Rational function model (RFM) is the most widely used sensor model in the remote sensing community. However, it suffers from ill-posedness, challenging its feasibility. This problem, i.e., ill-posedness, is mainly caused due to highly correlated coefficients of the RFM, which magnifies any small perturbations of observations, such as noise and instrumental error. This paper outlines a novel two-step method, called principal component analysis (PCA)-RFM, based on the integration of PCA and QR decomposition. In the first step, the PCA-RFM reduces the observational perturbations from the design matrix using the PCA. In the next step, the RFM's coefficients are estimated using a QR decomposition with column pivoting and least square method. According to the results, the PCA-RFM is less sensitive than its rivals to the changes of the ground control point (GCPs) distribution. Geometrically speaking, in addition, PCA-RFM is more accurate than recently established methods even in the presence of the small number of GCPs.

The combination of Remote Sensing and Deep Learning (DL) has brought about a revolution in converting digital surface models (DSMs) to digital terrain models (DTMs). DTMs are used in various fields, including environmental management, where they provide crucial topographical data to accurately model water flow and identify flood-prone areas. However, current DL-based methods require intensive data processing, limiting their efficiency and real-time use. To address these challenges, we have developed an innovative method that incorporates a physically informed autoencoder, embedding physical constraints to refine the extraction process. Our approach utilizes a normalized DSM (nDSM), which is updated by the autoencoder to enable DTM generation by defining the DTM as the difference between the DSM input and the updated nDSM. This approach reduces sensitivity to topographical variations, improving the model’s generalizability. Furthermore, our framework innovates by using subtractive skip connections instead of traditional concatenative ones, improving the network’s flexibility to adapt to terrain variations and significantly enhancing performance across diverse environments. Our novel approach demonstrates superior performance and adaptability compared to other versions of autoencoders across ten diverse datasets, including urban areas, mountainous regions, predominantly vegetation-covered landscapes, and a combination of these environments.

Deep learning has proved to be a breakthrough in depth generation. However, the generalization ability of deep networks is still limited, and they cannot maintain a satisfactory performance on some inputs. By addressing a similar problem in the segmentation field, a feature backpropagating refinement scheme (f-BRS) has been proposed to refine predictions in the inference time. f-BRS adapts an intermediate activation function to each input by using user clicks as sparse labels. Given the similarity between user clicks and sparse depth maps, this paper aims to extend the application of f-BRS to depth prediction. Our experiments show that f-BRS, fused with a depth estimation baseline, is trapped in local optima, and fails to improve the network predictions. To resolve that, we propose a double-stage adaptive refinement scheme (DARS). In the first stage, a Delaunay-based correction module significantly improves the depth generated by a baseline network. In the second stage, a particle swarm optimizer (PSO) delineates the estimation through fine-tuning f-BRS parameters—that is, scales and biases. DARS is evaluated on an outdoor benchmark, KITTI, and an indoor benchmark, NYUv2, while for both, the network is pre-trained on KITTI. The proposed scheme was effective on both datasets.

Global digital elevation models (GDEMs) are one of the most important sources of elevation data. Like other spatial datasets, GDEMs are inevitably affected by various types of errors in both vertical and horizontal dimensions. One of the main sources of horizontal errors is georeferencing error which in steep areas intensifies the vertical error. Since horizontal and vertical errors are interwoven with one another, any error introduced in horizontal dimension influences its vertical counterpart. In this paper, for the first time, we intend to answer this question: to what extent the impact of georeferencing error is really important in vertical accuracy of GDEMs and their vertical comparison. Hence, the main purposes of this study are evaluation of georeferencing effects on (i) the vertical accuracy of GDEMs and (ii) vertical comparison between GDEMs. In this regard, Advanced Spaceborne Thermal Emission and Reflection (ASTER), Shuttle Radar Topography Mission (SRTM), and Advanced Land Observing Satellite (ALOS) World 3D-30 m (AW3D30) GDEMs over three different study areas (BumeHen, TazehAbad and Sainte-Maxime regions) were used and assessed. In order to assess the effects of georeferencing error on GDEMs accuracy, studies were conducted in two general categories, namely Local to Global (LG) and Global to Global (GG). In the first category, these effects were studied on vertical and horizontal differences of ASTER, AW3D30, and SRTM GDEMs with their corresponding reference DEMs (REFDEMs). In the second category, these effects were assessed on vertical and horizontal differences of ASTER and SRTM GDEMs with AW3D30 GDEM. To this end, prior to making GDEMs georeferencing consistent, they were vertically assessed. For the sake of consistency of GDEMs georeferencing, a registration process was performed and then, the registered GDEMs were vertically and horizontally assessed. After the registration process, in the first category, 4.4%, 13%, and 3.3% and in the second category 2.3%, 5%, and 1.2% improvement occurred on average root mean square error (RMSE) over all GDEMs for BumeHen, TazehAbad and Sainte-Maxime regions, respectively. These results refer to the fact that GDEM registration always increases their vertical accuracy, which is in fact originated from the improvement in GDEM georeferencing consistency. Experimental results also indicate that the improvement rate of vertical errors after the DEM registration process is directly related to terrain slope angle. From another perspective, we illustrated that in general the amounts of achieved improvements in GDEMs vertical accuracy are much smaller than their nominal accuracies. Finally, our results show that the effect of horizontal error on vertical comparison between GDEMs is unavoidable, but this amount of error can be ignored because the ratio of improvements occurred in the GDEMs with respect to their nominal accuracies is very low.

Deep learning, specifically the supervised approach, has proved to be a breakthrough in depth prediction. However, the generalization ability of deep networks is still limited, and they cannot maintain a satisfactory performance on some inputs. Addressing a similar problem in the segmentation field, a scheme (f-BRS) has been proposed to refine predictions in the inference time. f-BRS adapts an intermediate activation function to each input by using user clicks as sparse labels. Given the similarity between user clicks and sparse depth maps, this paper aims at extending the application of f-BRS to depth prediction. Our experiments show that f-BRS, fused with a depth estimation baseline, is trapped in local optima, and fails to improve the network predictions. To resolve that, we propose a double-stage adaptive refinement scheme (DARS). In the first stage, a Delaunay-based correction module significantly improves the depth generated by a baseline network. In the second stage, a particle swarm optimizer (PSO) delineates the estimation through fine-tuning f-BRS parameters—that is, scales and biases. DARS is evaluated on an outdoor benchmark, KITTI, and an indoor benchmark, NYUv2 while for both the network is pre-trained on KITTI. The proposed scheme outperformed rival methods on both datasets.