A Comprehensive Evaluation of Monocular Depth Estimation Methods in Low-Altitude Forest Environment

Abstract

Monocular depth estimation (MDE) is a critical computer vision task that enhances environmental perception in fields such as autonomous driving and robot navigation. In recent years, deep learning-based MDE methods have achieved notable progress in these fields. However, achieving robust monocular depth estimation in low-altitude forest environments remains challenging, particularly in scenes with dense and cluttered foliage, which complicates applications in environmental monitoring, agriculture, and search and rescue operations. This paper presents a comprehensive evaluation of state-of-the-art deep learning-based MDE methods on low-altitude forest datasets. The evaluated models include both self-supervised and supervised approaches, employing different network structures such as convolutional neural networks (CNNs) and Vision Transformers (ViTs). We assessed the generalization of these approaches across diverse low-altitude scenarios, specifically focusing on forested environments. A systematic set of evaluation criteria is employed, comprising traditional image-based global statistical metrics as well as geometry-aware metrics, to provide a more comprehensive evaluation of depth estimation performance. The results indicate that most Transformer-based models, such as DepthAnything and Metric3D, outperform traditional CNN-based models in complex forest environments by capturing detailed tree structures and depth discontinuities. Conversely, CNN-based models like MiDas and Adabins struggle with handling depth discontinuities and complex occlusions, yielding less detailed predictions. On the Mid-Air dataset, the Transformer-based DepthAnything demonstrates a 54.2% improvement in RMSE for the global error metric compared to the CNN-based Adabins. On the LOBDM dataset, the CNN-based MiDas has the depth edge completeness error of 93.361, while the Transformer-based Metric3D demonstrates the significantly lower error of only 5.494. These findings highlight the potential of Transformer-based approaches for monocular depth estimation in low-altitude forest environments, with implications for high-throughput plant phenotyping, environmental monitoring, and other forest-specific applications.

1. Introduction

Forests are critical ecosystems that play a fundamental role in maintaining biodiversity, carbon storage, and climate regulation [1]. With increasing demands for environmental conservation, sustainable agriculture, and precise ecosystem monitoring, there is a growing need for advanced technologies to analyze and reconstruct inter-forest scenes. Depth estimation based on low-altitude images taken by unmanned aerial vehicles (UAVs) from different perspectives is an effective solution, as it provides detailed spatial information essential for tasks such as assessing tree structure, monitoring undergrowth, and navigating complex natural terrains [2].

Monocular depth estimation (MDE), which involves predicting a pixel-wise depth map from a single image, is an increasingly popular and fundamental research topic in computer vision [3]. Unlike stereo or multi-view depth estimation methods, which require multiple images of the same scene and accurate calibration of the cameras to provide relatively proper correspondence. MDE addresses depth estimation from monocular images, which are less expensive, less time-consuming, and do not require complex camera calibration. These advantages make MDE particularly suitable for use in remote or obstructed low-altitude forest environments, where line-of-sight issues and terrain complexity often challenge traditional depth estimation approaches. Estimating depth from a monocular image is an inherently ill-posed problem, as countless possible scene arrangements with varying object sizes and depths could produce the same 2D image projections. In recent years, the deep learning techniques have affected the progress of MDE methods by implicitly learning relevant scene geometric priors solely from monocular RGB images to estimate depth rather than just relying on correspondence matching [4,5]. This progress has resulted in many contributions, including supervised and unsupervised approaches, employing different novel structures such as convolutional neural networks (CNNs), and Transformer.

While existing MDE approaches produce nicely visual results, selecting an appropriate method for depth estimation in low-altitude forest environments still remains challenging. Dense foliage, low lighting, and frequent natural occlusions common in these environments often reduce the robustness and accuracy of the MDE method. Therefore, proper evaluation of estimated depth maps is crucial to improve MDE methods and to enhance their applicability for 3D understanding in complex scenarios. Moreover, commonly used evaluation metrics for MDE primarily focus on overall accuracy by reporting global statistics of depth errors across the entire scene. These metrics provide limited insight into depth estimation quality in some areas, such as areas with depth discontinuities or fine structural details like tree branches and dense foliage. This limitation results in similar error scores for models that differ significantly in their ability to capture complex spatial structures in forest environments. Addressing these gaps requires an evaluation scheme that incorporates geometry-aware metrics, crucial for accurately interpreting the spatial structure of forests, including the arrangement of trees, undergrowth, and occluded elements.

To address these challenges, this paper provides a comprehensive evaluation protocol of state-of-the-art MDE models for low-altitude forest scenarios. By employing the global and geometry-aware metrics, we evaluated various MDE models constructed using different network structures such as CNN and Transformer, on two typical forest datasets. The main contributions of this work are as follows:

1. We selected two low-altitude forest datasets for evaluation acquired from diverse outdoor forest scenarios, which contain synthetic and real RGB images alongside highly accurate depth maps;

2. We employed a set of systematic evaluation criteria that include geometrically interpretable error metrics in addition to traditional global metrics, allowing for a more precise analysis of depth estimation performance under different perspectives;

3. We present comprehensive generalization results qualitatively and quantitatively that analyze the performance of current state-of-the-art MDE models, including supervised and self-supervised models constructed by various network architectures, such as CNN and Transformer;

4. We provide insights into the suitability of various MDE models for forest-specific applications. This work aims to guide future research in developing more effective and adaptable MDE solutions for complex forest environments.

2. Related Work

In this section, we first provide an overview of the recent state of the art deep learning-based monocular depth estimation methods and some typical models are evaluated in this paper. Existing datasets used for training and evaluating the accuracy of these methods are reviewed in the second part of this section.

2.1. Monocular Depth Estimation Methods

In recent years, the rapid development of deep learning has driven significant progress in monocular depth estimation. Deep learning-based approaches utilize the powerful capabilities of neural networks to directly map color pixels to corresponding depth values. These methods can be broadly categorized based on the type of supervision and the network architecture employed. In terms of supervision, methods are classified into supervised and unsupervised approaches. The former one requires ground-truth depth labels, while the latter one relies on alternative cues, such as photometric consistency. Regarding network architecture, methods are primarily divided into those based on CNNs and those utilizing Vision Transformers. The following sections provide a detailed overview of these different approaches for deriving depth maps from monocular images. A summary including relevant studies is listed in Table 1. The methods highlighted in bold in the table are the ones evaluated in this paper. (Including MiDas [6], Adabins [7], GLP [8], DepthAnything [9], Metric3D [10], DPT [11] and ZoeDepth [12])

Supervised Methods. Supervised monocular depth estimation relies on datasets that include ground-truth depth information to train neural networks, typically using an end-to-end training approach. Saxena et al. [13] proposed the first supervised monocular depth estimation method that considers depth at individual points and the relation between depths at different points, leveraging Markov Random Fields (MRFs) for optimization. Later work on enhancing this method introduced a patch-based supervised model for unstructured environments, utilizing hand-crafted features [3]. This model enhanced depth estimation by incorporating monocular cues from local patches and applying global optimization to refine depth relations using MRFs. Karsch et al. [14] proposed a depth transfer-based framework that relies on non-parametric depth sampling, where depth information is retrieved from a large database of RGBD images by searching for candidate images similar to the input image. This approach assumes that similar images are more likely to have similar depths. However, the computation cost of retrieving depth information from such a large database during runtime is very high.

Early supervised methods extensively employed hand-crafted features to capture the correlation between a color image and its corresponding ground-truth depth. In recent developments, Lasinger et al. [6] (MiDas) improved depth estimation by integrating image information from various scenes, mixing multiple datasets with different features and biases during training. This approach uses a multi-scale feature module to improve accuracy and generalization performance, thus enhancing cross-dataset transferability. Bhat et al. [7] (Adabins) propose a Transformer-based architecture block that divides the depth range into bins whose center value is estimated adaptively per image. The final depth prediction is a linear combination of these unit centers. Kim et al. [8] (GLP) proposed a method that integrates both global and local feature representations by constructing a connection path between multi-scale local features and global decoding streams, which helps to restore detailed depth information.

Despite the advancements in supervised methods, their reliance on large amounts of annotated training data (ground-truth depth values) poses a significant limitation. Annotated data are often limited and challenging to obtain, particularly in complex environments. This has driven researchers toward unsupervised learning approaches, which do not require ground-truth annotations and instead leverage geometric cues inherent in the data to train models effectively.

Self-supervised or Unsupervised Methods. In contrast to supervised methods, self-supervised or unsupervised approaches can train models without requiring the ground-truth depth labels. These methods exploit the inherent geometric relationships within the data, generating pseudo-labels during training and mimicking a supervised learning paradigm.

One prominent strategy is monocular depth estimation using stereo supervision, where neural networks are trained on rectified stereo image pairs to predict depth from monocular images. These methods estimate pixel disparities, warping one image to align with the other. For instance, Garg et al. [15] computed photometric differences for disparity estimation, while Godard et al. [16] (Monodepth) predicted disparities for both left and right images, enforcing consistency with an L1 disparity penalty. Despite their effectiveness, stereo-based approaches face challenges such as stereo-disocclusions, where pixels or regions are visible in one image but not the other, leading to noisy image reconstruction and inaccuracies in disparity predictions. Another strategy involves monocular depth estimation using monocular video supervision, which relies on monocular image sequences for training. These methods focus on optimizing temporal or geometric consistency between adjacent frames, assuming a static scene. They estimate depth either using known camera parameters or by predicting camera pose and ego-motion through a separate network. For example, Monodepth2 [17] employed a dual-network structure where DepthNet estimates depth and PoseNet predicts camera motion. These methods minimize appearance matching loss and camera pose error, effectively learning depth while inferring scene geometry and camera pose. However, they also face challenges such as moving objects and non-rigid motions, requiring masking strategies for robustness [18,19,20].

Beyond these above-mentioned mainstream approaches, hybrid methods that employ both labeled and unlabeled data for supervision has also emerged. For instance, Yang et al. [9] (DepthAnything) highlighted the utility of unlabeled images to improve data diversity and coverage. Their training strategy involves using a large number of unannotated images to predict dense depth via a pre-trained MDE model as pseudo-labels, which are subsequently trained together with a small set of labeled images. Similarly, Tian and Li [21] proposed using a depth network to predict depth from unlabeled images, verifying its predictions with a confidence map to ensure accuracy against ground truth.

Self-supervised or unsupervised methods offer notable advantages, such as eliminating the need for ground-truth depth labels and demonstrating strong generalization to new datasets and unseen environments. These characteristics make them particularly valuable in scenarios where labeled data are scarce or unavailable. However, these methods usually require more computational resources during training. In general, their accuracy is not as good as supervised methods. The trade-off between accuracy, computational cost, and data availability continues to drive advancements in this field.

CNN-based Methods. The choice of network architecture also plays a crucial role in the performance of monocular depth estimation methods. Early approaches predominantly utilized CNN to directly aggregate image information and generate continuous depth maps through regression. Eigen et al. [4] proposed the first deep convolutional neural network framework for monocular depth estimation, which is a multi-scale network structure. The first stage used AlexNet [22] for learning global depth, while the second stage refined local details by using a fine-scale network. However, their network was unable to produce full-resolution depth maps. To address this issue, Laina et al. [23] proposed a residual connection-based up-sampling module, which effectively improved the spatial resolution of the output depth maps. Concurrently, Lee et al. [24] introduced multi-level local plane guidance layers in the decoding stage, which internally estimate 4D plane coefficients for each spatial unit to guide feature restoration, achieving full resolution depth outputs. Hu et al. [25] enhanced depth estimation further by designing a multi-scale feature fusion module and employing complementary loss functions—including depth, gradient, and surface normal—to improve predictive accuracy. To introduce higher-order constraints and reduce the noise impact on surface normals, Yin et al. [26] proposed more robust virtual normals to improve network robustness. Wang et al. [27] developed a multi-scale convolutional fusion architecture to generate high-quality depth predictions.

Transformer-based Methods. The Transformer [28] architecture, originally developed for natural language processing, has gained significant attention in computer vision, particularly following the success of Vision Transformer (ViT) [29]. However, directly applying Transformer to high-resolution 2D feature maps is computationally expensive and memory-intensive. To overcome these challenges, hybrid methods combining CNNs and Transformers have been explored. For example, Yang et al. [30] and Ranftl et al. [11] (DPT) initially employed CNNs to extract multi-scale features and then employed multiple layers of Vision Transformer to aggregate global information. Swin Transformer [31] improved computational efficiency by limiting self-attention to local windows, employing a sliding window strategy to achieve global attention. Agarwal et al. [32] proposed a skip attention module for feature fusion, effectively integrating global and local features through self-similarity between pixel queries and corresponding encoder feature maps. Shim et al. [33] further enhanced monocular depth estimation performance by adopting Swin Transformer as the backbone network. Bhat et al. [12] (ZoeDepth) achieved zero-shot transfer learning for single-image depth estimation by combining relative depth and metric depth, enabling robust predictions across diverse datasets without additional fine-tuning. While Yin et al. [10] (Metric3D) proposed a canonical camera space transformation method. This transformation aligns all training data into a canonical camera space, effectively addressing metric ambiguity and ensuring consistent performance across diverse datasets. These advancements show the potential of Transformer-based methods in achieving higher accuracy and adaptability for monocular depth estimation across diverse and challenging scenarios.

Table 1

Summary of the referred to MDE methods. The methods shown in bold were included in our evaluation.

Type of Supervision	Network Architecture	Method
Supervised	MRF-based	Saxena et al. (2005) [13], Saxena et al. (2008) [3];
	non-parametric depth sampling	Depth transfer (2014) [14];
	CNN-based	MiDas (2019) [6], Adabins (2020) [7], Eigen et al. (2014) [4], Alexnet (2012) [22], Laina et al. (2016) [23], Lee et al. (2019) [24], Hu et al. (2019) [25], Yin et al. (2019) [26], Cliffnet (2020) [27];
	Transformer-based	GLP (2022) [8], TransDepth (2021) [30], DPT (2021) [11], Agarwal et al. (2023) [32], ZoeDepth (2023) [12], Metric3D (2023) [10];
Self-supervised and Unsupervised	CNN-based	Garg et al. (2016) [15], Monodepth (2016) [16], Monodepth2 (2019) [17], Heo et al. (2018) [18], GeoNet (2020) [19], DF-Net (2018) [20], Tian et al. (2019) [21];
	Transformer-based	Shim et al. (2023) [33], DepthAnything (2024) [9];

2.2. Existing Benchmark Datasets

In computer vision, datasets play a critical role in deep learning-based depth estimation methods. The diversity and quality of datasets significantly influence how well models generalize, especially when transitioning from synthetic to real-world datasets. Currently, a wide range of publicly available datasets exist, generated through active sensors (e.g., RGB-D cameras or LiDAR) or passive methods (e.g., stereo images). Active sensors, such as Microsoft Kinect (versions 1 and 2), Occipital Structure Sensor, and Intel RealSense, are pre-calibrated and produce aligned depth maps in a large quantity with minimal manual effort. However, the measuring ranges are often limited to less than 20 m. In contrast, LiDAR sensors, having a measuring range up to several hundred meters and usually requiring additional cameras and registration techniques, produce higher-quality depth maps with higher resolution, range, and accuracy than RGB-D sensors.

Currently, widely used datasets include KITTI [34], Make3D [3], NYU Depth [35], and Cityscapes [36]. The NYU Depth dataset is mainly designed for indoor environments, which was captured using RGB-D cameras, comprises monocular videos of indoor scenes along with their corresponding true depth information [35]. The Make3D dataset [3], released by Stanford University, provides paired RGB and depth images for autonomous driving. The dataset of scenes mainly consists of urban and natural landscapes captured during the day. The KITTI dataset [34], jointly constructed by the Karlsruhe Institute of Technology and Toyota Technical Institute in the United States, is extensively utilized in outdoor and autonomous driving scenarios. It provides RGB images and ground-truth depth captured in urban, rural, and highway settings and supports tasks such as depth estimation, optical flow, visual odometry, and 3D object detection. Based on the KITTI dataset, the Motional team has developed a new public large-scale dataset for autonomous driving, NuScenes [37]. Its annotations and image quantity are seven times that of the KITTI dataset. Additionally, there are datasets composed of video sequences that can be employed for unsupervised monocular depth learning. The Cityscapes dataset [36], for example, includes binocular video sequences from various cities across different seasons, which can be utilized for training unsupervised monocular depth estimation models. To further expand the scale of datasets, constructed by the Toyota Research Institute, University of Chicago, and Beihang University, provides the DIODE dataset [38] that includes both indoor and outdoor scenes with depth maps and plane normal data. The Sceneflow [39] dataset, created by Mayer et al. in 2016, provides over 39,000 pairs of stereo images for stereo matching and optical flow tasks across diverse scenes and lighting conditions. The MegaDepth dataset [40] leverages multi-view internet photo collections to generate training data for image matching and single-view depth prediction, combining modern structure-from-motion and multi-view stereo techniques.

When focusing on specific domains, such as low-altitude forest environments, the availability of datasets emerges as a critical factor for MDE methods evaluation. Due to the scarcity of publicly available datasets for such scenarios, researchers often rely on synthetic datasets generated via virtual platforms or collect data directly through field acquisition. Liu et al. [41] collected a forest dataset using a ZED2 stereo depth camera, capturing diverse vegetation types, such as larch and pine. Niu et al. [42] created a dataset of RGB images and depth maps using the RealSense D435i depth camera under various weather and lighting conditions, capturing forest elements like trees, branches, and foliage. The LOBDM dataset [43] combines real-world and synthetic data to enable depth map learning for occluded tree branches in forest environments. It includes imagery from temperate Swiss forests and Masoala rainforests, as well as synthetic images generated using Unreal Engine [44] and the Unreal CV [45] plugin. The Forest Inspection Dataset [46], which combines real and synthetic data for forest monitoring tasks, including semantic segmentation and depth estimation, was captured under varying illumination conditions and viewing angles. The Mid-Air dataset is a multi-modal synthetic dataset designed for extremely low-altitude unmanned aerial vehicle (UAV) flights, comprising over 420,000 video frames simulated under diverse climatic conditions, including various weather, seasonal, and lighting scenarios [47]. The TartanAir dataset created for visual SLAM research features over one million frames of photo-realistic simulated environments, with long motion sequences and ground-truth labels [48]. The FRUC dataset was collected as part of the work conducted by the Forestry Robotics University of Coimbra team [49]. It provides many stereo images captured over an 800 m trajectory in a Portuguese forest environment.

All the above datasets, summarized in Table 2, provide a solid foundation for advancing depth estimation research, particularly in challenging settings such as forests, where depth discontinuities, occlusions, and complex lighting conditions pose unique challenges.

3. Materials and Methods

3.1. Summary of MDE Methods for Evaluation

In this study, we explored and evaluated the performance of various depth estimation methods in forest environments by selecting a set of representative network models. These models, which employ different network architectures and training strategies, are designed to address different depth prediction tasks. The selected models include MiDas [6], Adabins [7], GLP [8], DepthAnything [9], Metric3D [10], DPT [11], and ZoeDepth [12].

Adabins. The architecture includes an encoder-decoder block and an adaptive bin-width estimator called Adabins. The encoder is based on a pretrained EfficientNet B5 [50] model, and the decoder incorporates a feature up-sampling module. Adabins employs a Transformer-based architecture that divides the depth range into bins, with the center value of each bin adaptively estimated for each image. The final depth prediction is estimated as a linear combination of these bin centers. The training process is guided by two loss functions: pixel depth loss and bin-center density loss.

GLP. GLP utilizes a hierarchical transformer encoder to capture global context, which comprises multiple self-attention layers and an MLP-Conv-MLP block with residual connections. The model’s decoder is lightweight yet effective, designed to generate accurate depth maps while preserving local connectivity. The network employs a selective feature fusion module to connect multi-scale local features with the global context, enabling the recovery of fine details. The training is guided by a scale-invariant log-scale loss.

MiDas. MiDas introduces 3D movies as a new data source to expand the diversity and scale of training datasets. These data do not provide absolute depth but offer relative depth through stereo matching, thus enriching the training data. Moreover, due to the inconsistencies in scale and depth range across datasets, MiDas uses a multi-objective optimization approach to mix different datasets instead of simply performing dataset mixing. By treating each dataset as a separate task, a Pareto-optimal strategy is used to optimize the model parameters, allowing the model to perform well across different datasets. A scale- and bias-insensitive loss function is introduced to handle depth measurement inconsistencies between datasets. This loss function makes the model robust to mixed training on multiple datasets by adjusting the scale and offset of the predicted and true values. MiDas uses ResNet-based [51] multi-scale architecture for single image depth prediction.

DPT. DPT (Dense Prediction Transformer) replaces traditional convolutional networks with Vision Transformers as the backbone for dense prediction tasks. It generates tokens from various stages of the transformer and progressively combines them into full-resolution predictions using a convolutional decoder. The transformer backbone processes features at a constant high resolution and offers a global receptive field at every stage. DPT closely follows the protocol of Ranftl et al. [6], employing a scale- and shift-invariant loss on inverse depth representation, combined with a gradient-matching loss [40].

Metric3D. Metric3D introduces a canonical camera space transformation module to address ambiguity in monocular depth estimation. This module is easy to integrate into existing monocular models. Metric3D employs a U-Net architecture with a DINOv2 encoder backbone [52,53]. The training is guided by a random proposal normalization loss, enabling stable training across a dataset of over 8 million images with thousands of camera models.

DepthAnything. DepthAnything scales up the dataset by designing a data engine to automatically collect and annotate large-scale unlabeled data, which significantly enlarges the data coverage and reduces generalization error. Two simple but effective strategies are investigated to make data expansion promising. First, a more challenging optimization target is created through data augmentation, which encourages the model to seek additional visual knowledge. Second, auxiliary supervision is developed to leverage semantic priors from pre-trained encoders. Specifically, DepthAnything uses the DINOv2 encoder [53] for feature extraction and the DPT decoder for depth regression. The model is trained with an affine-invariant loss to handle scale and shift variations across samples.

ZoeDepth. ZoeDepth bridges the gap between relative and metric depth estimation. The authors propose a two-stage framework where relative estimation is based on the MiDas depth estimation framework [6]. In the first stage, an encoder-decoder architecture is pre-trained using relative depth on multiple datasets. The authors found that ZoeDepth performance is best when using the large BEiT384-L [54] backbone for the encoder, which is responsible for feature extraction for relative depth computation. In the second stage, they add domain-specific heads based on the new metric bins module to the decoder and fine-tune the model on one or more datasets for metric depth prediction. The metric bins module takes multiscale features from the MiDas decoder as input and predicts the bin centers to be used for metric depth prediction. A scale-invariant loss is used for pixel-level supervision.

3.2. Performance Metrics

To enable comprehensive analysis of predicted depth maps and facilitate robust comparisons of various algorithms in low-altitude forest environments, we employed a systematic set of evaluation criteria. These criteria include both traditional image-based global statistical metrics and geometry-aware metrics. The image-based metrics assess global statistics by comparing the predicted depth map with its ground-truth depth image across N depth pixels. Such metrics, exclusively used in recent influential studies (Eigen et al. [4]; Eigen and Fergus [5]; Laina et al. [23]; Li et al. [55]; Xu et al. [56]), are integral to establishing a standardized baseline for evaluation. The specific global metrics used in this study are detailed below.

3.2.1. Traditional Global Metrics

Root Mean Square Error (RMSE).

(1)$RMSE=\sqrt{{\displaystyle \frac{1}{\left|N\right|}}\sum _{i\in N}{‖d^i-d_i^{\ast }‖}^2}$

Logarithmic Root Mean Square Error (RMSE Log).

(2)$RMSE Log=\sqrt{{\displaystyle \frac{1}{\left|N\right|}}\sum _{i\in N}{‖\mathit{log}{d}_i-\mathit{log}{d}_i^{\ast }‖}^2}$

Relative Error (Abs Rel).

(3)$Abs Rel=\sum _{i\in N}{\displaystyle \frac{\left|d_i-d_i^{\ast }\right|}{d_i^{\ast }}}$

Accuracy (Acc).

(4)$Acc: \% of d_i s.t.max\left({\displaystyle \frac{d_i}{d_i^{\ast }}},{\displaystyle \frac{d_i^{\ast }}{d_i}}\right)=\delta <thr$

where $d_i$ represents the predicted depth value at pixel $i$, $d_i^{\ast }$ represents the true depth value, N represents the number of valid pixels, and $thr$ represents the threshold value, defining the allowable error range for predictions.

RMSE, RMSE Log, and Abs Rel were used to measure the error between predictions and ground truth, with smaller values indicating better performance. Accuracy (Acc) evaluates prediction precision, with higher values signifying superior results.

3.2.2. Geometry-Aware Metrics

Evaluating depth maps in low-altitude forest environments requires consideration for both specific scene ranges and depth discontinuities, as these factors are inherently linked. Forest scenes encompass a wide range of depths due to diverse elements like tree trunks, branches, and undergrowth, creating significant depth variations. Depth discontinuities, marked by sharp gradient changes between objects at different depths, are critical for capturing spatial relationships in these complex environments. Accurate assessment of depth predictions across scene ranges and the precise localization of these discontinuities is essential. To address these challenges, we introduced a set of geometry-based measures [57] that complement traditional error metrics, as described below:

Directed Depth Error (DDE). In some applications, especially in forest environments, the depth consistency across the entire image area is crucial. Traditional metrics like absolute or squared depth error and RMSE provide insights into the accuracy of predicted values in comparison to ground-truth values. However, they do not provide information to indicate whether the predicted depth is systematically underestimated or overestimated. The Directed Depth Error (DDE) addresses this limitation and is computed as the proportion of “too far” predicted pixels (${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{+}$) and “too close” predicted pixels (${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{-}$) relative to a reference depth plane π. All predicted depth pixels that lie in front of and behind this reference plane are masked and assessed according to their correctness using the reference depth maps. $d_{\mathrm{s}\mathrm{g}\mathrm{n}}$ represents the distance of the pixel from the reference depth plane. $T$ denotes the total number of pixels. The formula is as follows:

(5)${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{+}\left(\mathit{Y}\right)={\displaystyle \frac{\left|\left\{y_{i,j}\left|d_{\mathrm{s}\mathrm{g}\mathrm{n}}\right(\pi ,P_{i,j})>0\wedge d_{\mathrm{s}\mathrm{g}\mathrm{n}}(\pi ,P_{i,j}^{\ast })<0\right\}\right|}{T}}$

(6)${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{-}\left(\mathit{Y}\right)={\displaystyle \frac{\left|\left\{y_{i,j}\left|d_{\mathrm{s}\mathrm{g}\mathrm{n}}\right(\pi ,P_{i,j})<0\wedge d_{\mathrm{s}\mathrm{g}\mathrm{n}}(\pi ,P_{i,j}^{\ast })>0\right\}\right|}{T}}$

Depth Boundary Error (DBE). Depth discontinuities, represented as sharp gradient changes in depth maps, are critical for accurately capturing spatial relationships between objects at different depths. These discontinuities indicate transitions between distinct objects and play a key role in evaluating the quality of depth predictions. Accurate depth boundary evaluation involves assessing whether the predicted depth maps effectively represent all relevant discontinuities and avoid creating spurious ones influenced by texture.

To achieve this, edges $Y_{\mathrm{b}\mathrm{i}\mathrm{n}}$ and $Y_{\mathrm{b}\mathrm{i}\mathrm{n}}^{\ast }$ are extracted from the predicted and ground-truth depth maps, respectively, and compared using the truncated chamfer distance of the binary edge images. Specifically, a Euclidean distance transform is applied to the ground-truth edge image ${\mathit{E}}^{\ast }=DT\left({\mathit{Y}}_{\mathrm{b}\mathrm{i}\mathrm{n}}^{\ast }\right)$, while distances exceeding a given threshold $\theta$ are truncated to a maximum distance $\theta .$ This process results in two key metrics for assessing depth boundaries:

Accuracy of Depth Boundary (${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{a}\mathbf{c}\mathbf{c}}$). This metric evaluates the proximity of each predicted depth boundary to the closest ground-truth boundary, the predicted binary edge map by the ground-truth distance map, and summing the resulting pixel distances. High accuracy indicates that the predicted edges closely align with the actual depth discontinuities. The formula is as follows:

(7)${ \epsilon }_{\mathrm{D}\mathrm{B}\mathrm{E}}^{\mathrm{a}\mathrm{c}\mathrm{c}}\left({\mathit{Y}}_{\mathrm{b}\mathrm{i}\mathrm{n}},{\mathit{Y}}_{\mathrm{b}\mathrm{i}\mathrm{n}}^{\ast }\right)={\displaystyle \frac{1}{\sum _i \sum _j y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}}}\sum _i \sum _j e_{i,j}^{\ast }\cdot y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}$

Completeness of Depth Boundary (${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}}$). This metric assesses whether all relevant ground-truth depth boundaries are captured in the predicted depth map, penalizing both missing and dispensable edges. Completeness is calculated by summing the ground-truth edges weighted by their corresponding distances to the nearest predicted edges, ensuring that omitted or fictitious boundaries are identified and accounted for. The formula is as follows:

(8)${ \epsilon }_{\mathrm{D}\mathrm{B}\mathrm{E}}^{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}\left({\mathit{Y}}_{\mathrm{b}\mathrm{i}\mathrm{n}},{\mathit{Y}}_{\mathrm{b}\mathrm{i}\mathrm{n}}^{\ast }\right)={\displaystyle \frac{1}{\sum _i \sum _j y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}^{\ast }+y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}}}\sum _i \sum _j e_{i,j}^{\ast } \cdot y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}+e_{i,j}\cdot y_{\mathrm{b}\mathrm{i}\mathrm{n};i,j}^{\ast }$

Figure 1a,b visually illustrate these metrics, highlighting how DBE comprehensively evaluates the accuracy and completeness of depth discontinuities in the predicted maps. Where Figure 1a represents the average Euclidean distance on the predicted edge corresponding to the pixel position of the real edge, which can reflect the accuracy of the predicted edge. Figure 1b represents the average Euclidean distance on the real edge corresponding to the pixel position of the predicted edge, which can reflect the degree of fitting of the predicted edge to the real edge. Together, these measures ensure that depth predictions effectively capture critical transitions between objects while minimizing artifacts caused by texture confusion.

3.3. Evaluation Datasets

In order to evaluate comprehensively of various monocular depth estimation methods in low-altitude forest environments, three specialized forest datasets were selected: Low-Viewpoint Forest, LOBDM-Forest, and Mid-Air. These datasets represent diverse and challenging scenarios, including dense foliage, occluded branches, and varying altitudes, which are critical for assessing the robustness and accuracy of depth estimation methods. The origin and characteristics of each dataset, along with the specific evaluation protocols, are described in detail below.

Mid-Air. The Mid-Air dataset is a comprehensive multimodal synthetic dataset, which contains 54 flight trajectories and over 420,000 video frames simulated under diverse climatic conditions. High-quality images were generated using real-time rendering in Unreal Engine, ensuring detailed and realistic visual representation. The dataset is particularly valuable for tasks such as visual odometry, Simultaneous Localization and Mapping (SLAM), depth estimation, semantic segmentation, and stereo parallax estimation. Its inclusion of forested scenes makes it especially relevant for studies focusing on natural environments. Figure 2 illustrates a representative sample of the dataset.

LOBDM-Forest. This dataset, introduced in a study focused on learning depth maps for occluded tree branches in forest environments, contains both real-world and synthetic data. The real-world data were captured using an Intel RealSense D435 depth sensor. Approximately 20,000 RGB and depth images of trees in temperate forests and the Masoala rainforest in Switzerland were captured. The synthetic data were generated by simulating RGB-D sensors in Unreal Engine software 4 [44] with the UnrealCV 1.1.0 [45] plug-in. To create a diverse set of virtual data, SpeedTree 10.0 [58] was used to randomly generate models of various tree species, and a simulated drone trajectory was employed within Unreal Engine to capture image data as it navigated around the trees. To improve the realism of the synthetic data, several post-processing steps were applied, including the addition of simulated sensor noise, depth value truncation at ten meters, Gaussian blurring, and rounding of depth values to mimic the image quality of a real-world depth camera. Approximately 44,000 synthetic images, each with a resolution of 640 × 480 pixels, are included in the dataset. These images simulate a diverse array of tree species and environmental conditions. Figure 3a,b shows the examples of the real-world and virtual data, respectively, illustrating the dataset’s ability to represent both natural and simulated forest scenes.

Low-Viewpoint Forest. The Low-Viewpoint Forest was collected in woodland areas of Southampton Common, a 1.48 km² urban park located in Hampshire, UK. Data were acquired through the forest along five distinct routes, capturing a variety of environmental conditions, including different times of day and weather scenarios, to account for lighting variations. This dataset contains over 100,000 RGB-depth image pairs captured by a RealSense D435i depth camera (Intel Corporation, Santa Clara, CA, USA), with approximately 9700 image-depth map pairs selected for quality, offering a variety of forest scenes under different conditions. The resolution of the image is 640 × 480 pixels. Ground-truth depth data were stored as 8-bit grayscale maps. Figure 4 illustrates an example of the original RGB image alongside its corresponding visualized depth map. Due to the low accuracy of real-world acquired depth maps, we did not include them in our analysis for the quantitative evaluation in this paper.

Depth Distribution of evaluation datasets. Given the poor quality of real-world depth data acquired by RGB-D cameras, only synthetic data were used for accuracy evaluation to ensure reliable results. From the LOBDM-Forest dataset, the big-test branch subset was selected, comprising 900 images. The depth value distribution of this dataset is shown in Figure 5a. Since invalid pixel depths in the dataset are represented by a maximum value of 10 m, the prediction and ground truth were clamped to this upper limit for evaluation. For the Mid-Air dataset, trajectory 0027 was selected, containing 801 images. The depth value distribution of this dataset, shown in Figure 5b, indicates that most values are concentrated between 0 m and 100 m. Accordingly, both predicted and ground-truth depths were clamped to 100 m for consistency.

4. Experimental Results and Analysis

4.1. Evaluation Procedure

In this study, we selected seven state-of-the-art depth estimation networks, namely MiDas [6], Adabins [7], GLP [8], DepthAnything [9], Metric3D [10], DPT [11], and ZoeDepth [12]. The training data details of the model are shown in Table 3. All models were implemented and tested using the PyTorch 2.0.1 deep learning framework. Normally, most monocular depth estimation methods generate unscaled disparity predictions at the resolution of the training images. For evaluation purposes, the predicted depth maps were bilinearly up-sampled to match the resolution of the ground-truth images. To ensure proper alignment between predicted and ground-truth depths, median scaling was applied. All experiments were conducted on an NVIDIA GeForce RTX 4090 GPU. A detailed qualitative and quantitative analysis of the experimental results is presented in the sections below.

4.2. Performance Evaluation of Synthetic Forest Datasets

This section systematically compares and analyzes the performance of different depth estimation models on two synthetic forest scene datasets, namely Mid-Air and LOBDM-Forest (Synthetic). The Mid-Air dataset represents key forest components, including trees, rocks, grasslands, and the sky, making it highly relevant for UAV path-path planning research in forested environments. In contrast, the LOBDM-Forest (Synthetic) dataset focuses on the depth relationship between individual tree elements, such as trunks and leaves, which is critical for organ-level tree phenotyping data estimation.

4.2.1. Visual Results of Depth Images

We evaluate each MDE method using its default configuration on synthetic forest images. Depth maps were visualized using color-coded representations, where brighter colors indicate objects closer to the camera, and darker colors denote objects further away. This approach facilitates an intuitive understanding of depth variations within scenes. Figure 6 and Figure 7 present the visual comparison of depth predictions on the Mid-Air and LOBDM-Forest (Synthetic) datasets, respectively. Through these visual analyses, we assessed the strengths and limitations of each model in depth estimation tasks.

Figure 6 illustrates the performance of various models on the Mid-Air dataset. Specifically, Transformer-based models, such as ZoeDepth, DepthAnything, and Metric3D, show superior performance. Among all models, Metric3D produced the most detailed depth maps, particularly in capturing edge information in regions with depth discontinuities. For example, as shown in the red boxes in Figure 6, clear edge information can be observed between tree trunks and branches or between leaves and surrounding objects. However, its foreground predictions appeared brighter than the ground-truth depth maps, suggesting a tendency to underestimate depth values. In contrast, predictions of DepthAnything demonstrated the closest alignment with ground-truth depth maps in terms of color mapping while maintaining rich detail. MiDas and DPT produced comparable results, but with fewer details and only showing the main branches of trees. GLP can effectively capture unobstructed tree trunks but struggled with the contours and details of leaves. Adabins, trained primarily on indoor datasets, failed to generate meaningful predictions for outdoor forest scenes due to insufficient generalization capability. In contrast, models trained on diverse outdoor datasets, such as ZoeDepth and DPT, have shown robust performance and generalization.

Figure 7 shows the depth estimation results on the LOBDM-Forest (Synthetic) dataset. The results were the same as for the Mid-Air dataset; both DepthAnything and Metric3D outperform other models, accurately capturing the structures of tree branches and leaves and distinguishing depth levels between overlapping foliage. This performance can be attributed to their training on large-scale datasets, which enhances their generalization capabilities. While other models, such as ZoeDepth and DPT, effectively predicted overall tree contours and detailed structures, the color mapping of ZoeDepth differed significantly from ground-truth depth maps. GLP and MiDas performed moderately well in predicting the primary tree trunk but struggled with depth relationships between branches and leaves. The performance was the same as on the Mid-Air dataset. Adabins performed the poorest, capturing only limited trunk details.

Overall, from the above visual results of depth predictions, DepthAnything and Metric3D, both Transformer-based models, generate predicted depth maps with rich, detailed structures, especially around the edges of tree branches. This is critical for tree phenotyping in cluttered environments. However, traditional CNN-based models, such as MiDas and Adabins, struggle with handling depth discontinuities, producing smoother depth maps with less detail. These visual results demonstrate that Transformer-based models generally outperform CNN-based models in generalizing to outdoor forest scenes.

4.2.2. Image-Based Global Error Assessment

Visual analysis of depth maps provides only a rough qualitative understanding of network performance due to the inherent limitations of human perception, making it insufficient for precise and objective conclusions. In this section, we provide a quantitative accuracy analysis of the depth maps predicted by various network models, ensuring alignment with corresponding ground-truth data to guarantee evaluation reliability.

As shown in Table 4, DepthAnything demonstrates significant advantages across several key evaluation metrics on the Mid-Air dataset. Specifically, DepthAnything outperforms other models in terms of RMSE, RMSE Log, and Abs Rel. These results show that DepthAnything consistently provides more accurate depth predictions across the whole depth range in forest scenes. This performance aligns with the visualization results discussed earlier, where DepthAnything’s color-mapped predictions closely matched the true depth maps. In contrast, although the Metric3D network shows more detailed depth information in visual comparison, its d1 metric achieves only 34.6% on the Mid-Air dataset. This suggests that Metric3D misestimates a substantial number of depth values, supporting the earlier observation that its predictions tended to be underestimated. One potential explanation for this limitation is that Metric3D trained on the NYU-v2 dataset (depth range: 1–10 m) struggles to generalize to Mid-Air datasets with broader depth ranges. By comparison, DepthAnything’s training data spans a wide variety of labeled and unlabeled scenes with diverse depth ranges, enabling it to handle datasets with large depth variations effectively.

On the LOBDM-Forest (Synthetic) dataset, which primarily emphasizes detailed tree structures, the range of depth variation is relatively small. As a result, the quantitative performance differences among the networks are minimal, with variations of approximately 0.1 m. Nonetheless, Metric3D achieves the best performance on this dataset, obtaining the highest scores in RMSE, d2, and d3 metrics. DepthAnything follows closely, delivering very comparable results. Metric3D’s superior performance on this dataset highlights its ability to accurately capture fine details, while DepthAnything remains a robust generalization capability.

4.2.3. Depth-Related Global Error Assessment

To comprehensively evaluate the performance of each model across different depth ranges, this section statistically analyzes the global errors at different depth intervals. The results are presented as a line graph with depth intervals of 5 m for the Mid-Air dataset and 0.5 m for the LOBDM-Forest dataset to illustrate the trends in global error across different depth ranges. Figure 8 provides a detailed quantitative comparison of the global error metrics for the various network models within each depth interval.

As shown in Figure 8, the error distribution trends differ significantly between the two datasets. On the Mid-Air dataset, the RMSE and RMSE log metrics for DPT, MiDas, DepthAnything, and Adabins show a clear pattern of increasing error with greater depth. This is due to the fact that the depth distribution of the Mid-Air dataset has fewer pixels in large depth regions and the model struggles to handle large depth regions. Among these, Adabins has the largest error growth rate, which confirms the hypothesis discussed in Section 4.2.1 that Adabins is trained mainly on the indoor scene dataset, and thus it struggles to generalize to scenes with a large depth of field. However, by looking at the depth range larger than 80 m, we found that the prediction accuracies of the three models (GLP, Metric3D, and ZoeDepth) gradually improve with depth and outperform the other models, especially in terms of the Abs Rel metric. This indicates that these three models have good depth prediction performance in large depth regions.

On the LOBDM-Forest (Synthetic) dataset, where depth variations primarily capture finer details of individual trees, the overall depth range is relatively narrow. The variations in depth between tree trunks, branches, and foliage are minimal, leading to smaller differences in accuracy metrics among networks across all depth networks. The error metrics for all networks follow an increasing-decreasing-increasing trend. This pattern may be attributed to the structural characteristics of trees: the front (<3 m) and back (>6 m) regions of the trunk are dense with branches and leaves, making depth prediction more challenging. In contrast, the middle trunk region (approximately 6 m) is less obstructed, facilitating more accurate depth prediction.

Overall, there is a strong positive correlation between the error metrics and depth. As the target distance increases, prediction errors tend to grow. Across most depth ranges, DepthAnything delivers superior prediction performance, while GLP and Adabins perform relatively poorly.

4.2.4. Directed Depth Error Assessment

To analyze the prediction bias of each model across different depth ranges, this study evaluates the proportions of correctly estimated ${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^0$, overestimated ${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{+}$, and underestimated ${\epsilon }_{\mathrm{D}\mathrm{D}\mathrm{E}}^{-}$ depth values based on reference planes, as defined in Section 3.2. For the Mid-Air dataset, the reference plane is set to 20 m, reflecting its depth distribution range. For the LOBDM-Forest (Synthetic) dataset, the reference plane is set to 6 m. Table 5 summarizes the directed depth evaluation for the different network models. Figure 9 illustrates the percentages of correctly and incorrectly predicted depth values for various reference depth planes.

On the Mid-Air dataset, as shown in Table 5, when the reference depth surface is set to 20 m, DepthAnything and MiDas exhibit excellent performance. Both networks achieve high accuracy, with a large proportion of correct estimates and relatively few over- or underestimates. In contrast, Metric3D and GLP demonstrate significant underestimation, indicating that their predicted depth values are generally lower than the ground truth for specific elements in the images. This observation confirms the findings from the visualization analysis, which showed that Metric3D tends to underestimate depths in the foreground regions. As shown in Figure 9a, for all networks, the highest proportion of underestimates is observed at the 20 m reference depth surface; as the reference depth surface exceeds 20 m, the proportion of accurate estimates increases. Notably, GLP and Metric3D show higher underestimation rates for smaller reference depth surfaces. On the LOBDM-Forest (Synthetic) dataset, with the reference depth surface set to 6 m, DepthAnything and Metric3D perform well. As indicated in Figure 9b, when different reference depth surfaces are considered, DepthAnything consistently generates more accurate depth estimates. All networks exhibit the lowest accuracy when the reference depth surface is 6 m. However, accuracy improves as the reference depth surface exceeds 6 m. Between 5 m and 10 m, overestimation decreases consistently, while underestimation peaks at 7 m.

Overall, DepthAnything demonstrates robust performance across both datasets, achieving a high percentage of correct estimates, low rates of overestimation and underestimation in the directed depth error metric. In addition, Figure 10 visualizes the directional depth prediction outcomes, offering an intuitive basis for further analysis.

As shown in Figure 10, the depth predictions of Metric3D and GLP on both sides of the reference depth plane are generally lower than the ground-truth values, showing a high percentage of underestimation on the Mid-Air dataset. These findings are consistent with the data presented in Table 5. MiDas and DepthAnything have relatively low proportions of overestimated and underestimated pixels. The visualization results further show that the overestimated or underestimated pixels across all networks are primarily concentrated near the reference depth plane. This indicates that the estimation bias of pixels is closely related to the choice of the reference depth plane.

4.2.5. Depth Boundaries Accuracy Assessment

The visualization results in Section 4.2.1 show that Metric3D provides rich details. However, its quantitative evaluation on the Mid-Air dataset in Table 3 reveals unsatisfactory results. This indicates that visualization results do not correlate well with the traditional global evaluation metrics. To address this, we evaluated the prediction accuracy of different network models in depth discontinuity regions, focusing on object boundaries. This analysis complements traditional metrics by assessing edge prediction accuracy and completeness using depth edge evaluation metrics. A distance threshold of the truncated chamfer distance was set to $\theta$ = 10 pixels, which defines the upper bound for accuracy and completeness errors. The edge prediction results are summarized in Table 6.

As shown in Table 6, the evaluation results are consistent with the visualization results for Metric3D, demonstrating the validity of depth boundary metrics as a complement to traditional metrics. For instance, the poor depth prediction performance of Adabins in the visualization directly affects the quality of its edge extraction. On the Mid-Air dataset, Adabins has a high edge completeness error of 213.491, significantly worse than the best performing Metric3D. In contrast, Metric3D and DepthAnything demonstrate superior edge prediction performance on both datasets, excelling in edge accuracy and completeness. On the LOBDM dataset, Metric3D significantly outperforms MiDas in terms of edge completeness. In order to show the analysis results more intuitively, Figure 11 provides a visual comparison of edge extraction, with different colors distinguishing results from each network.

As shown in Figure 11, Metric3D and DepthAnything model, both using Transformer-based architectures, provide richer and more precise depth edge predictions, effectively capturing detailed edge information between tree trunks and branches, trees and grass, rocks, and trees and the sky. This strong performance is attributed to the self-attention mechanism in the Transformer architecture, which captures positional dependencies within the input sequence. This mechanism is good at modeling long-range dependencies, which is crucial for edge prediction tasks requiring global contextual information. In contrast, the traditional CNN-based MiDas struggles with edge extraction, often predicting partial or invalid edges. This limitation underscores the challenges of predicting depth discontinuities with CNN. The frequent use of convolutions and spatial pooling operations in CNN reduces output resolution. Furthermore, the shallow layers primarily capture localized intensity changes, neglecting broader contextual information and producing smoother depth predictions.

Overall, Metric3D and DepthAnything outperform other networks in predicting depth discontinuities. They consistently provide effective and accurate depth edge predictions, making them highly suitable for tasks requiring detailed edge detection.

4.3. Performance Evaluation of Real-World Forest Datasets

Synthetic datasets, despite their idealized conditions, often fail to capture the variability and complexity of real-world environments. These shortcomings include an inability to simulate dynamic lighting, textural richness, and complex shading caused by trees and other vegetation commonly found in real forest scenes. Therefore, this section provides a visualization of prediction results from different network models applied to real forest datasets, namely Low-view-forest and LOBDM-Forest (Real). These datasets contain complex textures, light shading, and challenging occlusions. By comparing network performance on these datasets, we aimed to evaluate the robustness and accuracy of different models in handling complex forest environments. Notably, while the ground truth for the real forest data were captured by depth cameras, the poor quality of these captures limits their reliability, and therefore, they are used only as a visual reference in this evaluation. Figure 12 illustrates the prediction results of various network models applied to the real forest datasets.

As shown in Figure 12, unlike synthetic forest datasets, real datasets impose higher demands on depth estimation networks due to the complexity of spatial distribution, rich details, and occlusions. Models using Transformer-based architectures, such as Metric3D, ZoeDepth, and DepthAnything, achieve better performance, accurately recovering tree structures completely. Among these, the DepthAnything model performs outstandingly in capturing the overall structure and size of tree branches but struggles with dimly shaded areas, as highlighted by red boxes in Figure 12. On the other hand, these methods produce predictions with richer contour details, effectively differentiating foreground and background depth levels. This indicates that these models are capable of accurately predicting depth hierarchies in real forest environments. However, models such as DPT, MiDas, and GLP predict only the basic tree trunk structures and contours, with minimal detail. Adabins, meanwhile, performs the worst in forest scenes, likely due to its training predominantly on indoor datasets, which limits its ability to generalize to outdoor forest scenarios.

The entire Section 4 provides a comprehensive evaluation of the performance of depth estimation networks on both synthetic and real forest datasets. On the synthetic datasets, the Transformer-based models, DepthAnything and Metric3D, achieve notable results, particularly in detail prediction and edge accuracy. DepthAnything performs best in terms of several key evaluation metrics, demonstrating its high prediction accuracy and generalization ability. These performances can be attributed to its training strategy, which incorporates extensive unlabeled data. While Metric3D excels in capturing fine details, as evidenced by visualization results and edge evaluations, it occasionally underestimates depth values. On the real forest dataset, Transformer-based models still maintain super performance despite challenges in dimly shaded regions. Traditional CNN-based models, such as MiDas, perform poorly in regions with depth discontinuities, producing overly smooth depth predictions that lack detail. Overall, in complex forest environments, Transformer-based networks exhibit strong performance and generalization capability, making them more effective for depth estimation tasks in challenging real-world scenarios.

Furthermore, it is worth noting that recent research has already begun to build upon the foundations laid by Metric3D. Some metric depth estimation methods have explored ways to obtain absolute depth directly without requiring camera parameters. This highlights the potential of Metric3D to serve as a foundational framework for addressing more complex challenges in depth estimation. Specifically, Metric3D could be leveraged to tackle scenarios such as low-light environments, where depth estimation remains a significant challenge. By providing a robust baseline, Metric3D can facilitate further advancements in these areas, enabling more accurate and reliable depth estimation under various challenging conditions.

5. Conclusions

This study provides a comprehensive evaluation of the state-of-the-art deep learning-based monocular depth estimation methods in low-altitude forest environments. The evaluated models include both supervised and self-supervised methods, with diverse network architectures such as CNNs and Transformers. By conducting experiments on synthetic and real forest datasets, the study offers both qualitative insights into the visual prediction capabilities and quantitative assessment using a robust set of global and geometry-aware evaluation metrics.

The results demonstrate that Transformer-based network models, particularly DepthAnything and Metric3D, outperform CNN-based models in handling the unique challenges posed by forest environments. DepthAnything demonstrates superior performance on the Mid-Air dataset, excelling in global error metrics and directed depth error (DDE) evaluations. Its ability to accurately restore depth structures makes it a reliable choice for large-scale forest scene analysis. Meanwhile, Metric3D achieves the best results on the LOBDM-Forest (Synthetic) dataset, excelling in depth boundary error (DBE) metrics and effectively capturing fine details, such as depth discontinuities and tree branch edges. In contrast, traditional CNN-based models, such as MiDas and Adabins, struggle to handle depth discontinuities, producing smoother depth maps with less detail in regions with dense foliage or occlusions. These limitations underscore the importance of Transformer architectures, which leverage global contextual understanding and self-attention mechanisms to better generalize to outdoor forest scenes. These findings provide valuable insights for high-throughput plant phenotyping, environmental monitoring, and other forest-specific applications.

While the performance of Transformer-based models demonstrates significant progress in MDE tasks, challenges remain in achieving robust depth estimation under extreme occlusions and dense foliage areas. Future research could explore the integration of multimodal data, such as LiDAR or hyperspectral imaging, to complement monocular RGB inputs. Additionally, refining deep learning architectures to enhance their ability to model 3D spatial relationships and dynamic lighting conditions could further improve accuracy and robustness.

Author Contributions

Conceptualization, J.K. and J.J.; methodology, J.J. and J.K.; validation, J.J.; formal analysis, J.J. and J.K.; data curation, B.Z.; writing—original draft preparation, J.J. and J.K.; writing—review and editing, J.K., L.C., X.G. and G.Y.; supervision, J.K. and G.Y.; project administration, J.K. and G.Y. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Low-Viewpoint Forest dataset: https://zenodo.org/records/3945526 (accessed on 1 November 2024); LOBDM-Forest dataset: https://doi.org/10.3929/ethz-b-000634419 (accessed on 17 November 2024); Mid-Air: https://midair.ulg.ac.be (accessed on 4 November 2024).

Acknowledgments

We would like to express our gratitude to the following organizations for providing the datasets used in this study: The Environmental Robotics Laboratory, Dept. of Environmental Systems Science, ETH Zurich; Montefiore Institute; Chaoyue Niu, Danesh Tarapore, and Klaus-Peter Zauner from the University of Southampton.

Conflicts of Interest

Author Lin Chen was employed by the company VISCODA GmbH. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Depth Boundary Error (blue line: pred edge; black line: true edge; green line: euclidean distance). (a) [Forumla omitted. See PDF.]; (b) [Forumla omitted. See PDF.].

Figure 2. Sample images and ground-truth depth maps of the Mid-Air dataset.

Figure 3. Sample images and ground-truth depth maps of the LOBDM-Forest dataset. (a) Real-world data; (b) Synthetic data.

Figure 4. Sample real-world images and depth maps of the Low-Viewpoint Forest.

Figure 5. Distribution of depth values. (a) LOBDM-Forest (Synthetic); (b) Mid-Air.

Figure 6. The visual comparison of depth maps predicted by various MDE methods on the Mid-Air dataset.

Figure 6. The visual comparison of depth maps predicted by various MDE methods on the Mid-Air dataset.

Figure 7. The visual comparison of depth maps predicted by various MDE methods on the LOBDM-Forest (Synthetic).

Figure 8. Comparison of distance-related global errors for various MDE methods. (a) Mid-Air; (b) LOBDM-Forest.

Figure 9. Directed Depth Error (DDE) analysis across different depth planes for various MDE methods. (a) Mid-Air; (b) LOBDM-Forest (Synthetic).

Figure 10. Visualization of Directed Depth Error (DDE) on Mid-Air and LOBDM-Forest (Synthetic) datasets: color-coded depth estimation errors (yellow: underestimated, red: overestimated).

Figure 11. Visual results after applying Depth Boundary Error (DBE), the left two columns are the Mid-Air dataset, the right two columns are the LOBDM-Forest (Synthetic) dataset.

Figure 12. The visual comparison of depth maps predicted by different MDE methods on the real-world forest datasets: Low-Viewpoint Forest (Left) vs. LOBDM-Forest (Real) (Right).

Table 2

Summary of common datasets. The datasets shown in bold were included in our evaluation.

Name	Applicable Scenarios	Acquisition Tools	Image Resolution	Number of Images
KITTI [34]	Automatic driving	Lidar	1242 × 375	93,000+
NYU depth [35]	Indoor	RGB-D	640 × 480	1449
Cityscapes [36]	City	manual annotation	2048 × 1024	22,973
Make3D [3]	Outdoor	Lidar	2272 × 1704	534
Nuscenes [37]	Automatic driving	Lidar	1600 × 900	1000
DIODE [38]	Synthesis	Faro	1024 × 768	27,858+
Scene Flow [39]	Synthesis	synthetic	960 × 540	39,000+
MegaDepth [40]	Architecture	SFM+MVS	1600 × 1600	130,000+
LANet [41]	Forest	RGB-D	1280 × 720	400
Low-Viewpoint Forest [42]	Forest	RGB-D	640 × 480	9700
LOBDM [43]	Forest	synthetic	640 × 480	44,000+
Forest Inspection Dataset [46]	Wild/Forest	synthetic	1024 × 1024	34,000+
Mid-Air [47]	Wild/Forest	synthetic	1024 × 1024	42,0000
TartanAir [48]	Synthesis	synthetic	640 × 480	1,000,000
FRUC multiple sensor forest dataset [49]	Forest	RGB-D	1280 × 720	-

Table 3

Network training data details.

Method	Train Datasets	Type of Dataset	Number of Images	Model Resolution
Adabins [7]	NYU Depth v2 [59]	Indoor	50 K	320 × 240
GLP [8]	KITTI [34]	Autonomous driving	23 K	512 × 512
MiDas [6]	DIML [60]; MegaDepth [40]; ReDWeb [61]; WSVD [62]; 3DMovies [6]	Indoor; Synthesis	1.92 M	384 × 384
DPT [11]	DIML [60]; MegaDepth [40]; ReDWeb [61]; WSVD [62]; 3DMovies [6]; ApolloScape [63]; IRS [64]; TartanAir [48]; HRWSI [65]; BlendedMVS [66];	Indoor; Autonomous driving; Synthesis (including Forest)	1.4 M	384 × 384
Metric3D [10]	DDAD [67]; Lyft [68]; Driving Stereo (DS) [69]; DIML [60]; Arogoverse2 [70]; Cityscapes [36]; DSEC [71]; Mapillary PSD [72]; Pandaset [73]; UASOL [74]; Taskonomy [75]	Autonomous driving; Indoor; City; Outdoor	9.08 M	512 × 960
ZoeDepth [12]	DIML [60]; MegaDepth [40]; ReDWeb [61]; WSVD [62]; 3DMovies [6]; ApolloScape [63]; IRS [64]; TartanAir [48]; HRWSI [65]; BlendedMVS [66]; KITTI [34]; NYU Depth v2 [59]	Indoor; Autonomous; Synthesis (including Forest)	-	384 × 512
DepthAnything [9]	BlendedMVS [66]; DIML [60]; HRWSI [65]; IRS [64]; MegaDepth [40]; TartanAir [48]; BDD100K [76]; Google Landmarks [77]; ImageNet-21K [78]; LSUN [79]; Objects365 [80]; Open Images V7 [81]; Places365 [82]; SA-1B [83]	Architecture; Indoor; Autonomous driving; Synthesis (including Forest)	63.5 M	518 × 518

Table 4

Quantitative evaluation of global error metrics for various MDE methods. The bolded values in the table represent the results with the highest precision.

Method	Mid-Air (0–100m)						LOBDM-Forest (Synthetic) (0–10m)
	d1↑	d2↑	d3↑	RMSE (m)↓	RMSE Log↓	Abs Rel↓	d1↑	d2↑	d3↑	RMSE (m)↓	RMSE Log↓	Abs Rel↓
Adabins	0.518	0.672	0.753	24.975	0.658	0.515	0.592	0.904	0.990	1.606	0.260	0.211
GLP	0.355	0.655	0.769	18.438	0.618	0.396	0.575	0.894	0.989	1.651	0.266	0.218
MiDas	0.701	0.865	0.936	12.157	0.318	0.213	0.593	0.904	0.991	1.605	0.259	0.211
Metric3D	0.346	0.651	0.786	15.364	0.552	0.364	0.644	0.941	0.994	1.504	0.236	0.190
DPT	0.649	0.834	0.914	13.631	0.362	0.245	0.613	0.913	0.991	1.580	0.252	0.204
DepthAnything	0.717	0.883	0.949	11.430	0.301	0.197	0.664	0.938	0.992	1.506	0.235	0.187
ZoeDepth	0.572	0.777	0.875	17.773	0.423	0.324	0.592	0.904	0.991	1.624	0.260	0.211

Table 5

Quantitative evaluation of Directed Depth Error for various MDE methods. The bolded values in the table represent the results with the highest precision.

Method	Mid-Air			LOBDM-Forest (Synthetic)
	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^0$↑	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^{+}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^{-}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^0$↑	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^{+}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{D}\mathbf{E}}^{-}$↓
Adabins	80.213	4.331	15.456	67.359	10.489	22.152
GLP	77.362	0.455	22.183	65.511	10.523	23.967
MiDas	89.951	3.481	6.568	67.253	10.542	22.205
Metric3D	77.940	0.113	21.947	72.205	9.160	18.635
DPT	87.578	2.543	9.879	68.539	10.556	20.905
DepthAnything	91.091	2.395	6.514	73.107	10.067	16.826
ZoeDepth	86.965	1.318	11.716	66.886	10.562	22.552

Table 6

Quantitative evaluation of depth boundary accuracy for various MDE methods. The bolded values in the table represent the results with the highest precision.

Method	Mid-Air		LOBDM-Forest (Synthetic)
	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{a}\mathbf{c}\mathbf{c}}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{a}\mathbf{c}\mathbf{c}}$↓	${\mathit{\epsilon }}_{\mathbf{D}\mathbf{B}\mathbf{E}}^{\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}}$↓
Adabins	2.221	213.491	3.841	74.092
GLP	2.385	50.597	2.529	33.267
MiDas	3.002	79.888	3.713	93.361
Metric3D	1.712	27.253	1.524	5.494
DPT	2.589	63.783	2.369	26.860
DepthAnything	1.690	37.169	1.597	8.951
ZoeDepth	2.004	86.188	2.074	32.678

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