Nested Radially Monotone Polar Occupancy Estimation: Clinically-Grounded Optic Disc and Cup Segmentation for Glaucoma Screening

Rimsa Goperma; Rojan Basnet; Liang Zhao

cs.CVApr 10, 2026

Nested Radially Monotone Polar Occupancy Estimation: Clinically-Grounded Optic Disc and Cup Segmentation for Glaucoma Screening

Authors: Rimsa Goperma, Rojan Basnet, Liang Zhao

Organizations: Graduate School of Advanced Integrated Studies in Human Survivability (GSAIS), Kyoto University, Kyoto 606-8306, Japan

Abstract

Valid segmentation of the optic disc (OD) and optic cup (OC) from fundus photographs is essential for glaucoma screening. Unfortunately, existing deep learning methods do not guarantee clinical validness including star-convexity and nested structure of OD and OC, resulting corruption in diagnostic metric, especially under cross-dataset domain shift. To adress this issue, this paper proposed NPS-Net (Nested Polar Shape Network), the first framework that formulates the OD/OC segmentation as nested radially monotone polar occupancy estimation.This output representation can guarantee the aforementioned clinical validness and achieve high accuracy. Evaluated across seven public datasets, NPS-Net shows strong zero-shot generalization. On RIM-ONE, it maintains 100% anatomical validity and improves Cup Dice by 12.8% absolute over the best baseline, reducing vCDR MAE by over 56%. On PAPILA, it achieves Disc Dice of 0.9438 and Disc HD95 of 2.78 px, an 83% reduction over the best competing method.

Figures & tables

Fig. 1: Overview of the proposed NPS-Net pipeline.

Stage	Channels	Norm	Convolution	Params
Enc 1	$3\!\to\!64$	GN (8)	$2\!\times\!$ CircPad $3\!\times\!3$	31.04 M
Enc 2	$64\!\to\!128$	GN (8)	$2\!\times\!$ CircPad $3\!\times\!3$
Enc 3	$128\!\to\!256$	BN	$2\!\times\!$ CircPad $3\!\times\!3$
Enc 4	$256\!\to\!512$	BN	$2\!\times\!$ CircPad $3\!\times\!3$
Bottleneck	$512\!\to\!1024$	BN	$2\!\times\!$ CircPad $3\!\times\!3$
Shape Prior	—	BN1d	$3\!\times\!$ Circ1D	0.24 M

TABLE I: Architecture and Parameter Budget

Fig. 2: Illustration of monotone occupancy and factorized nesting.

Loss	Supervises	$\lambda$	Epoch
Dice + BCE	Cartesian masks	1.0	0
Dice + BCE	Polar masks	0.7	0
SmoothL1	Rim profile ( 16 )	0.5	0
Cross-entropy	Shape distributions	0.3	20
SmoothL1	Shape radii	0.5	20
SmoothL1	Contour smoothness	0.05	20

TABLE II: Training Losses and Activation Schedule

Dataset	Ethnicity	Hardware	Country	Images
Internal Train / Validation / Test (70/15/15%)
RIGA–BinRushed	Arab	Topcon TRC-NW7SF	Saudi Arabia	233
RIGA–Messidor	Caucasian	Topcon TRC-NW6	France	463
ORIGA	Malay	Canon CR-DGi	Singapore	654
NETRA [ 36 ]	Nepalese	Canon	Nepal	480
Cross-Domain Benchmark (DRISHTI-GS ${}_{\text{test}}$ + REFUGE Combined)

TABLE III: Summary of the datasets

	Dice $\uparrow$		HD95 $\downarrow$		vCDR $\downarrow$	Rim ${}_{\text{M}}$ $\downarrow$	Rim ${}_{\text{C}}$ $\uparrow$
	Cup	Disc	Cup	Disc
UNet	.8929	.9643	4.65	0.90	.0480	.0258	.6309
Attn-UNet	.8946	.9649	4.19	0.71	.0481	.0254	.6450
ResUNet	.8941	.9650	4.70	0.86	.0520	.0253	.6408
Polar UNet	.8830	.9719	5.08	0.76	.0527	.0268	.6520
TransUNet	.8852	.9710	4.69	0.28	.0534	.0255	.6194

TABLE IV: Internal Test Set (275 Samples).

	Dice $\uparrow$		HD95 $\downarrow$		vCDR $\downarrow$	Rim ${}_{\text{M}}$ $\downarrow$	Rim ${}_{\text{C}}$ $\uparrow$
	Cup	Disc	Cup	Disc
UNet	.5162	.5733	19.01	33.00	.1781	.1046	.0828
Attn-UNet	.5035	.5399	20.37	31.26	.1913	.1114	.0380
ResUNet	.4625	.5230	21.33	38.88	.2171	.1114	.1338
Polar UNet	.6094	.7285	19.30	23.50	.1546	.0783	.1999
TransUNet	.6789	.8539	18.53	13.51	.1189	.0646	.2076

TABLE V: RIM-ONE Zero-Shot (64 Samples). All baselines collapse under domain shift; NPS-Net maintains robust performance.

	Cup Dice $\uparrow$		Disc Dice $\uparrow$		vCDR MAE $\downarrow$
	$\Delta$	$p$	$\Delta$	$p$	$\Delta$	$p$
UNet	+.29	∗∗∗	+.34	∗∗∗	$-$ .11	∗∗
Attn-UNet	+.30	∗∗∗	+.37	∗∗∗	$-$ .12	∗∗∗
ResUNet	+.34	∗∗∗	+.39	∗∗∗	$-$ .15	∗∗∗
Polar UNet	+.20	∗∗∗	+.19	∗∗∗	$-$ .09	∗∗∗
TransUNet	+.13	∗∗	+.06	∗∗∗	$-$ .05	∗∗∗

TABLE VI: Statistical Significance on RIM-ONE (Wilcoxon Signed-Rank,

N\!=\!64

{}^{***}\!p\!<\!0.001

;

{}^{**}\!p\!<\!0.01

	Dice $\uparrow$		HD95 $\downarrow$		vCDR $\downarrow$	Rim ${}_{\text{M}}$ $\downarrow$	Rim ${}_{\text{C}}$ $\uparrow$
	Cup	Disc	Cup	Disc
UNet	.3786	.4199	28.84	55.86	.2404	.2322	$-$ .043
Attn-UNet	.4023	.4232	27.01	54.88	.2694	.2349	$-$ .074
ResUNet	.3222	.3640	29.40	62.79	.2689	.2347	.030
Polar UNet	.4937	.7316	33.69	24.93	.2924	.1847	.085
TransUNet	.6153	.8185	26.71	18.15	.2260	.1441	.307

TABLE VII: PAPILA Zero-Shot (488 Samples). NPS-Net leads on disc metrics by wide margins and achieves the best clinical geometry scores.

	Dice $\uparrow$		HD95 $\downarrow$		vCDR $\downarrow$	Rim ${}_{\text{M}}$ $\downarrow$	Rim ${}_{\text{C}}$ $\uparrow$
	Cup	Disc	Cup	Disc
UNet	.8603	.9065	7.65	6.30	.0858	.0642	.6130
Attn-UNet	.8512	.8997	8.21	6.78	.0744	.0579	.6108
ResUNet	.8497	.9132	8.73	5.08	.0692	.0535	.6372
Polar UNet	.8166	.9349	11.66	2.69	.0859	.0625	.6595
TransUNet	.8565	.8536	8.14	11.82	.1158	.0780	.5717

TABLE VIII: DRISHTI-GS

{}_{\text{test}}

+ REFUGE Combined (451 Images).

† Violation rate = 0% from M3 onward ( $P_{c}\!=\!P_{d}\!\cdot\!Q\Rightarrow P_{c}\!\leq\!P_{d}$ everywhere).
Model	Cup ${}_{\text{D}}$ $\uparrow$	Disc ${}_{\text{D}}$ $\uparrow$	HD95 ${}_{\text{C}}$ $\downarrow$	vCDR $\downarrow$	Rim ${}_{\text{M}}$ $\downarrow$	Rim ${}_{\text{C}}$ $\uparrow$
M1: Polar UNet	.609	.729	19.30	.155	.078	.200
M2: +Monotone	.760	.929	13.64	.084	.045	.425
M3: +Nesting †	.781	.935	11.48	.079	.040	.431
M4: +Shape prior	.783	.930	11.29	.071	.037	.519
M5: +Polar-TTA	.806	.914	10.25	.068	.035	.555

TABLE IX: Ablation on RIM-ONE (64 Samples, Zero-Shot). Each row adds one component.

Fig. 3: Qualitative comparison on RIM-ONE (zero-shot) including best cases (top), worst cases (middle), and extreme cases (bottom): Disc in green, cup in blue.

Fig. 4: Representative ResUnet predictions illustrating nesting violations for the cup (blue) and the disc (green).

Fig. 5: Predicted vs. ground-truth vCDR on RIM-ONE and Papila for TransUNet and NPS-Net. NPS-Net clusters tightly along the identity line, reflecting the 56% reduction in vCDR MAE on RIM-ONE and 24% reduction on Papila dataset.

Fig. 6: Angular rim profile

\mathrm{rim}(\theta)\!=\!r_{d}(\theta)\!-\!r_{c}(\theta)

for a representative RIM-ONE image. NPS-Net (dottet) tracks the ground truth (solid) with high fidelity, preserving the ISNT pattern. Direct rim supervision ( 16 ) ensures this is a first-class training objective.

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Aug 9, 2026J/K move · Enter open · S save

UPolarSQ: Polar Representation Learning for Optic Disc and Peripapillary Atrophy Segmentation and Quantification in Fundus Photographs

Mengxian He, Yunyun sun, Ziyue Gao, Wengkei Lam+2

Department of Biomedical Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China · Capital Medical University, Beijing, China

Medical Image Analysis Medical Image Segmentation Fundus Imaging Boundary-Aware Segmentation Optic Disc Segmentation Ophthalmic Image Analysis

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Myopia-induced posterior-pole remodeling is frequently accompanied by Optic Disc (OD) deformation and Peripapillary Atrophy (PPA), both of which provide clinically relevant structural biomarkers. In Cartesian fundus images, however, PPA often appears as an irregular and partially visible crescent adjacent to the OD, leading to fragmented segmentation and post-processing-dependent quantification. We propose UPolarSQ, a unified polar-domain framework for OD/PPA segmentation and biomarker quantification in myopic fundus images. UPolarSQ first maps an OD-centered region of interest into polar coordinates, where OD and PPA boundaries can be represented as radial profiles. It then employs UPolarSeg, a U-Net-based segmentation network enhanced with a Radial-Angular-Decoupled Module and boundary-aware auxiliary supervision to model anisotropic polar features and radial boundary transitions. Clinical biomarkers, including disc shape and PPA-width-related measurements, are deterministically extracted from the predicted polar masks, aligning segmentation and quantification within a shared geometric representation. Experiments on internal and external cohorts demonstrate that UPolarSQ improves OD/PPA segmentation and supports reliable polar-native biomarker estimation for myopic analysis.

Abstract

Optic Disc Segmentation

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