Terrain Map Generation (TMG)

Updated 12 July 2026

Terrain Map Generation (TMG) is the computational synthesis of digital terrains using methods like procedural noise, simulation, and deep generative models.
It employs diverse representations such as heightmaps, DEMs, and BEV semantic maps to address challenges from local reconstruction to planetary-scale mapping.
Practical implementations leverage noise algorithms, erosion simulations, and neural style transfer to control terrain features including slope, roughness, and semantic details.

Terrain Map Generation (TMG) denotes the computational generation of digital terrain representations, including heightmaps, Digital Elevation Models (DEMs), textured terrain pairs, bird’s-eye-view (BEV) semantic terrain maps, and hierarchical outdoor map structures. The recent literature spans procedural synthesis, interpolation and extrapolation from incomplete spatial surveys, learning-based generation from remote sensing data, and task-driven terrain mapping for simulation, virtual reality, and autonomous systems. Across these settings, recurring objectives are morphological fidelity to real landscapes, controllability over slope, roughness, or semantics, computational efficiency, reproducibility, and scalability from local tiles to planetary or effectively unbounded worlds (Merizzi, 2024, Garg et al., 2022, Wallin, 24 Jun 2025, Goslin, 9 Dec 2025).

1. Representations and problem formulations

TMG is organized around several distinct map representations. In procedural and generative work, the dominant object is the heightmap, a 2D grid whose scalar values encode elevation. In remote-sensing and reconstruction settings, the corresponding term is usually DEM, often represented as a raster organized as a 2D array with elevation per grid cell. Other works generate paired modalities, such as RGB satellite textures aligned with DEMs or heightmaps, while robotics-oriented systems increasingly treat terrain as a semantic or metric-semantic map rather than only an elevation field (Panagiotou et al., 2020, Borne--Pons et al., 9 Apr 2025, Kim et al., 2024, Samuelson et al., 23 Sep 2025).

Representation	Role	Representative works
Heightmap / DEM	Elevation field for synthesis, reconstruction, or rendering	(Merizzi, 2024, Easson et al., 2019)
Paired RGB + DEM / heightmap	Joint geometry and appearance generation	(Panagiotou et al., 2020, Higo et al., 7 May 2025)
BEV semantic terrain map	Dense terrain classification for navigation	(Kim et al., 2024)
Terrain-aware 3DSG	Metric-semantic outdoor abstraction with places and regions	(Samuelson et al., 23 Sep 2025)

These representational choices induce different technical problem statements. A heightmap generator may optimize for realism, diversity, or artist control; a DEM updater may prioritize geometric accuracy and computational complexity; a BEV semantic terrain estimator must fuse appearance and geometry under uncertainty; and a terrain-aware 3D scene graph must support downstream querying and navigation. This suggests that TMG is not a single algorithmic task but a family of terrain-centric generation and mapping problems whose outputs differ in topology, semantics, and intended downstream use.

2. Procedural, analytic, and simulation-based terrain synthesis

Procedural methods remain a foundational branch of TMG. A representative hybrid approach generates initial content images using either multi-layered smoothed Gaussian noise or Perlin noise, then refines them by transferring morphology from real-world heightmaps (Merizzi, 2024). The Gaussian-noise variant creates multiple noise layers at different scales, smooths them by convolution with Gaussian kernels, upscales them, and averages them into a non-uniform base terrain. The Perlin variant sums interpolated values over multiple octaves with increasing frequency and diminishing amplitude, producing smoother and more coherent structures. In a different line, a modular Python library constructs terrains by chaining modules such as Basic, Octaves, Plane, Gaussian, WeightedSum, SetSlope, and SetRoughness, thereby making slope, roughness, and object counts explicitly parameterizable and reproducible (Wallin, 24 Jun 2025).

Simulation-based procedural work often encodes geomorphic processes more directly. A graph-based fluvial erosion algorithm models each tile as draining to a single downslope neighbor, forming a drainage tree that supports efficient flow accumulation, gorge carving, and constrained erosion. Its core erosion term uses the stream power law

$\Delta h = k_e D^n s^m ,$

with erosion proportional to drainage and slope, while additional mechanisms introduce height constraint maps, rainfall-driven erosion strength, and realistic gorge carving (Lim et al., 2022). The same paper argues that efficiency, interactivity, variety, realism, and independence are distinct evaluation dimensions, with independence defined as the degree to which the system requires external resources to achieve high-quality results.

Other procedural branches focus on geometric style or application-specific terrain statistics. A low-poly method abandons the regular grid in favor of Poisson Disc Sampling and Delaunay triangulation, then applies layered Perlin noise, terrace banding, and biome-specific coloring to generate stylized terraced terrain with vegetation (Tivolt, 14 May 2025). A multifractal method for off-road testing uses the 3D Weierstrass-Mandelbrot function to control roughness through the fractal dimension $D$ , combines low-, mid-, and high-frequency DEMs, and classifies local roughness by gradient thresholds into low-, semi-, and high-roughness areas (Majhor et al., 4 Jan 2025). For planetary games, multi-resolution rendering couples a low-resolution spherical base mesh and quadtree control structure with tessellation shaders and fractal noise, so that coarse planetary form and close-range detail are generated at different levels of detail without preprocessing (d'Oliveira et al., 2018).

Procedural generation also includes example-driven local pattern synthesis. A WaveFunctionCollapse adaptation for terrain uses SRTM elevation data, but replaces raw heights with local slopes

$G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$

extracts $2 \times 2 \times 2$ slope patterns, learns adjacency rules, and reconstructs heights from generated gradients (Dajkhosh, 2024). This shift from absolute elevation to gradient structure is intended to preserve landform organization while reducing pattern diversity enough for WFC constraint propagation to remain effective.

Deep generative modeling entered TMG first through adversarial pipelines. One early two-stage system uses a DCGAN to synthesize heightmaps and a pix2pix conditional GAN to map those heightmaps to realistic textures, using openly available NASA heightmap and texture imagery from the "Visible Earth" project. The dataset consists of paired $512 \times 512$ crops filtered to avoid mostly-black ocean regions and to focus training on a reference biome such as desert (Beckham et al., 2017). A related 3D terrain pipeline first generates plausible RGB satellite images with Progressive Growing GANs, then predicts a corresponding DEM with a pix2pix-style CGAN using a U-Net generator and PatchGAN discriminator, combining the result into a textured 3D terrain mesh (Panagiotou et al., 2020).

A different neural route retains procedural content control while importing real geomorphology through Neural Style Transfer. The method in (Merizzi, 2024) uses a pre-trained VGG-19 network to transfer morphological “style” from a real-world heightmap to a procedurally generated content map. Its optimization objective combines content loss, style loss via Gram matrices, and total variation loss:

$Loss = \alpha L_{content} + \beta L_{style} + \gamma L_{TV},$

with empirically chosen weights

$\alpha = 1 \times 10^{-5},\ \beta = 2.5 \times 10^{-11},\ \gamma = 1 \times 10^{-10}.$

The paper reports optimization over 2000 iterations using SGD with exponential decay, about 2 min 46 s per image on a GPU, and SSIM improvements relative to the source terrain class, including $0.180 \rightarrow 0.208$ for mountains, $0.232 \rightarrow 0.241$ for rivers, and $0.346 \rightarrow 0.468$ for deserts. The same workflow allows hand-drawn features, such as a cross-shaped ridge, to be converted into realistic mountain terrain.

Recent work increasingly models geometry and appearance jointly. MESA adapts Stable Diffusion 2.1 to generate co-registered optical images and DEMs from text prompts using a shared VAE, a frozen CLIP text encoder, and the Major TOM Core-DEM dataset, which contains about $D$ 0 million $D$ 1 km patches derived from Copernicus DEM and Sentinel-2 data (Borne--Pons et al., 9 Apr 2025). Prompts combine biome, geological region or landform, country, and month. TerraFusion also uses a latent diffusion model, but operates on a concatenated latent for heightmap and texture, adds a heightmap-specific VAE, and introduces sketch-based control through a ControlNet-style adapter. Its best reported texture quality is $D$ 2, compared with $D$ 3 for training from scratch, $D$ 4 for a GAN-based PSGAN baseline, and $D$ 5– $D$ 6 for two-stage baselines (Higo et al., 7 May 2025).

The trajectory from GAN pipelines to joint diffusion models reflects a recurring theme in TMG: terrain geometry and surface appearance are statistically coupled. The literature increasingly treats this coupling as a first-class modeling target rather than a downstream translation problem.

4. Multi-scale, large-area, and infinite terrain generation

Scale is a defining technical axis in TMG. For planetary terrain in games, the principal challenge is to preserve visual continuity across changes in observer distance while respecting large-scale curvature and local detail. A multi-resolution planetary system addresses this by combining a low-resolution planetary base mesh, quadtree-based level-of-detail management, GPU tessellation, and procedural height displacement, with additional fractal detail synthesized in the fragment shader at the highest level of detail (d'Oliveira et al., 2018). Edge cracks between LOD patches are handled by bisecting mesh edges as needed.

At terrestrial scales, EarthGen formulates large-area terrain imagery generation as a cascade of super-resolution diffusion models combined with tiled synthesis. The model factors generation across scales, with each level performing a $D$ 7 super-resolution conditioned on the previous scale, and uses Mixture of Diffusers to blend denoising scores from overlapping tiles. On an extreme $D$ 8 super-resolution benchmark, the reported FID/KID values are $D$ 9 on a general set and $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 0 on urban data, compared with $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 1 for the Stable Diffusion x4 upscaler, $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 2 for Real-ESRGAN, $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 3 for HAT, $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 4 for LIIF, and $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 5 for interpolation (Sharma et al., 2024). The same system is presented as scalable to “thousands of square kilometers” and extendable to controllable world generation and 3D scene generation.

Terrain Diffusion pushes the same axis further by redefining the procedural-noise role for the diffusion era. Its central claim is that InfiniteDiffusion enables seamless infinite extent, seed-consistency, and constant-time random access, properties historically associated with Perlin noise rather than learned models. The method uses a hierarchical stack of diffusion models to couple planetary context with local detail, a compact Laplacian encoding to stabilize Earth-scale dynamic ranges, and few-step consistency distillation for real-time inference (Goslin, 9 Dec 2025). A plausible implication is that the traditional distinction between “fast but unrealistic” procedural noise and “realistic but bounded” learned generation is becoming less rigid.

Large-area terrain map generation also includes terrain updating from sparse contemporary evidence. LTM leverages outdated DEMs as geometric priors for image-based reconstruction in wildfire-prone landscapes, and aligns pixels to DEM cells using on-raster ray tracing rather than expensive feature matching. The paper states a DEM-based alignment complexity of $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 6, versus much worse feature-matching complexity such as $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 7, and describes the raster representation as computationally efficient and scalable for areas as large as $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 8 km (Fu et al., 9 Jul 2026). Here the output is not merely a new image tile but a high-fidelity depth map and updated semantic fuel map.

5. Terrain generation for sensing, virtual reality, and autonomous systems

A substantial branch of TMG begins not from a random seed or text prompt but from incomplete or noisy measurements. In terrain surveying, shadow zones arise in photogrammetry, LiDAR, Sonar, and seismic studies, requiring interpolation and extrapolation before a continuous terrain model can be formed. One mathematically explicit framework normalizes discrete spatial data with a Gaussian distribution and a Poisson transition, represents the continuous terrain surface using a Laurent series, performs analytic tests through Riemann mapping, and uses Cauchy’s residue theorem and Picard’s theorem to handle singularities and quantify certainty (Garg et al., 2022). Its certainty score is grounded in a Gaussian probability density, with lower certainty near gaps or singularities.

A more engineering-oriented automatic DTM pipeline ingests massive LiDAR point clouds, removes statistical outliers using kernel density estimation, rasterizes returns, extracts ground points using lowest and highest returns per cell, fits a smooth polynomial surface with SVD, fills holes by inpainting, and renders the result with textures, normal maps, and multiple LoDs for real-time VR (Easson et al., 2019). The authors emphasize that the pipeline is non-iterative and designed for large-scale point clouds with real-time performance over large terrestrial landforms.

For off-road autonomy, terrain generation often means semantic map estimation rather than only elevation synthesis. UFO generates dense BEV terrain classification maps from a single RGB image and LiDAR sweep by fusing image and LiDAR features at multiple scales and by training on uncertainty-aware pseudo-labels aggregated from temporally aligned image segmentations. Pseudo-label uncertainty is computed as normalized class entropy, and the training loss downweights ambiguous cells (Kim et al., 2024). On RELLIS-3D, the reported results are $G_x[x,y] = H[x+1,y]-H[x,y], \qquad G_y[x,y] = H[x,y+1]-H[x,y],$ 9 accuracy and $2 \times 2 \times 2$ 0 mIoU, compared with $2 \times 2 \times 2$ 1 for a LiDAR-only BEVNet baseline and about $2 \times 2 \times 2$ 2 accuracy for image-only baselines. The improvement is described as especially relevant for classes requiring both geometry and texture understanding, such as dirt, puddle, grass, and bush.

Terrain maps also function as test environments for learning and control. A curriculum-RL study compares Perlin, Diamond Square, Worley, CPPN, and GAN-generated terrains using representation-agnostic MAP-Elites descriptors such as Terrain Ruggedness Index, Topographic Position Index, roughness, and a traversability predictor. CPPN achieves the highest coverage, such as $2 \times 2 \times 2$ 3 for the $2 \times 2 \times 2$ 4 archive, whereas GAN coverage is only $2 \times 2 \times 2$ 5, and Perlin yields faster learning due to smoother regularity (Howard et al., 2022). A complementary off-road evaluation study uses 60 multifractal terrains and 20 straight-line missions per terrain, and reports that increasing the high-frequency fractal dimension from $2 \times 2 \times 2$ 6 and $2 \times 2 \times 2$ 7 decreases median vehicle success rate by $2 \times 2 \times 2$ 8 and $2 \times 2 \times 2$ 9, respectively, while increasing RMS vertical accelerations, pitch and roll rates, and traversal times for successful runs (Majhor et al., 4 Jan 2025).

At a higher semantic level, Terra constructs a terrain-aware outdoor 3D scene graph from sparse LiDAR geometry and visual semantics. It uses LIO-SAM as a geometric backbone, terrain segmentation with YOLO-v11n-seg, CLIP embeddings for terrain classes and open-set objects, and per-terrain generalized Voronoi diagrams to build terrain-aware place nodes. Hierarchical regions are then formed by agglomerative or spectral clustering over combined geometric and semantic distances (Samuelson et al., 23 Sep 2025). In this setting, terrain map generation becomes the production of a lightweight, task-agnostic metric-semantic graph suitable for object retrieval, region monitoring, and terrain-aware navigation.

6. Evaluation criteria, controllability, and recurrent issues

TMG lacks a single canonical evaluation protocol. Instead, the literature uses metrics that are tightly coupled to representation and application. Morphological similarity is measured with SSIM in neural style transfer terrain synthesis (Merizzi, 2024). WFC-based terrain generation compares histograms of slope magnitudes and reports mean, median, and standard deviation of slope distributions (Dajkhosh, 2024). Diffusion-based imagery models use FID, KID, or $512 \times 512$ 0 and correlation between textures and heightmaps (Sharma et al., 2024, Higo et al., 7 May 2025). Off-road semantic mapping uses IoU, mIoU, and accuracy (Kim et al., 2024). Image-plus-DEM wildfire mapping evaluates depth with RMSE, segmentation with F-1 score or per-cell classification error, and sim-to-real fidelity with SSIM, LPIPS, and FID (Fu et al., 9 Jul 2026). Simulation papers add task metrics such as success rate, RMS vertical acceleration, RMS pitch and roll rates, traversal time, archive coverage, and maximum difficulty reached (Majhor et al., 4 Jan 2025, Howard et al., 2022). This suggests that cross-paper comparison remains difficult because “terrain quality” is operationalized differently across geomorphology, graphics, and robotics.

Controllability is equally heterogeneous. Procedural systems expose explicit parameters such as octaves, frequency, amplitude, slope, roughness, rainfall, rock density, and module order (Wallin, 24 Jun 2025, Lim et al., 2022). Neural style transfer permits hand-drawn semantic structure before morphology transfer (Merizzi, 2024). Diffusion systems accept text prompts structured by biome, geology, country, and season, or sketches that encode ridges, valleys, and cliffs through color channels (Borne--Pons et al., 9 Apr 2025, Higo et al., 7 May 2025). Terrain-aware scene graphs encode terrain classes as topological and semantic constraints for downstream planning (Samuelson et al., 23 Sep 2025). A common misconception is that greater realism necessarily implies weaker user control; the surveyed literature does not support that simplification, although the form of control differs sharply between parameterized procedural systems and learned generative models.

Several recurrent limitations also appear. GAN-based terrain generators report instability, artifacts, lack of joint training, and unresolved neighboring-tile consistency (Beckham et al., 2017, Panagiotou et al., 2020). WFC terrain generation can fail through contradictions and is reported to succeed in only about $512 \times 512$ 1 of runs per input (Dajkhosh, 2024). Some diffusion works emphasize qualitative results and explicitly note the absence of quantitative benchmarks (Borne--Pons et al., 9 Apr 2025). Reconstruction pipelines note the continuing difficulty of sparse features, shadow zones, semantic ambiguity, or large-scale memory constraints (Garg et al., 2022, Fu et al., 9 Jul 2026, Samuelson et al., 23 Sep 2025). The overall direction of the field, however, is clear: TMG is moving from isolated heightfield synthesis toward multi-modal, multi-scale, and task-aware terrain generation in which elevation, texture, semantics, uncertainty, and downstream utility are modeled jointly.