Depth Edge Alignment Loss

• Depth Edge Alignment Loss is a technique that aligns predicted depth discontinuities with ground-truth or pseudo edge cues using methods like gradient matching and multi-scale edge losses.
• It encompasses various approaches such as direct L1 gradient matching, preservation of initial edge maps during adaptation, and implicit alignment via architectural gating.
• This alignment improves boundary sharpness and structural detail in depth estimation and semantic segmentation, leading to enhanced performance across benchmarks.

Depth Edge Alignment Loss denotes a class of objectives that constrain predicted boundaries to agree with boundary cues derived from depth itself, from a reference depth map, or from auxiliary structure such as semantic or image edges. In the narrowest sense, the name is used explicitly by the weakly supervised semantic segmentation loss DEAL, which aligns class activation map boundaries with depth discontinuities (Schmidt et al., 22 Sep 2025). In depth estimation literature, closely related formulations appear under names such as “Gradient Edge Loss,” “multi-scale edge loss,” “edge-preserving loss,” and “edge-aware smoothness,” but they differ materially in what is being aligned: predicted depth gradients to ground-truth depth gradients, current depth to initial depth edges during adaptation, or disparity smoothness to learned edge maps (Hafeez et al., 2024, Oda et al., 2022, Kosheleva et al., 2023, Song et al., 2019).

1. Scope of the term

The literature does not present a single canonical definition of Depth Edge Alignment Loss. Instead, several distinct mechanisms recur. One family performs direct depth-to-depth gradient matching under full supervision. Another preserves edge locations already present in an initial depth estimate during test-time adaptation. A third uses pseudo edge labels when dense edge supervision is unavailable. A fourth enforces edge alignment implicitly through architectural gating or masked regularization rather than through an explicit penalty. A fifth, represented by DEAL, uses depth edges to supervise semantic boundaries rather than depth prediction itself (Schmidt et al., 22 Sep 2025, Talker et al., 2022, Huang et al., 6 Aug 2025).

Paper	Alignment target	Mechanism
(Hafeez et al., 2024)	Predicted depth vs. ground-truth depth edges	L1 difference of horizontal and vertical depth gradients
(Oda et al., 2022)	Predicted vs. ground-truth depth edge maps	Multi-scale edge loss with per-pixel max across $3\times3,5\times5,7\times7$ differentials
(Kosheleva et al., 2023)	Current depth vs. initial depth edges	Multi-scale gradient loss and contrastive ratio-gradient loss
(Talker et al., 2022)	Predicted depth-edge probabilities vs. pseudo labels	Balanced BCE on an Edge Detection Block
(Schmidt et al., 22 Sep 2025)	CAM edges vs. depth edges	Sobel edge correlation after normalization and logit-tanh activation

This range suggests that “alignment” may refer either to explicit correspondence of edge magnitudes and locations or to indirect preservation of discontinuities by suppressing cross-edge smoothing. A common misconception is that these losses always align depth to RGB-image edges. Several of the most explicit formulations do not: the supervised gradient-matching loss in monocular depth estimation compares predicted depth only to ground-truth depth, the endoscopic multi-scale edge loss compares predicted and target depth edge maps only, and the stereo-video test-time training losses preserve edges from the initial depth map rather than from image intensity (Hafeez et al., 2024, Oda et al., 2022, Kosheleva et al., 2023).

2. Direct alignment to ground-truth depth gradients

A particularly explicit formulation appears in supervised monocular depth estimation as “Gradient Edge Loss,” described here as Depth Edge Alignment Loss. The loss is computed between predicted and ground-truth depth maps at the working resolution and measures the L1 discrepancy between horizontal and vertical depth derivatives:

$$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$

The same work optimizes a weighted sum of MAE, this edge term, and SSIM,

$$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$

with weights selected by grid search and random search on NYU Depth v2. The paper states that the loss “encourages the model to capture the depth transitions and edges accurately,” reports that it is computed on downsampled $320\times240$ depth maps, and notes that no multi-scale formulation, boundary masking, cosine similarity, cross-correlation, or RGB-image edges are used (Hafeez et al., 2024).

In that setting, the final model uses an EfficientNet encoder pretrained on ImageNet with a simple upsampling decoder and skip connections. The reported test-set results on NYU Depth v2 are RMSE $=0.386$, REL $=0.113$, $\log_{10}=0.049$, and threshold accuracies $\delta_1=0.872$, $\delta_2=0.973$, $\delta_3=0.996$. Qualitative discussion emphasizes sharper object boundaries, improved recovery of thin structures, and cases in which the model reconstructs missing ground-truth structures such as chair legs (Hafeez et al., 2024).

A related but distinct fully supervised formulation appears in monocular endoscopic depth estimation as a multi-scale edge loss. Let $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$0 be the ground-truth depth image, $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$1 the prediction, and let edge maps at scales $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$2 be computed by first-order differential filters with intervals $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$3. The paper defines

$$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$4

and combines it with an L1 depth term and an SSIM-based loss,

$$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$5

with $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$6. The scales are realized by increasing differential support rather than by Gaussian pyramids or downsampling, and the per-pixel max acts as a worst-case scale selector. Reported downstream evidence includes anatomical location identification improving from $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$7 to $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$8 when estimated depth images are used, and a reported correlation coefficient of $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$9 between estimated and measured depths on real colonoscopic images (Oda et al., 2022).

Taken together, these two supervised variants show that direct edge alignment can be implemented either as gradient matching in $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$0 and $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$1 or as multi-scale edge-map matching. In both cases, the alignment target is the ground-truth depth map itself, not RGB structure (Hafeez et al., 2024, Oda et al., 2022).

3. Alignment to reference depth edges under weak or indirect supervision

When dense ground-truth depth edges are unavailable, alignment losses often use a reference depth field other than the final supervision target. In stereo-video test-time training, the edge-preserving objective is designed to prevent the current depth estimate $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$2 from blurring relative to the initial prediction $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$3. The paper introduces two differentiable, scale-invariant losses. The first uses a normalized finite-difference operator

$$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$4

at scales $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$5, together with masks computed only where the initial depth has strong edges. The multi-scale loss penalizes differences between $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$6 and $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$7 at masked locations. The second, contrastive ratio-gradient loss,

$$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$8

does not require exact gradient matching; it enforces that an edge remains present at the same location. These losses are added to a geometric stereo and temporal consistency objective during test-time training, with reported hyperparameters including $$\mathcal{L}_{\text{total}} = 0.6\,\mathcal{L}_{\text{MAE}} + 0.2\,\mathcal{L}_{\text{edge}} + 1.0\,\mathcal{L}_{\text{SSIM}},$$9, $320\times240$0, $320\times240$1, $320\times240$2, ADAM, and about 20 epochs (Kosheleva et al., 2023).

The empirical evidence in that work is framed around adaptation quality rather than stand-alone edge accuracy. On ETH3D monocular test-time training ablations, CVDE yields $320\times240$3, $320\times240$4, $320\times240$5, and $320\times240$6; adding $320\times240$7 changes these to $320\times240$8, and adding $320\times240$9 changes them to $=0.386$0. The paper states that both edge-aware terms improve over CVDE and that the contrastive loss yields the most consistent gains across all metrics and visibly sharper boundaries (Kosheleva et al., 2023).

A different weakly supervised strategy appears in sparsely supervised monocular depth estimation with LiDAR. There, depth edges are first detected by a separate network trained on synthetic dense data, and the resulting pseudo labels $=0.386$1 supervise an Edge Detection Block operating on the predicted depth. The paper defines an edge probability

$=0.386$2

where $=0.386$3 is a directional derivative perpendicular to the pseudo edge normal $=0.386$4. Alignment is then enforced by a Balanced Binary Cross-Entropy loss,

$=0.386$5

within the total objective

$=0.386$6

The reported gains are substantial in edge metrics while per-pixel depth accuracy remains comparable on sparse datasets. On KITTI-DE, Packnet-SAN improves from AUC $=0.386$7 $=0.386$8 to $=0.386$9 $=0.113$0 with ARE changing from $=0.113$1 to $=0.113$2; on DDAD-DE, Packnet-SAN improves from AUC $=0.113$3 $=0.113$4 to $=0.113$5 $=0.113$6 with ARE changing from $=0.113$7 to $=0.113$8 (Talker et al., 2022).

These two approaches share an important structural feature: the alignment target is not dense ground-truth depth. Instead, it is either an initial depth estimate preserved during adaptation or a pseudo edge map inferred from another model. This suggests that Depth Edge Alignment Loss is especially useful when edge localization is easier to supervise than full depth values (Kosheleva et al., 2023, Talker et al., 2022).

4. Implicit edge alignment through regularization and architecture

Not all edge-alignment methods introduce a standalone loss. In sparse depth upsampling, the guided convolutional design itself encodes edge alignment. The Edge Guided Convolutional Layer multiplies both the data and normalization terms by an edge-distance field $=0.113$9, whose minima lie on edges and whose values increase away from them:

$\log_{10}=0.049$0

The paper explicitly states that it does not define a “Depth Edge Alignment Loss”; any such loss is a derived formalization of its mechanism rather than part of the original objective. The architectural effect is to prevent depth aggregation across discontinuities and to reduce texture copy and depth blur (Guo et al., 2020).

In stereo matching, edge alignment appears as an edge-aware smoothness loss rather than direct edge matching. EdgeStereo defines

$\log_{10}=0.049$1

where $\log_{10}=0.049$2 is disparity and $\log_{10}=0.049$3 is the predicted edge probability map. The edge branch and disparity branch are also coupled through feature embedding. The paper reports that edge-aware smoothness outperforms compared smoothness formulations and improves near-boundary performance; on KITTI 2012 validation, the baseline has $\log_{10}=0.049$4 px error $\log_{10}=0.049$5 and EPE $\log_{10}=0.049$6, while adding $\log_{10}=0.049$7 and edge features yields $\log_{10}=0.049$8 and $\log_{10}=0.049$9 (Song et al., 2019).

DET-GS uses yet another indirect construction. It combines hierarchical geometric depth supervision, Canny-masked edge-aware depth regularization, and an RGB-guided edge-preserving TV loss. The masked local-mean depth regularizer is

$\delta_1=0.872$0

with $\delta_1=0.872$1 and $\delta_1=0.872$2 from Canny on the ground-truth RGB image. The paper states that DET-GS does not add a separate explicit alignment term, but that masked smoothing and TV modulation already enforce the desired effect implicitly. Reported ablations on Mip-NeRF 360 show PSNR dropping from $\delta_1=0.872$3 to $\delta_1=0.872$4 without $\delta_1=0.872$5, and to $\delta_1=0.872$6 without $\delta_1=0.872$7 (Huang et al., 6 Aug 2025).

ECFNet occupies an intermediate position. It uses explicit edge maps as input modalities and employs guided filtering, a gradient-domain ranking loss, and a depth consistency module, but it does not define a training term that directly compares depth edges to image edges. The paper explicitly states that the closest “Depth Edge Alignment” constraints are the gradient-domain ranking loss and cross-resolution consistency, not an $\delta_1=0.872$8-weighted edge penalty. Reported NYU-v2 results include SqRel improving from $\delta_1=0.872$9 to $\delta_2=0.973$0 for a DPT base model and ESR improving from $\delta_2=0.973$1 to $\delta_2=0.973$2 (Li et al., 2024).

These methods show that edge alignment may be realized by gating, masked smoothing, cross-task coupling, or multi-branch fusion. The absence of an explicit edge-matching loss does not imply the absence of an edge-alignment objective in functional terms (Guo et al., 2020, Song et al., 2019, Huang et al., 6 Aug 2025, Li et al., 2024).

5. DEAL as an explicit loss for semantic boundaries

The most literal use of the term appears in “Depth Edge Alignment Loss: DEALing with Depth in Weakly Supervised Semantic Segmentation.” In this formulation, depth edges are not used to supervise a depth predictor; instead, they regularize semantic boundaries in class activation maps. Let $\delta_2=0.973$3 be the CAM tensor, $\delta_2=0.973$4 the depth map, and let Sobel filters produce gradient magnitudes $\delta_2=0.973$5 for each class channel and $\delta_2=0.973$6 for the depth map. After per-sample normalization to $\delta_2=0.973$7, the method applies

$\delta_2=0.973$8

to obtain semantic and depth alignment activations $\delta_2=0.973$9 and $\delta_3=0.996$0 in $\delta_3=0.996$1. The loss is

$\delta_3=0.996$2

where only present classes contribute. The combined objective is

$\delta_3=0.996$3

or, when auxiliary losses are included,

$\delta_3=0.996$4

The paper reports $\delta_3=0.996$5, $\delta_3=0.996$6 with internal scaling by $\delta_3=0.996$7, $\delta_3=0.996$8, and warm-up schedules of 20 epochs for WeakTr and 3 epochs for SEAM (Schmidt et al., 22 Sep 2025).

The reported improvements are on segmentation mIoU rather than depth metrics. On PASCAL VOC with WeakTr, DEAL alone gives mean improvements of $\delta_3=0.996$9 on train and $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$00 on val over the baseline; DEAL with ISL/FSL yields average scores of $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$01 vs. $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$02 on train and $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$03 vs. $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$04 on val. On SEAM for PASCAL VOC, the best-seed gains with DEAL+ISL/FSL are $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$05 on train and $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$06 on val. On HOPE with WeakTr, the paper reports improvements up to $$\mathcal{L}_{\text{edge}} = \frac{1}{N}\sum_{i=1}^{N} \left( \left| \frac{\partial Y_{\text{pred}}}{\partial x}(i) - \frac{\partial Y_{\text{true}}}{\partial x}(i) \right| + \left| \frac{\partial Y_{\text{pred}}}{\partial y}(i) - \frac{\partial Y_{\text{true}}}{\partial y}(i) \right| \right).$$07 mIoU on the static split (Schmidt et al., 22 Sep 2025).

DEAL is therefore an explicit Depth Edge Alignment Loss in name and in algebraic form, but its application domain differs from the depth-estimation formulations summarized above. It aligns semantic activation boundaries with physical depth discontinuities, using depth as an auxiliary supervisory modality during training (Schmidt et al., 22 Sep 2025).

6. Recurring design principles, limitations, and misconceptions

Several design principles recur across these formulations. First, edge extraction is usually simple and local: finite differences in supervised depth estimation, discrete multi-interval differentials in endoscopy, Sobel filters in DEAL, learned or Canny-derived edge maps in sparse or stereo settings (Hafeez et al., 2024, Oda et al., 2022, Schmidt et al., 22 Sep 2025, Talker et al., 2022). Second, alignment is often restricted to reliable locations by masks, whether these are strong-edge masks from the initial depth, valid LiDAR support, non-edge masks from Canny, or class-presence masks in segmentation (Kosheleva et al., 2023, Talker et al., 2022, Huang et al., 6 Aug 2025, Schmidt et al., 22 Sep 2025). Third, edge-aware losses are commonly auxiliary rather than standalone; they are paired with MAE, SSIM, geometric reprojection, disparity regression, photometric color losses, or image-level classification objectives (Hafeez et al., 2024, Kosheleva et al., 2023, Song et al., 2019, Schmidt et al., 22 Sep 2025).

The main limitations are equally consistent. Methods that preserve initial depth edges can preserve wrong edges when the initial map is noisy or misses boundaries; the stereo-video paper states this explicitly (Kosheleva et al., 2023). Pseudo-label supervision inherits domain-gap errors from synthetic-to-real edge detectors and can improve edge AUC without materially improving per-pixel sparse-depth metrics (Talker et al., 2022). RGB-derived edge masks can be noisy or misaligned, especially under low contrast, heavy texture, or imperfect RGB-depth registration, which the sparse upsampling and DET-GS papers both identify as practical concerns (Guo et al., 2020, Huang et al., 6 Aug 2025). DEAL assumes depth availability at training time and can be degraded by modality misalignment or sensor artifacts (Schmidt et al., 22 Sep 2025).

Two misconceptions are especially common. The first is that Depth Edge Alignment Loss is synonymous with edge-aware smoothness. The literature shows otherwise: some methods penalize disagreement with target depth gradients, whereas others merely relax smoothing near edges or preserve previously detected edges (Hafeez et al., 2024, Song et al., 2019). The second is that edge-aware methods necessarily sharpen edges. Some works, notably the sparse-LiDAR monocular depth study, emphasize that their contribution is edge localization rather than sharpening of blurred transitions (Talker et al., 2022). This suggests that “alignment” should be read primarily as correspondence of boundary placement and structural coherence, with edge acuity depending on the surrounding architecture, supervision density, and complementary losses.