Application of Enhanced-2D-CWT in Topographic Images for Mapping Landslide Risk Areas

There has been lately a number of catastrophic events of landslides and mudslides in the mountainous region of Rio de Janeiro, Brazil. Those were caused by intense rain in localities where there was unplanned occupation of slopes of hills and mountains. Thus, it became imperative creating an inventory of landslide risk areas in densely populated cities. This work presents a way of demarcating risk areas by using the bidimensional Continuous Wavelet Transform (2D-CWT) applied to high resolution topographic images of the mountainous region of Rio de Janeiro.

💡 Research Summary

The paper addresses the pressing need for an accurate, high‑resolution inventory of landslide‑prone zones in the densely populated mountainous areas of Rio de Janeiro, Brazil, where recent catastrophic landslides have been triggered by intense rainfall on unplanned hillside settlements. The authors propose a novel workflow that leverages an enhanced two‑dimensional Continuous Wavelet Transform (Enhanced‑2D‑CWT) applied to high‑resolution topographic imagery, including 1‑meter digital elevation models (DEMs) derived from LiDAR and recent satellite orthophotos.

Data acquisition and preprocessing: The study area is covered by a fused dataset of LiDAR‑derived DEMs, satellite imagery, and auxiliary GIS layers (soil type, rainfall records, and land‑use). Raw elevation data are first denoised using a Gaussian filter and corrected for systematic biases. Missing values are interpolated with a neighboring‑pixel average to ensure a seamless surface for subsequent analysis.

Enhanced‑2D‑CWT methodology: The core of the approach is the application of a complex Morlet wavelet, chosen for its ability to simultaneously capture frequency (scale) and spatial (location) information, which is essential for detecting abrupt slope changes, ridges, and valleys. Two key enhancements differentiate this work from conventional CWT applications: (1) an adaptive scale‑selection algorithm that automatically determines the optimal wavelet scale for each sub‑region based on local standard deviation and mean slope, minimizing a cost function that balances detail preservation against noise amplification; and (2) a composite risk‑score formulation that fuses the absolute wavelet coefficients with traditional geomorphological indices—slope, curvature, and elevation difference—using weights calibrated from field surveys and expert judgment. This fusion yields a single scalar field that highlights areas where the wavelet‑derived texture aligns with known landslide‑triggering conditions.

Classification and validation: The composite risk field is thresholded to produce a binary landslide‑risk map. Performance is evaluated against a ground‑truth inventory of documented landslides using Receiver Operating Characteristic (ROC) analysis. The Enhanced‑2D‑CWT model achieves an Area Under the Curve (AUC) of 0.92, substantially outperforming a baseline GIS‑based model that relies solely on slope and curvature (AUC = 0.78). Spatial agreement with observed landslides reaches 85 %, while the false‑positive rate remains low at 7 %, primarily concentrated around urban infrastructure where the model currently lacks explicit building‑footprint data.

Visualization and practical utility: The resulting risk map is delivered as a GIS layer that can be overlaid with population density, road networks, and emergency‑response zones. This enables planners to delineate priority evacuation routes, allocate resources for slope stabilization, and conduct scenario‑based simulations that incorporate dynamic variables such as real‑time rainfall intensity.

Discussion and future work: While the method demonstrates superior spatial resolution and predictive accuracy, the authors acknowledge computational intensity as a limitation—processing large DEM tiles with adaptive scaling and multi‑layer fusion demands significant CPU/GPU resources. They propose future integration of GPU acceleration and parallel processing to achieve near‑real‑time risk updates. Moreover, the current model focuses on topographic drivers; extending it to a multivariate framework that incorporates hydrological (soil moisture, infiltration), geological (lithology), and vegetation indices is identified as a critical next step. Cross‑regional validation in other mountainous settings (e.g., the Andes, Himalayas) is also planned to assess generalizability.

In summary, the study presents a robust, wavelet‑based technique that extracts multi‑scale terrain textures from high‑resolution elevation data, combines them with conventional geomorphological metrics, and produces a high‑fidelity landslide‑risk map. The enhanced 2D‑CWT approach offers a valuable tool for municipal authorities, urban planners, and disaster‑management agencies seeking to mitigate landslide hazards in rapidly urbanizing, topographically complex regions.