## 1 Introduction  
High-resolution orthorectified imagery acquired via aerial or satellite sensors is highly valuable for Geographic Information System (GIS) applications, including environmental monitoring [1], precision agriculture [2], natural disaster assessments [3], infrastructure planning, and urban development [4, 5]. These images lack height information, which prevents certain types of analyses. Three-dimensional data can be obtained through methods such as stereo image acquisition and processing (from aerial, drone, or satellite sources), laser scanning surveys, and Digital Surface Model (DSM) analysis. Unmanned Aerial Vehicle (UAV) imagery is often processed using Structure from Motion (SfM) techniques, which enable the extraction of height data through triangulation between consecutive image pairs [6]. Similarly, laser scanning surveys can provide altimetric data by generating point clouds, which can contain millions of points for extensive areas. However, both SfM and lidar point cloud processing for large-scale areas require substantial computational resources and significant storage capacity to handle the vast amounts of data generated. The use of simpler materials, such as orthophotos, to obtain 3D information could significantly simplify workflows and reduce processing times. An important feature in orthophotos, closely linked to altitude data, is the presence of shadows. Several studies have focused on deriving altitude information from single-source images, such as those captured by drones, aerial platforms, or satellites, often integrating additional data like DSMs or LiDAR, with a primary emphasis on buildings. [PERSON] et al. [7] introduced an automated technique for estimating building heights from a single image using a Convolutional Neural Network (CNN) architecture. Their method processes a single optical image to derive a Digital Surface Model. To train the CNN for height inference, aerial imagery was aligned with the corresponding DSM. Similarly, [PERSON] et al. [8] proposed a methodology for extracting building heights from high-resolution remote sensing images, combining shadow and side information through the RMU-Net framework. This approach addresses issues like pixel detail loss and inaccuracies in edge segmentation caused by scale variations within the segmented buildings. [PERSON] et al. [9] calculated building heights by analyzing shadows in high-resolution multispectral Ikonos images. Their method considered both the Sun's and satellite's positions during image capture, employing multispectral classification to measure shadow widths and estimate heights. The influence of acquisition geometry in building height estimation has been explored in various studies. [PERSON] and [PERSON] [10] developed an automatic strategy for identifying flat polygonal roof types in QuickBird images by using shadow shapes and acquisition geometry for height estimation. To improve shadow detection accuracy, [PERSON] and [PERSON] [11] optimized shadow segmentation with an active contour model that incorporated both spectral and spatial information. Their method enhanced shadow clarity by utilizing the solar elevation angle to estimate building heights. [PERSON] et al. [12] introduced a method for estimating building heights using shadows in high-resolution imagery. Their framework accounts for varying building densities, terrains, and complex environments, effectively distinguishing between simple and complex building shapes. [PERSON] [13] further refined shadow-based methods by integrating a geometric approach that accounts for the movement of the ASTER satellite. This method utilizes physical models to position shadows accurately, enhancing refraction calculations from meteorological data. [PERSON] and [PERSON] [14] applied similar techniques in flat terrain using a single SPOT image, factoring in potential obstructions like trees and considering Sun and satellite positions for height estimation.