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

Alemam, Mustafa K.; YONG, Bin; Sani-Mohammed, Abubakar

doi:10.2478/arsa-2023-0009

Figures & Tables

The position of overlap area on SRTM DEM

Elevation differences between DEMSRTM and DEMGNSS

Elevation differences between the conventional DEMs merging methods and DEMGNSS

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

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

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

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

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

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

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

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

DEMs of the slopes and aspects for the GNSS points

DEMs of the slopes and aspects for the SRTM data

Slopes distribution of the conventional DEMs merging methods

Aspects distribution of the 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

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

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 additional observations at the study area border

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 additional observations at the study area border

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

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 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
DEM type	MAE	Max.	Min.	RMSE	Median	Whisker (max.)	Whisker (min.)	25^th percentile	75^th percentile
DEM_SRTM	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
Merged DEMs	MAE	Max.	Min.	RMSE	Median	Whisker (max.)	Whisker (min.)	25^th percentile	75^th percentile
MDEM_First	3.26	19.64	0.00	4.41	2.27	8.67	-4.07	0.71	3.89
MDEM_Last	3.63	19.64	0.00	4.78	2.46	8.74	-3.44	1.13	4.17
MDEM_Min	3.59	19.64	0.00	4.75	2.46	8.74	-3.44	1.13	4.17
MDEM_Max	3.30	19.64	0.00	4.44	2.27	8.68	-4.08	0.71	3.89
MDEM_Mean	3.38	19.64	0.00	4.45	2.36	8.43	-3.47	0.99	3.97
MDEM_Blend	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	1^st category high accuracy	2^nd category medium accuracy	3^rd category low accuracy	4^th category very low accuracy
Merged DEMs	diff. ≤ 1 m [%]	1 m < diff. ≤ 3 m [%]	3 m< diff. ≤ 5 m [%]	diff. > 5 m [%]
MDEM_First	21	38	23	18
MDEM_Last	15	40	24	21
MDEM_Mm	15	40	24	21
MDEM_Max	20	38	23	19
MDEM_Mean	16	41	24	19
MDEM_Blend	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
Merged DEMs	MAE	Max.	Min.	RMSE	Median	Whisker (max.)	Whisker (min.)	25^th percentile	75^th percentile
*a. Zeros border*
MDEM⁰_Kriging	2.86	19.97	0.00	4.14	-1.71	5.01	-8.63	-3.52	-0.11
MDEM⁰_IDW	2.98	22.17	0.00	4.30	-1.87	4.91	-8.75	-3.63	-0.22
MDEM⁰_Spline	2.85	20.17	0.00	4.20	-1.60	5.12	-8.55	-3.43	-0.01
MDEM_ANN	2.19	22.01	0.00	3.71	0.37	5.53	-4.69	-0.86	1.70
*b. H border*
MDEM^P_Kriging	1.99	19.54	0.00	3.23	-0.01	4.46	-4.79	-1.32	0.99
MDEM^P_IDW	2.12	21.93	0.00	3.51	-0.06	4.48	-5.11	-1.51	0.88
MDEM^P_Spline	2.15	20.25	0.00	3.48	-0.02	4.89	-5.38	-1.53	1.04
MDEM^P_ANN	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	1^st category high accuracy	2^nd category medium accuracy	3^rd category low accuracy	4^th category very low accuracy
Merged DEMs	diff. ≤ 1 m [%]	1 m < diff. ≤ 3 m [%]	3 m < diff. ≤ 5 m [%]	diff. > 5 m [%]
*a. Zeros border*
MDEM⁰_KRIGING	29	36	19	16
MDEM⁰_IDW	27	37	20	16
MDEM⁰_Spline	31	36	17	16
MDEM_ANN	41	28	19	12
*b. H border*
MDEM^P_KRIGING	46	34	10	10
MDEM^P_IDW	45	34	9	12
MDEM^P_Spline	43	35	10	12
MDEM^P_ANN	71	12	7	10

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

Merged DEMs	Improvement [%]
Merged DEMs	Elevations	Slopes	Aspects
*a. Conventional DEMs merging methods*
MDEM_First	7.74	1.24	20.12
MDEM_Last	0.00	-3.18	42.96
MDEM_Mm	0.63	-3.87	38.14
MDEM_Max	7.11	-3.59	23.11
MDEM_Mean	6.90	6.77	-23.36
MDEM_Blend	7.74	11.19	20.12
*b. Proposed DEMs merging methods*
MDEM⁰_KRIGING	13.39	19.61	20.12
MDEM⁰_IDW	10.04	11.46	20.17
MDEM⁰_Spline	12.13	1.38	20.18
MDEM_ANN	22.38	34.67	40.28
MDEM^P_KRIGING	32.43	29.70	42.49
MDEM^P_IDW	26.57	27.62	41.72
MDEM^P_Spline	27.20	18.51	41.09
MDEM^P_ANN	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]
Merged DEMs	Min.	Max.	Mean	RMSE	Min.	Max.	Mean	RMSE
MDEM_First	-168.94	46.22	3.91	7.15	-352.30	360.97	219.42	89.99
MDEM_Last	0.02	51.63	5.16	7.47	1.00	360.97	237.57	64.26
MDEM_Min	-155.92	50.42	4.93	7.52	-351.15	360.97	234.90	69.68
MDEM_Max	-204.99	50.37	4.33	7.50	-352.30	360.97	221.85	86.62
MDEM_Mean	-123.96	46.22	4.15	6.75	-354.10	360.72	48.57	138.97
MDEM_Blend	-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]
Merged DEMs	Min.	Max.	Mean	RMSE	Min.	Max.	Mean	RMSE
*a. Zeros border*
MDEM⁰_KRIGING	-24.70	40.51	3.60	5.82	-352.30	360.97	219.35	89.99
MDEM⁰_IDW	-27.28	45.06	3.95	6.41	-352.30	360.97	219.39	89.93
MDEM⁰_Spline	-30.56	50.98	4.40	7.14	-352.30	360.97	219.40	89.92
MDEM_ANN	-19.93	32.33	2.92	4.73	-264.23	270.73	164.67	67.28
*b. H border*
MDEM⁰_KRIGING	-21.51	35.01	3.15	5.09	-253.66	259.90	157.93	64.79
MDEM⁰_IDW	-22.14	36.09	3.23	5.24	-257.18	263.51	160.15	65.65
MDEM⁰_Spline	-25.02	41.07	3.64	5.90	-260.00	266.39	161.92	66.36
MDEM_ANN	-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
GNSS surveying type	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	1^st category high accuracy	2^nd category medium accuracy	3^rd category low accuracy	4^th category very low accuracy
	diff. ≤ 1 m [%]	1 m < diff. ≤ 3 m [%]	3 m < diff. ≤ 5 m [%]	diff. > 5 m [%]
DEM_SRTM	14	41	24	21

The summary of slope and aspects differences between DEMSRTM and DEMGNSS

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

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

Figures & Tables

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The differences in elevations between the DEMSRTM and DEMGNSS

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

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

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

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

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

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

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

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

The parameters involved in the ANN algorithm

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

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

The summary of slope and aspects differences between DEMSRTM and DEMGNSS