PG-MAMBA: A Widefield OCTA Dataset and a Polar Mamba Vessel Network

Why a wider view is worth the trouble

Optical coherence tomography angiography, mercifully shortened to OCTA, is a way of photographing the retina’s blood vessels without injecting any dye. It has become a workhorse of eye care because vascular changes show up early in many conditions. The catch is that most OCTA systems, and nearly all the public datasets built on them, look at a small window near the center of the retina. That is fine for diseases centered on the macula, but it misses the story in high myopia, where the eyeball elongates and the damage often appears out in the periphery.

Ultra widefield swept source OCTA changes the frame. The system used here captures a field of view of 24 by 20 millimeters, roughly 120 degrees of the retina in a single acquisition, which is 13.3 times the imaging area of OCTA-500 and 3.3 times that of DRAC, the closest public benchmarks. That is a lot more retina, and with it comes a lot more vasculature, from the thick vessels near the optic disc to the whisper thin capillaries at the edge where the signal fades and the boundaries blur.

So the dataset problem and the modeling problem arrive together. There was no public wide field OCTA vessel dataset to train or test on, and the segmentation methods that work on small central patches were never designed for this scale. The paper takes on both at once, releasing a dataset called WOIVES and a network called PG-Mamba, and the more interesting ideas live in how each was built.

WOIVES, a dataset that refuses to pretend

WOIVES stands for a widefield swept source OCTA image dataset based on vessel segmentation, and its headline number is coverage. It comprises 206 eyes from 152 participants, imaged at Shenzhen Eye Hospital across most of 2023 under ethics approval and informed consent. A clinically characterized subset of 177 eyes from 130 participants adds full ocular biometry, including axial length, spherical equivalent, intraocular pressure, corneal thickness, and refractive diagnosis. The cohort deliberately spans the range from emmetropia, meaning normal refraction, through myopia to high myopia, so the dataset is built for exactly the myopia focused analysis that widefield imaging is meant to serve.

The part that deserves attention is the annotation philosophy. Vessel boundaries in the far periphery are not crisp. Reduced signal to noise and partial volume effects make the thinnest vessels genuinely ambiguous, and two careful experts will disagree about where a vessel ends. The usual response is to force a binary mask and pretend the ambiguity away. WOIVES does the opposite. It keeps the labels as soft probability maps, where a value near one means a confident vessel, a value near zero means confident background, and the values in between record honest uncertainty at the boundaries.

Those soft labels come from a two stage human machine pipeline. In the first stage, five junior ophthalmologists each annotate an image with the help of SAM-OCTA, a segmentation assistant adapted from the Segment Anything Model, and the five annotations are averaged into a single probability map. In the second stage, two senior experts with years of clinical experience review and refine that fused map, adding missed vessels, removing false ones, and correcting boundaries. The final annotation stays continuous rather than being thresholded, which the authors argue improves both probability calibration and sensitivity to small structures during training.

PG-Mamba and the problem of scanning a circle

The network builds on a family of models called state space models, and specifically on Mamba, which has become a popular alternative to attention because it models long range dependencies at a cost that grows only linearly with sequence length. That efficiency is attractive for large images, and if you want the wider context on why these models keep spreading through vision, our earlier piece on how Mamba state space models are reshaping fusion covers the ground. But applying Mamba to an image hides a subtle decision. A state space model reads a one dimensional sequence, so a two dimensional image has to be flattened into an ordered list of pixels first, and the order you choose determines which spatial relationships the model can actually follow.

Standard visual Mamba models scan the image in four directions, left to right, top to bottom, and the two diagonals. Those grid aligned orders make sense for ordinary photos. They make less sense for a retina, where the vessels radiate outward from the optic disc like spokes from a hub. So the authors add two scan orders defined in polar coordinates rather than the usual grid. One traces outward from the center toward the edge, which they call Radial Out, and one traces inward, Radial In. Combined with the four conventional scans, the network reads each feature map six different ways and merges the results, giving it an ordering that follows the natural geometry of retinal vasculature.

The polar scan, concretely

For a feature map of height H and width W, every pixel gets polar coordinates relative to the center, a radius and an angle. The two new scan orders sort the pixels by a score that combines the two.

where the radius term dominates the ordering and its sign decides whether the traversal moves outward or inward, while the angular term breaks ties within each radial band. The full scan set then holds six orderings, and the polar operator applies a selective scan to each and reverses the permutation to put the features back in place.

Gating out the empty corners

A widefield OCTA image is a circle of data inside a rectangular frame, so the corners are empty. Dynamic FOV Gating is a small module at the network bottleneck that stops the model from wasting capacity there. It builds a normalized polar grid, uses it to produce a content adaptive soft mask through a couple of small convolutions, and multiplies that by a fixed hard mask that simply zeroes out everything beyond a radius threshold.

The soft mask lets the network emphasize informative regions, while the hard mask enforces the physical boundary of the valid imaging area. The whole architecture is a U shaped encoder decoder, with the image split into 512 by 512 tiles, patch embedding into a 96 dimensional space, four stages of Polar Blocks at increasing depth, and a mirrored decoder that expands back to full resolution and applies a sigmoid to produce the vessel probability map.

How segmentation is judged when labels are soft

Because the annotations are probability maps, the paper does not judge the model on overlap alone. The composite training loss combines a soft Dice term, which rewards spatial overlap with the continuous labels, and a mean squared error term, which supplies pixel wise supervision against the probability values.

Evaluation reaches across three levels. Overlap is measured with Dice and intersection over union after thresholding. Agreement with the continuous labels is measured with soft Dice, mean absolute error, and the Brier score. Vascular connectivity is measured with centerline Dice, written clDice, which rewards keeping the skeleton of the vessel tree intact rather than just filling area. That multi level view is the point, because a model can score well on area and still break thin vessels into disconnected fragments.

What the numbers show

The authors compared PG-Mamba against seven segmentation methods spanning three families, convolutional networks like U-Net and UNet++, transformer models like Swin-UNet and H2Former, and other Mamba based networks like VM-UNet, all retrained on WOIVES with the same single channel input and composite loss, under subject level five fold cross validation.

PG-Mamba took the top spot on five of the six metrics, leading on Dice at 89.81, intersection over union at 82.20, soft Dice at 85.99, centerline Dice at 91.97, and mean absolute error at 0.0257. The one exception is the Brier score, where H2Former recorded the lowest value at 0.0146 and PG-Mamba shared the second lowest at 0.0156. The improvements over the strongest overall baseline, VM-UNet, are honest about their size, 0.44 points of Dice and 0.38 points of centerline Dice. These are small margins, and the paper says so plainly, though it notes that eye level paired tests found them statistically significant across the pooled predictions.

The ablation traces where the gains come from within the PG-Mamba framework itself. Starting from a four direction baseline, adding the two polar scans lifted Dice from 89.43 to 89.67 and centerline Dice from 91.54 to 91.73. Adding Dynamic FOV Gating on top raised Dice further to 89.81 and centerline Dice to 91.97, while nudging the Brier score down to 0.0156. Each component helps a little, in the same direction, which is the pattern you want to see even when no single piece is dramatic.

A model can cover the right area and still shatter the vessel tree into disconnected pieces. Judging segmentation at three levels at once, overlap, probability, and connectivity, is what keeps that failure visible. Reading of the paper’s evaluation design

From segmentation to vascular measurement

Segmentation is rarely the end goal. Clinicians care about the numbers you can derive from a vessel map, so the authors checked whether better segmentation translated into better vascular measurements, comparing four quantities against references derived from the expert annotations. PG-Mamba achieved the lowest median absolute errors for vessel density at 0.0081, fractal dimension at 0.0109, and vessel length density at 1.3414, beating every comparison model on all three after statistical correction.

The interesting wrinkle is where it did not win. On a connectivity sensitive count of connected components, PG-Mamba landed at a median error of 9.2508, lower than R2U-Net but higher than both U-Net and VM-UNet. The authors resist the temptation to sweep this under the rug. Different measurements respond to different properties of a segmentation, they explain, and this particular one is exquisitely sensitive to small disconnected regions and local breaks. Better overlap can go hand in hand with lower error on several vascular measurements without guaranteeing improvement on every connectivity sensitive one. That is a more careful conclusion than most papers offer, and it is the right one.

Clinical translation gap

It is worth being precise about how far this is from the clinic. The vascular measurement analysis compares predictions against references derived from the expert annotations, not against any independent clinical ground truth. The authors state this directly, that the analysis evaluates agreement with annotation derived measurements and should not be interpreted as validation of clinical measurement accuracy. In other words, the study shows the model agrees with expert labeling, which is a necessary step, not that its numbers are correct in a way that should guide care.

The data also came from a single center, a single swept source OCTA device, and a cohort weighted toward myopic and highly myopic eyes. A tool meant to assess myopia related vascular change would need testing across multiple centers, multiple devices, and more balanced populations before its behavior could be trusted in general. Retinal vessel analysis that informs a diagnosis or a treatment decision sits under the regulatory pathway for clinical software, and nothing in this work claims to have crossed it. The soft probability maps, the authors caution, represent consensus among annotators and should not be read as calibrated biological probabilities. Read as a benchmark and a method, the contribution is real. Read as a clinical instrument, it is early.

Honest limitations

The paper lists its own limitations with unusual candor, and they are worth repeating with the numbers attached. The single center and single device design limits external validity, and the cohort’s tilt toward high myopia, while appropriate for the intended use, is not a balanced population. The annotation pipeline covers only superficial retinal vessels, so the deeper retinal and choroidal layers are outside the current label space, and extending to them would be needed for fuller layer specific analysis.

On the modeling side, the polar scan construction is fixed rather than learned, and Dynamic FOV Gating is applied only at the bottleneck, so the spatial modulation is coarse. The authors point to adaptive scan strategies and multi scale gating as future directions, which is a fair admission that the current design is a first cut. The performance gains, as noted, are modest, and the connectivity measurement did not improve uniformly, so the method is not a clean sweep across every axis. Finally, the vascular measurements assess agreement with annotation derived references rather than independent clinical measurements, which bounds what the downstream analysis can claim.

None of this diminishes the dataset, which is the more durable contribution. A publicly available wide field OCTA vessel dataset with soft probability annotations and paired ocular biometry did not exist before, and its value will outlast any single network trained on it.

Why it matters beyond the eye

Two ideas here travel well past ophthalmology. The first is that scan order is a design choice, not a detail. Any model that flattens a two dimensional signal into a sequence is making an implicit claim about which spatial relationships matter, and matching that ordering to the geometry of the data, radial for a retina, can help. The same reasoning would apply to any imaging problem with a natural coordinate system that a grid scan ignores.

The second is that soft labels change what good means. When the ground truth itself is uncertain, a binary evaluation rewards false confidence, and keeping the labels and the metrics continuous gives a truer picture of what a model knows. That lesson reaches into any domain where expert annotators disagree, which is most of medical imaging and a great deal beyond it. The habit of reporting overlap, probability, and structural connectivity together, rather than a single overlap score, is a small methodological upgrade that other fields could borrow tomorrow.

Conclusion

This work is really two contributions bound together by a shared problem, and the binding is what makes it coherent. Widefield imaging opens up the retinal periphery where myopic damage lives, but it also outruns the datasets and the scan strategies built for small central patches. WOIVES supplies the missing data, at a field of view many times larger than existing benchmarks, and PG-Mamba supplies a network whose scanning matches the radial shape of the thing it is reading.

The conceptual move worth remembering is the respect for uncertainty. Rather than forcing crisp masks onto boundaries that even experts cannot agree on, the dataset preserves the disagreement as soft probabilities, and the evaluation judges models on how well they reproduce that graded confidence rather than a thresholded caricature of it. That choice ripples through everything, from the composite loss to the six metrics reported, and it is the kind of methodological honesty that makes a benchmark trustworthy.

The evidence supports a measured claim. PG-Mamba led on five of six segmentation metrics and on three of four downstream vascular measurements under strict subject level cross validation, which is a real and consistent result. It is also a modest one, with sub point margins over the strongest baseline and one connectivity measure that did not improve, and the paper reports both the wins and that shortfall without spin.

The honest limitations keep the picture grounded. The data is single center and single device, tilted toward high myopia, and labeled only for superficial vessels. The polar scans are fixed and the gating is coarse. The downstream numbers measure agreement with expert annotation rather than independent clinical truth. Each of these is a specific place to push next, not a reason to discount the work, and the authors name most of them themselves.

For anyone building segmentation systems where the field of view is large, the labels are uncertain, or the structures have a natural geometry, the transferable lessons are clear. Match your scan order to the shape of your data. Keep your labels soft when your experts disagree. Judge your models at more than one level. And when your headline improvements are small, say so, because a careful small result is worth more than an oversold large one. The wide field of the retina is a demanding test bed for all three habits, which is exactly why a method that practices them here is worth watching as the ideas spread.

Reference implementation in PyTorch

The code below is a compact, runnable sketch of the PG-Mamba ideas, the polar scan orderings, a lightweight state space scan approximation, a Polar Block that merges six scan directions, the Dynamic FOV Gating module with its soft and hard masks, and the composite soft Dice plus mean squared error loss, with a smoke test on dummy data. It stands in for the full network with a simplified recurrence so it runs anywhere, and it is meant for study rather than as the authors’ training code.

# pg_mamba.py
# Study reference for the PG-Mamba ideas, polar scans plus FOV gating.
# Not the authors' full network. Approximates the state space scan so it runs
# anywhere. Ends with a smoke test on dummy data.

import torch
import torch.nn as nn
import torch.nn.functional as F


def polar_orders(h, w, lam=10.0, device="cpu"):
    """Return Radial Out and Radial In pixel orderings for an h by w map."""
    ii, jj = torch.meshgrid(torch.arange(h, device=device),
                            torch.arange(w, device=device), indexing="ij")
    ch, cw = h // 2, w // 2
    r = torch.sqrt((ii - ch).float() ** 2 + (jj - cw).float() ** 2)
    theta = torch.atan2((ii - ch).float(), (jj - cw).float())
    L = h * w
    q_out = (L + 1) * r + lam * (theta + torch.pi)
    q_in = -(L + 1) * r + lam * (theta + torch.pi)
    ro = torch.argsort(q_out.flatten())
    ri = torch.argsort(q_in.flatten())
    return ro, ri


def grid_orders(h, w, device="cpu"):
    """Four conventional scans, horizontal, vertical, and two diagonals."""
    idx = torch.arange(h * w, device=device).view(h, w)
    hor = idx.flatten()
    ver = idx.t().flatten()
    ii, jj = torch.meshgrid(torch.arange(h, device=device),
                            torch.arange(w, device=device), indexing="ij")
    md = torch.argsort((ii + jj).flatten())        # main diagonal
    ad = torch.argsort((ii - jj).flatten())        # anti diagonal
    return [hor, ver, md, ad]


class GatedScan(nn.Module):
    """A cheap gated running summary standing in for a selective state scan."""
    def __init__(self, dim):
        super().__init__()
        self.gate = nn.Linear(dim, dim)
        self.val = nn.Linear(dim, dim)

    def forward(self, seq):
        # seq shape B, L, C. Forward gated accumulation.
        g = torch.sigmoid(self.gate(seq))
        v = self.val(seq)
        out = torch.zeros_like(v)
        acc = torch.zeros(seq.shape[0], seq.shape[2], device=seq.device)
        for t in range(seq.shape[1]):
            acc = g[:, t] * acc + (1 - g[:, t]) * v[:, t]
            out[:, t] = acc
        return out


class PolarScanSS2D(nn.Module):
    """Scan a feature map six ways, four grid plus two polar, then merge."""
    def __init__(self, dim):
        super().__init__()
        self.scan = GatedScan(dim)

    def forward(self, x):
        B, C, H, W = x.shape
        flat = x.flatten(2).transpose(1, 2)  # B, L, C
        orders = grid_orders(H, W, x.device) + list(polar_orders(H, W, device=x.device))
        acc = torch.zeros_like(flat)
        for order in orders:
            inv = torch.argsort(order)
            scanned = self.scan(flat[:, order])   # reorder, scan
            acc = acc + scanned[:, inv]           # inverse scan back to place
        return acc.transpose(1, 2).view(B, C, H, W)


class DynamicFOVGating(nn.Module):
    """Content adaptive soft mask times a radius thresholded hard mask."""
    def __init__(self, dim, tau=1.15):
        super().__init__()
        self.tau = tau
        self.gate = nn.Sequential(
            nn.Conv2d(dim + 2, dim, 3, padding=1), nn.GroupNorm(1, dim), nn.ReLU(True),
            nn.Conv2d(dim, 1, 3, padding=1))

    def forward(self, x):
        B, C, H, W = x.shape
        ii, jj = torch.meshgrid(torch.linspace(-1, 1, H, device=x.device),
                                torch.linspace(-1, 1, W, device=x.device), indexing="ij")
        r = torch.sqrt(ii ** 2 + jj ** 2)
        theta = torch.atan2(ii, jj) / torch.pi
        grid = torch.stack([r, theta])[None].expand(B, -1, -1, -1)
        soft = torch.sigmoid(self.gate(torch.cat([x, grid], 1)))
        hard = (r <= self.tau).float()[None, None]
        return x * soft * hard


class PolarBlock(nn.Module):
    """Depthwise conv, polar scan, gated projection, residual."""
    def __init__(self, dim):
        super().__init__()
        self.dw = nn.Conv2d(dim, dim, 3, padding=1, groups=dim)
        self.norm = nn.GroupNorm(1, dim)
        self.ss2d = PolarScanSS2D(dim)
        self.proj = nn.Conv2d(dim, dim, 1)

    def forward(self, x):
        y = self.ss2d(F.silu(self.dw(self.norm(x))))
        return x + self.proj(y)


def composite_loss(pred, target, eps=1e-6):
    """Soft Dice plus mean squared error on continuous probability maps."""
    p = pred.flatten(1); g = target.flatten(1)
    dice = 1 - (2 * (p * g).sum(1) + eps) / (p.sum(1) + g.sum(1) + eps)
    mse = F.mse_loss(pred, target)
    return 0.5 * dice.mean() + 0.5 * mse


def smoke_test():
    torch.manual_seed(0)
    x = torch.randn(2, 16, 32, 32)
    block = PolarBlock(16)
    gate = DynamicFOVGating(16)
    y = gate(block(x))
    print(f"block output shape {tuple(y.shape)}")
    pred = torch.sigmoid(torch.randn(2, 1, 32, 32))
    target = torch.rand(2, 1, 32, 32)  # soft probability labels in 0 to 1
    print(f"composite loss {composite_loss(pred, target).item():.4f}")
    ro, ri = polar_orders(32, 32)
    print(f"polar order lengths {ro.numel()} and {ri.numel()}")


if __name__ == "__main__":
    smoke_test()

Running the smoke test confirms the Polar Block preserves the feature map shape after six directional scans and gating, evaluates the composite loss on soft probability targets, and prints the lengths of the two polar orderings. The gating step is the one to watch, since it shows the radial hard mask taking effect on the feature map before the loss is computed.

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