Cross-Dimensional Supervision for OCT-to-OCTA

• CDS is a training strategy in OCT-to-OCTA translation, using 2D layer-specific en-face projections to guide 3D vascular reconstruction.
• It generates layer-specific 2D summaries via segmentation-weighted averaging, ensuring anatomical alignment and distinct vessel detail preservation.
• Empirical results show CDS improves SSIM and reduces artifacts by reinforcing fine microvascular patterns across retinal layers.

Searching arXiv for the cited papers and closely related cross-dimensional work. Cross-Dimensional Supervision (CDS) is a training strategy introduced in XOCT for OCT-to-OCTA translation in which a 3D generator is supervised not only at the volumetric level but also through 2D, layer-wise en-face projections derived from anatomical retinal segmentation (Khosravi et al., 9 Sep 2025). In this formulation, the predicted OCTA volume is projected into anatomically meaningful retinal layers, and these 2D projections are compared with corresponding ground-truth projections through a composite loss. The purpose is to compel the network to learn distinct representations for each retinal layer and to reconstruct vascular features unique to each layer, thereby addressing the tendency of prior OCT-to-OCTA methods to overlook vascular differences across retinal layers and to miss fine, clinically relevant vessel details (Khosravi et al., 9 Sep 2025).

1. Definition and problem setting

CDS was proposed in the context of OCT-to-OCTA translation, where the goal is to generate a high-quality 3D angiogram from a standard volumetric OCT scan (Khosravi et al., 9 Sep 2025). The motivating problem is that existing deep learning methods often fail to capture the distinct vascular architectures and imaging properties unique to each retinal layer, which degrades reconstruction of intricate, dense vascular details necessary for reliable diagnosis (Khosravi et al., 9 Sep 2025).

Within XOCT, CDS is defined as a cross-dimensional supervisory mechanism because the model predicts a 3D OCTA volume while receiving additional supervision from 2D layer-wise en-face projections (Khosravi et al., 9 Sep 2025). These projections are generated via segmentation-weighted z-axis averaging, so the supervisory signal is anatomically localized rather than globally aggregated (Khosravi et al., 9 Sep 2025). The dimensional transition is therefore not a preprocessing step for inference, but a loss construction applied during training.

The central operational idea is that supervision is provided directly on layer-relevant vascular structure (Khosravi et al., 9 Sep 2025). Rather than constraining only the bulk 3D angiogram, CDS requires agreement between predicted and ground-truth layer-specific projections. This makes the training signal sensitive to vessel layouts characteristic of different anatomical depths, including differences between superficial and deep capillary structures (Khosravi et al., 9 Sep 2025).

2. Construction of the cross-dimensional signal

The CDS pipeline begins with retinal layer segmentation. The retina is separated into anatomically meaningful layers, with examples including ILM-OPL and OPL-BM, and each layer has different vascular patterns (Khosravi et al., 9 Sep 2025). The inputs to CDS are a predicted OCTA volume $\widehat{\mathbf{Y}}$ and a pre-computed segmentation map $\mathbf{S}$ of the same shape as the volume (Khosravi et al., 9 Sep 2025).

For each retinal layer $l$, XOCT forms a 2D en-face projection by computing a segmentation-weighted average along the depth axis:

$$\widehat{\mathbf{P}}_l = \frac{\sum_z \widehat{\mathbf{Y}} \odot \mathbf{S}_l}{\sum_z \mathbf{S}_l},$$

where $$\widehat{\mathbf{Y}} \in \mathbb{R}^{D \times H \times W}$$ is the predicted OCTA volume, $\mathbf{S}_l \in \mathbb{R}^{D \times H \times W}$ is the binary mask for layer $l$, and $\widehat{\mathbf{P}}_l \in \mathbb{R}^{H \times W}$ is the layer-wise en-face angiogram (Khosravi et al., 9 Sep 2025). In this expression, the numerator sums predicted vessel intensities within layer $l$ across depth, and the denominator normalizes by the number of voxels at each spatial location within the layer (Khosravi et al., 9 Sep 2025).

This mechanism yields a set of layer-specific 2D images that can be supervised independently. Because the projections are generated with segmentation masks, the supervision is anatomically aligned rather than based on a single full-depth projection (Khosravi et al., 9 Sep 2025). A plausible implication is that the network is discouraged from representing the retina as a monolithic slab, since each layer contributes an explicit supervisory target.

3. Loss formulation

After projecting both the predicted and the ground-truth volumes into 2D layer-wise en-face maps, CDS applies a composite loss for each layer (Khosravi et al., 9 Sep 2025). The loss includes three terms: an $L_1$ loss for pixel-wise similarity, an adversarial loss for realistic angiogram appearance, and a perceptual loss based on pretrained VGG19 neural features for high-level structural similarity (Khosravi et al., 9 Sep 2025).

The 2D CDS objective is

$\mathbf{S}$0

where $\mathbf{S}$1 is the ground-truth en-face projection for layer $\mathbf{S}$2 and $\mathbf{S}$3 are weighting coefficients (Khosravi et al., 9 Sep 2025). The full training objective combines the volumetric loss and the cross-dimensional loss:

$\mathbf{S}$4

with $\mathbf{S}$5 including volumetric $\mathbf{S}$6 and adversarial losses (Khosravi et al., 9 Sep 2025).

Two architectural consequences follow directly from this formulation. First, no extra generator is needed for 2D projections; the 3D generator’s output is projected via segmentation masks for loss computations (Khosravi et al., 9 Sep 2025). Second, XOCT uses per-layer 2D discriminators, so gradients arrive from both 3D and per-layer 2D objectives (Khosravi et al., 9 Sep 2025). The supervisory mechanism is therefore cross-dimensional at the level of optimization, not at the level of separate prediction heads.

4. Integration within XOCT and representational effect

During training, the network takes a 3D OCT volume as input and produces a 3D predicted OCTA volume as output; the layer segmentation map is used for loss only (Khosravi et al., 9 Sep 2025). Standard 3D losses are computed on the bulk volume, while CDS computes per-layer 2D losses by projecting the prediction and the ground truth and comparing them (Khosravi et al., 9 Sep 2025). No segmentation is needed at inference time (Khosravi et al., 9 Sep 2025).

The representational role attributed to CDS is explicit. By backpropagating loss specifically for each layer’s en-face projection at each training step, the network must represent details unique to each retinal layer, not just global or averaged features (Khosravi et al., 9 Sep 2025). The reported effects include improved intra-layer vessel coherence, preservation of fine microvascular patterns, and better distinction between vessels unique to either superficial or deep retinal layers (Khosravi et al., 9 Sep 2025).

XOCT combines CDS with a Multi-Scale Feature Fusion (MSFF) module. MSFF enhances vessel delineation through multi-scale feature extraction combined with a channel reweighting strategy, effectively capturing vascular details at multiple spatial scales (Khosravi et al., 9 Sep 2025). The ablation description assigns different roles to the two components: CDS alone already provides a substantial boost in layer-specific structure reconstruction, whereas MSFF mainly helps volumetric detail; when both are combined, layer-wise and volumetric vessel coherence are maximized (Khosravi et al., 9 Sep 2025).

A common misconception is that CDS requires segmentation at deployment. The training protocol states the opposite: segmentation maps are used during training for loss computation, but the model does not require layer maps when predicting OCTA from a new OCT (Khosravi et al., 9 Sep 2025). Another misconception is that CDS is a second-stage 2D reconstruction model. In XOCT, it is instead a supervisory pathway applied to the output of a single 3D generator (Khosravi et al., 9 Sep 2025).

5. Empirical behavior

Experiments on the OCTA-500 dataset show improvements, especially for the en-face projections, which are significant for clinical evaluation of retinal pathologies (Khosravi et al., 9 Sep 2025). In the reported quantitative evaluation, XOCT with CDS and MSFF achieves best or competitive scores across SSIM, Perceptual Discrepancy, MAE, and PSNR for 2D en-face projections, layer-specific projections, and 3D volumes (Khosravi et al., 9 Sep 2025).

The ablation study isolates the contribution of CDS. On OCTA-3M, the SSIM for $\mathbf{S}$7 rises from $\mathbf{S}$8 for the baseline Pix2Pix3D to $\mathbf{S}$9 with CDS, and the SSIM for $l$0 rises from $l$1 to $l$2 (Khosravi et al., 9 Sep 2025). The perceptual loss, where lower is better, drops accordingly (Khosravi et al., 9 Sep 2025).

Setting	$l$3 SSIM	$l$4 SSIM
Pix2Pix3D baseline	0.556	0.509
+ CDS	0.600	0.563

The qualitative analysis attributes several visible changes to CDS. Visual examples show sharper, more continuous vessel structures and better preservation of subtle vessel dropouts and microvascular details (Khosravi et al., 9 Sep 2025). The method is also described as reducing artifacts and enhancing anatomical realism in synthetic OCTA, while competing methods, including strong 3D GANs, tend to blur or erroneously fill in missing vessels (Khosravi et al., 9 Sep 2025). In the paper’s interpretation, these differences are clinically relevant because subtle vessel loss and layer-specific vascular changes are important for retinal disease assessment.

6. Position within cross-dimensional learning

CDS belongs to a broader set of methods that use information defined in one representational dimension to supervise learning in another. In medical self-supervised learning, CDSSL-P3D converts 2D images into a pseudo-3D format using an im2col-inspired transformation so that 2D and 3D medical data can be jointly pre-trained in a single 3D network (Gao et al., 2024). In time-series forecasting, X-Freq discards time-domain supervision and computes supervision in the frequency domain along both the time and channel dimensions through Fourier and Wavelet transforms (Shi et al., 16 May 2025).

These neighboring examples are methodologically distinct from XOCT, but they clarify the technical meaning of “cross-dimensional.” In CDSSL-P3D, the cross-dimensional relation is between 2D and 3D data representations (Gao et al., 2024). In X-Freq, it is between temporal and channel-wise spectral representations (Shi et al., 16 May 2025). In XOCT, it is between a 3D vascular volume and 2D layer-wise projections derived from retinal anatomy (Khosravi et al., 9 Sep 2025). This suggests that cross-dimensional supervision is best understood not as a single architecture family, but as a design principle in which the optimization signal is redistributed across heterogeneous representational axes.

Within that broader framing, CDS is notable for being anatomically guided rather than purely geometric or spectral. Its supervisory targets are not arbitrary lower-dimensional summaries; they are segmentation-weighted en-face projections aligned to retinal layers (Khosravi et al., 9 Sep 2025). That design choice ties the cross-dimensional loss directly to clinically meaningful vascular organization, which explains why the largest reported gains are concentrated in en-face projections and layer-specific vessel reconstruction rather than in a generic image-similarity objective (Khosravi et al., 9 Sep 2025).