Efficient Continuous DEM Reconstruction under Limited Target-Resolution Supervision

Zekai Shi; Meng Zhang; Haokun Zhang; Bo Zhang

cs.CVSep 24, 2026

Efficient Continuous DEM Reconstruction under Limited Target-Resolution Supervision

Authors: Zekai Shi, Meng Zhang, Haokun Zhang, Bo Zhang

Organizations: School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China · School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University, Xi’an, 710072, China

Abstract

High-resolution digital elevation models (DEMs) support Earth observation applications, but paired training references are often available only at coarser output resolutions. Reconstructing finer terrain grids therefore requires both effective transfer beyond the supervised scale and control of dense-query computation. To address this problem, SCOPE learns a continuous terrain representation from coarser-resolution pairs. It predicts a latent coefficient field on the low-resolution grid and reuses local Fourier residual functions through basis evaluation and geometry-guided ensemble fusion. This separates high-dimensional coefficient prediction from output-grid construction. Experiments on geographically distributed land--ocean samples assess supervised reconstruction, unseen-scale inference, cross-domain generalization, and theoretical computation. SCOPE leads the compared methods across six metrics in the main supervised-scale evaluation. At an unseen factor three times the training factor, land reconstruction reduces RMSE and MAE by approximately 12% relative to bicubic interpolation, with errors close to target-scale fine-tuning. Ninefold output density increases counted multiply--accumulate operations by only about 2%. Frozen-model validation on held-out external marine regions reduces RMSE relative to the DEM-specific implicit baseline EBCF-CDEM by approximately 19% under self-downsampling and 2% with cross-product inputs, while also yielding lower RMSE than LIIF-MS in both settings. These results demonstrate the value of reusable coefficient fields for accurate reconstruction beyond the supervised resolution with low incremental arithmetic cost.

Figures & tables

Figure 1: Schematic architectural trends in scale-dependent computational burden from

1\times

30\times

for fixed-grid reconstruction, coordinate-wise INR decoding, and SCOPE. SCOPE concentrates coefficient prediction on the LR grid and uses lightweight local evaluation for denser output. Solid curves extend through

15\times

; dashed extensions illustrate conceptual trends to

30\times

. Markers identify the supervised

5\times

scale and the maximum accuracy-evaluation factor of

15\times

. Quantitative GMACs and computation–latency trajectories are reported in Sec. 5 .

Figure 2: Conceptual distinction among representative continuous reconstruction methods and SCOPE. The comparison highlights the predicted object, supervision setting, and decoding mechanism: query-wise implicit value prediction, query-centered frequency-aware reconstruction, DEM-specific elevation-bias prediction, and reusable latent coefficient-field evaluation.

Product	Coverage	Grid spacing	Role in this study
TanDEM-X EDEM	Global land	30 m	Land HR reference
GEBCO_2024	Global ocean and land	$\sim$ 450 m	Ocean background
NOAA CRMs (A–C, E)	U.S. coastal zones	$\sim$ 30 m	Land–sea transition reference
Torres Strait 2023 (F)	139–146 ∘ E, 8–13 ∘ S	30 m	Reef and island reference
Bass Strait 2022 (G)	143–149 ∘ E, 38–41 ∘ S	30 m	Shelf bathymetry reference
EMODnet DTM 2024 (D)	Caribbean tile	$\sim$ 100 m	Fixed- $5\times$ evaluation only

Table 1: DEM and bathymetric source products and their experimental roles. Parenthetical region identifiers refer to Fig. 3 . The first six products support the main study; GEBCO_2023 and the four regional products below it support frozen-model external evaluation. All external reference rasters are prepared on a nominal 90 m evaluation grid. The external subset contains 12 reference rasters and 3,825 valid patches; Great Barrier Reef blocks B–D are used, with block A excluded for spatial overlap with the main-study region.

Figure 3: Geographic distribution and coverage context of the source products. Brown and purple outlines distinguish main-study and external-evaluation product extents, respectively. A, B, C, and E identify NOAA CRMs Vols. 10, 7, 1–5, and 9; D identifies the EMODnet DTM 2024 Caribbean tile; F and G identify Torres Strait 2023 and Bass Strait 2022. H 1 /H 2 , I, J, and K identify CHS NONNA-100, MH370 bathymetry, Northern Australia, and Great Barrier Reef sources, respectively. The evaluated subsets are defined in Table 1 and Sec. 2.3 . Red triangles locate representative regions, insets enlarge selected areas, and gray shading marks latitudes outside the $65^{\circ}$ N– $65^{\circ}$ S study limits.

Figure 4: Architecture of SCOPE network. (a) Overall framework. The LR DEM is encoded into an LR-aligned terrain feature field and transformed by NAF into a latent coefficient field. For a continuous query coordinate $\mathbf{q}$ , coefficients sampled at neighboring LR locations $\mathbf{x}_{i}$ are evaluated using the relative offsets $\Delta\mathbf{q}_{i}$ to produce local residual candidates $r_{i}(\mathbf{q})$ . These candidates are fused by LAE into $r(\mathbf{q})$ and added to the bicubic base surface $B(\mathbf{q})$ . (b) LAE module. Four neighboring residual candidates are fused using geometry-guided compatibility weights.

Category	Variant	RMSE $\downarrow$	MAE $\downarrow$	Slope $\downarrow$	Aspect $\downarrow$	PSNR $\uparrow$	Corr. $\uparrow$
Full model	SCOPE network ∗	4.150	2.816	12.051	46.473	77.48	0.659
Base & Fusion	No base	4.682	3.238	14.718	57.076	73.88	0.521
	Bilinear base	4.153	2.817	12.051	46.571	77.43	0.659
	Nearest base	4.176	2.830	12.223	47.227	77.19	0.651
	Bilinear fusion	4.186	2.830	12.285	47.013	77.16	0.652
Refinement & Loss	No post-refinement	4.885	3.372	17.468	63.935	73.64	0.436

Table 2: Ablation study of the SCOPE network under the fixed

5\times

reconstruction setting. Slope and Aspect denote slope-based and aspect-based reconstruction errors, respectively. Corr. denotes the slope-consistency score between reconstructed and reference terrain structures.

Category	Method	Params (M)	GMACs	RMSE $\downarrow$	MAE $\downarrow$	Slope $\downarrow$	Aspect $\downarrow$	PSNR $\uparrow$	Corr. $\uparrow$
Interpolation	Bicubic	0	–	4.733	3.205	13.304	47.041	76.16	0.640
	Bilinear	0	–	5.551	3.747	14.172	49.389	74.81	0.618
	Nearest	0	–	8.059	5.535	36.380	80.548	71.06	0.216
Fixed-scale SR	SRCNN	0.479	19.150	7.844	3.890	13.858	50.629	67.75	0.576
	EDSR	21.582	34.577	4.417	2.973	12.981	49.803	75.36	0.612
	SwinIR	17.555	41.848	4.456	3.067	13.095	50.560	74.82	0.606

Table 3: Quantitative comparison with interpolation, fixed-scale super-resolution, and implicit neural reconstruction baselines under the fixed

5\times

setting. All baseline architectures follow their official implementations or recommended model configurations and are trained and evaluated under the unified data and evaluation protocol. Params and GMACs are reported for batch size 1 with a

40\times 40

LR input and a

200\times 200

output, counting convolution, linear projection, attention matrix multiplication, and explicit basis-evaluation matrix multiplication. Red and blue indicate the best and second-best results for each metric, respectively. Lower RMSE, MAE, Slope, and Aspect indicate better performance, while higher PSNR and Corr. indicate better performance.

Figure 5: Fixed-scale visual comparison on a representative land patch under the $5\times$ reconstruction setting. Panels (a)–(g) show the LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network, respectively, while panel (h) shows the GT HR DEM. All panels are compared over the same elevation range. The enlarged regions highlight local terrain details, where the SCOPE network better preserves ridge–valley structures and fine-scale relief variations.

Figure 6: Fixed-scale visual comparison on a representative marine and coastal patch under the $5\times$ reconstruction setting. Panels (a)–(g) show the LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network, respectively, while panel (h) shows the GT HR DEM. All panels are shown with a shared elevation range. The enlarged regions illustrate the reconstruction of coastal and bathymetric transition structures, where the SCOPE network produces a sharper and more coherent terrain surface.

Figure 7: Absolute elevation-error comparison on the representative land patch under the fixed $5\times$ reconstruction setting. Panels (a)–(g) show the absolute elevation errors of the LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network, respectively, with respect to the GT HR DEM shown in panel (h). The enlarged regions highlight error distributions around local ridge–valley structures.

Figure 8: Absolute elevation-error comparison on the representative marine and coastal patch under the fixed $5\times$ reconstruction setting. Panels (a)–(g) show the absolute elevation errors of the LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network, respectively, with respect to the GT HR DEM shown in panel (h). The enlarged regions emphasize errors near coastal and bathymetric transition zones.

Figure 9: Elevation profile comparison on representative land and ocean patches under the fixed

5\times

reconstruction setting. For each case, the HR reference and SCOPE network reconstruction are shown with the same A–B profile line, while the full and zoomed elevation profiles compare HR, LR, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network. The zoomed profiles provide a detailed view of local peak–valley reconstruction fidelity.

Figure 10: Aspect-based directional terrain comparison on the representative land patch under the fixed $5\times$ reconstruction setting. The HR reference, LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network are visualized with the same cyclic aspect color mapping. The enlarged regions highlight local ridge–valley directional structures, where the SCOPE network better preserves fine-scale terrain orientation and directional continuity.

Figure 11: Aspect-based directional terrain comparison on the representative marine and coastal patch under the fixed $5\times$ reconstruction setting. The HR reference, LR input, bicubic interpolation, EDSR, SwinIR, LIIF, EBCF-CDEM, and the SCOPE network are visualized with the same cyclic aspect color mapping. The enlarged regions emphasize coastal and bathymetric directional transitions, where the SCOPE network produces aspect patterns that are more consistent with the HR terrain structure.

Method	RMSE $\downarrow$	MAE $\downarrow$	Slope $\downarrow$	Aspect $\downarrow$	PSNR $\uparrow$	Corr. $\uparrow$
Bicubic	8.452	6.145	15.230	57.081	69.53	0.537
Bilinear	8.989	6.544	15.931	57.565	69.17	0.528
Nearest	10.774	7.733	37.668	83.901	67.16	0.172
SCOPE-Direct	8.164	5.880	15.184	60.453	69.05	0.507
SCOPE-Transfer	8.546	6.223	14.963	61.152	68.78	0.496

Table 4: Matched-product supervision and transfer in the existing LR–HR paired experiment, distinct from the frozen external tests in Table 5 . SCOPE-Direct is trained directly on matched paired data, while SCOPE-Transfer is trained with synthetic downsampling and evaluated on the paired data. Red and blue indicate the best and second-best results for each metric, respectively. Lower RMSE, MAE, Slope, and Aspect indicate better performance, while higher PSNR and Corr. indicate better performance.

Figure 12: Cross-dataset visual comparison on a representative land patch under the matched LR–HR paired setting. The HR reference, LR input, bicubic interpolation, and SCOPE network reconstruction are shown together with local error and aspect insets. Here, the SCOPE network corresponds to the directly trained SCOPE-Direct variant reported in Table 4 .

Figure 13: Cross-dataset visual comparison on a representative marine and coastal patch under the matched LR–HR paired setting. The HR reference, LR input, bicubic interpolation, and SCOPE network reconstruction are shown together with local error and aspect insets. Here, the SCOPE network corresponds to the directly trained SCOPE-Direct variant reported in Table 4 .

Input setting	Method	RMSE $\downarrow$	MAE $\downarrow$	Slope $\downarrow$	Aspect $\downarrow$	PSNR $\uparrow$	Corr. $\uparrow$
Self-downsampled	Bicubic	3.7834	2.3876	15.0834	51.3582	77.4655	0.6045
	LIIF-MS	73.6168	73.3150	15.7968	53.3109	44.5991	0.5898
	EBCF-CDEM	4.2196	2.8100	20.5145	71.4522	73.6952	0.3776
	EDSR	3.5019	2.2343	14.1920	52.4866	77.5683	0.5953
	SCOPE-5F	3.4009	2.1734	13.9307	51.0133	78.3732	0.6241
Matched GEBCO_2023	Bicubic	9.0587	5.7358	17.6567	68.0274	68.6858	0.4574

Table 5: Frozen-model external marine evaluation at

5\times

(nominal

450\rightarrow 90

m), using the same 12 reference rasters and 3,825 valid patches per method in both input settings. All metrics are averaged over patches. Slope, Aspect, and Corr. follow the definitions used throughout the paper and correspond to RMSE-Slope, RMSE-Aspect, and SlopeCorr in the evaluation logs. Red and blue indicate the best and second-best distinct values within each setting, including ties at the displayed precision.

Method	Params (M)	GMACs	RMSE $\downarrow$	MAE $\downarrow$	Slope $\downarrow$	Aspect $\downarrow$	PSNR $\uparrow$	Corr. $\uparrow$
Bicubic	0	–	7.657	5.212	21.468	71.386	69.57	0.447
LIIF-MS	15.375	946.533	8.620	5.909	22.293	73.185	68.61	0.426
EBCF-CDEM	1.450	84.799	10.265	7.215	29.331	96.334	65.01	0.182
SCOPE-5F	15.400	26.208	6.753	4.609	19.824	71.534	70.45	0.455
SCOPE-5MS	15.400	26.208	6.769	4.613	19.915	71.667	70.43	0.454
SCOPE-15D	15.400	26.208	6.789	4.629	19.839	72.028	70.37	0.446

Table 6: Quantitative comparison at the target

15\times

reconstruction scale. LIIF-MS is trained with

5\times

as the primary scale and random downsampling across

\{2\times,3\times,4\times\}

for multi-scale supervision. SCOPE-5F denotes fixed

5\times

training only, SCOPE-5MS denotes multiscale training up to

5\times

, SCOPE-15D denotes direct

15\times

training, and SCOPE-15FT denotes

5\times

training followed by

15\times

fine-tuning. Params and GMACs are reported for batch size 1 with a

40\times 40

LR input and a

600\times 600

Figure 14: Scale-transfer behavior of different SCOPE network training protocols from

2\times

15\times

. The top row reports absolute RMSE, MAE, and slope error, while the bottom row reports metric differences computed as each compared protocol minus SCOPE-5F at the same scale. SCOPE-5F denotes fixed

5\times

training, SCOPE-5MS denotes multiscale training, SCOPE-15D denotes direct

15\times

training, and SCOPE-15FT denotes

5\times

training followed by

15\times

fine-tuning.

Fusion	RMSE	MAE	Slope	Aspect
MLP-based LAE	4.150	2.816	12.051	46.473
Transformer-style fusion	4.186	2.832	12.302	47.061

Table 7: Comparison between MLP-based LAE and Transformer-style local fusion. Lower values indicate better performance.

Figure 15: Computation–latency trajectories across reconstruction scales. Both axes are logarithmic; lower-left positions indicate lower cost. Marker sizes encode

2\times

3\times

5\times

10\times

15\times

20\times

, and

30\times

; lines connect increasing factors within each model. Dashed lines partition the cost space.

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Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

Abstract

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