSpline 2.15 20.25 0.00 3.48 -0.02 4.89 -5.38 -1.53 1.04
MDEMPANN 0.85 4.85 0.00 1.16 0.18 2.77 -2.34 -0.43 0.85

Classification of the elevations differences between DEMGNSS and the merged DEMS in the case of PDMMs

Merged DEMs 1st category high accuracy 2nd category medium accuracy 3rd category low accuracy 4th category very low accuracy
diff. ≤ 1 m [%] 1 m < diff. ≤ 3 m [%] 3 m < diff. ≤ 5 m [%] diff. > 5 m [%]
a. Zeros border
MDEM0KRIGING 29 36 19 16
MDEM0IDW 27 37 20 16
MDEM0Spline 31 36 17 16
MDEMANN 41 28 19 12
b. H border
MDEMPKRIGING 46 34 10 10
MDEMPIDW 45 34 9 12
MDEMPSpline 43 35 10 12
MDEMPANN 71 12 7 10

The improvement in elevations, slopes, and aspects by the merged DEMs compared to DEMSRTM based on RMSE

Merged DEMs Improvement [%]
Elevations Slopes Aspects
a. Conventional DEMs merging methods
MDEMFirst 7.74 1.24 20.12
MDEMLast 0.00 -3.18 42.96
MDEMMm 0.63 -3.87 38.14
MDEMMax 7.11 -3.59 23.11
MDEMMean 6.90 6.77 -23.36
MDEMBlend 7.74 11.19 20.12
b. Proposed DEMs merging methods
MDEM0KRIGING 13.39 19.61 20.12
MDEM0IDW 10.04 11.46 20.17
MDEM0Spline 12.13 1.38 20.18
MDEMANN 22.38 34.67 40.28
MDEMPKRIGING 32.43 29.70 42.49
MDEMPIDW 26.57 27.62 41.72
MDEMPSpline 27.20 18.51 41.09
MDEMPANN 75.73 54.83 52.22

Statistics of the slope and aspects differences between DEMGNSS and the merged DEMs in the case of conventional DEMs merging methods

Merged DEMs Slope [%] Aspects [deg]
Min. Max. Mean RMSE Min. Max. Mean RMSE
MDEMFirst -168.94 46.22 3.91 7.15 -352.30 360.97 219.42 89.99
MDEMLast 0.02 51.63 5.16 7.47 1.00 360.97 237.57 64.26
MDEMMin -155.92 50.42 4.93 7.52 -351.15 360.97 234.90 69.68
MDEMMax -204.99 50.37 4.33 7.50 -352.30 360.97 221.85 86.62
MDEMMean -123.96 46.22 4.15 6.75 -354.10 360.72 48.57 138.97
MDEMBlend -134.84 41.07 3.51 6.43 -352.30 360.97 219.42 89.99

Corners’ coordinates of the study area and the reference point R

Point UTM Coordinates Geodetic Coordinates
Easting Northing Orthometric height (H) Longitude Latitude Ellipsoid height (h)
m m m ° ′ ″ ° ′ ″ m
P1 327256.448 3021899.541 86.214 31 15 15.321 27 18 33.418 98.977
P2 328756.137 3023120.616 102.135 31 16 9.246 27 19 13.765 114.913
P3 330325.359 3022440.421 127.317 31 17 6.662 27 18 52.371 140.085
P4 328521.254 3020944.203 96.403 31 16 1.802 27 18 2.955 109.153
R 329450.670 3019874.311 109.047 31 16 36.137 27 17 28.615 121.783

Characteristics of the slope and aspects differences between DEMGNSS and the merged DEMs in the case of PDMMs

Merged DEMs Slope [%] Aspects [deg]
Min. Max. Mean RMSE Min. Max. Mean RMSE
a. Zeros border
MDEM0KRIGING -24.70 40.51 3.60 5.82 -352.30 360.97 219.35 89.99
MDEM0IDW -27.28 45.06 3.95 6.41 -352.30 360.97 219.39 89.93
MDEM0Spline -30.56 50.98 4.40 7.14 -352.30 360.97 219.40 89.92
MDEMANN -19.93 32.33 2.92 4.73 -264.23 270.73 164.67 67.28
b. H border
MDEM0KRIGING -21.51 35.01 3.15 5.09 -253.66 259.90 157.93 64.79
MDEM0IDW -22.14 36.09 3.23 5.24 -257.18 263.51 160.15 65.65
MDEM0Spline -25.02 41.07 3.64 5.90 -260.00 266.39 161.92 66.36
MDEMANN -13.71 21.99 2.02 3.27 -211.38 216.58 131.73 53.82

The parameters involved in the ANN algorithm

Epoch Goal Max_fail Min_fail Mu Learning rate
1000 0 6 1e-7 0.001 0.01

Root Mean Square Error (RMSE) of the different GNSS surveying types for TRIMBLE receivers (R8s)

GNSS surveying type RMSE
Horizontal Vertical
Static 3 mm + 0.1 ppm 3.5 mm + 0.4 ppm
PPK 8 mm + 1 ppm 15 mm + 1 ppm
RTK 8 mm +1 ppm 15 mm + 1 ppm

Classification of the difference between DEMGNSS and DEMSRTM into four categories of accuracy

DEM type 1st category high accuracy 2nd category medium accuracy 3rd category low accuracy 4th category very low accuracy
diff. ≤ 1 m [%] 1 m < diff. ≤ 3 m [%] 3 m < diff. ≤ 5 m [%] diff. > 5 m [%]
DEMSRTM 14 41 24 21

The summary of slope and aspects differences between DEMSRTM and DEMGNSS

DEM type Slope [%] Aspects [deg]
Min. Max. Mean RMSE Min. Max. Mean RMSE
DEMSRTM -18.47 50.47 0.30 7.24 -351.69 359.07 32.67 112.65
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