Geometrically Constrained Stenosis Editing in Coronary Angiography via Entropic Optimal Transport

01 / Overview

Local control, throughout generation.

Useful synthetic data needs more than a plausible appearance. For localized image editing, the output must follow a specified geometry and preserve structures outside the target region. This is especially demanding for thin, connected vascular structures.

OT-Bridge Editor formulates this task as constrained entropic optimal transport. A Schrödinger bridge connects a structure-conditioned start state to the image domain, and geometric generation-path guidance (GPG) imposes constraints during the trajectory.

The paper studies coronary stenosis editing as a concrete application. We evaluate both the edited images and their value for training downstream detectors on held-out real data.

01

Specify the geometry

Control the location and shape of an edit through an edited mask, image edges, and boundary cues.

02

Constrain the path

Guide intermediate bridge states, enforcing target geometry and preserving the protected region.

03

Measure usefulness

Evaluate synthetic augmentation across four detector families and two real-data settings.

02 / Method

From an editing specification to an image.

Build the structural condition
An editing mask separates the target region from the protected background. The vessel-structure composite representation combines the edited mask, masked edges, and boundary information.
Construct a constrained bridge
The entropic OT formulation seeks a transport that satisfies the geometry and preservation constraints. Its Schrödinger-bridge formulation provides the generative trajectory.
Apply geometric generation-path guidance
GPG acts on intermediate states using boundary alignment and protected-region stability. The reported implementation uses 50 rollout steps and applies GPG every 5 steps.

Guidance brings intermediate bridge states toward a geometry-feasible trajectory. — Why guide the trajectory? Intermediate constraints counter geometric drift before the final image is produced. Reproduced from the paper.

The constrained transport objective

The bridge minimizes divergence from a reference process while matching endpoint distributions and respecting the feasible set:

P* = arg min_P KL(P ∥ R)
P₀ = μ₀, P₁ = μ₁, geometry and preservation constraints

Outside the editing mask, the source appearance is protected. Inside it, a structural operator constrains the output to the requested target geometry. GPG combines the bridge transition with a geometry-aware projection.

Reported settings: entropic regularization ε = 0.01, protected-region weight λ_out = 10, geometric alignment weight λ_geo = 1. Full definitions and derivations are in Section 3 of the paper.

03 / Visual results

What changes, and what stays.

Proximal, mid, distal, and terminal edits with separate original and edited region-of-interest enlargements. — Location-controlled editing Original and edited regions are shown side by side at four target locations. The examples are exported from the paper's qualitative results.

Original angiograms, target masks, baseline synthesis results, and OT-Bridge Editor outputs with enlarged target regions. — Comparison with baselines Input images and edited masks are followed by baseline outputs and OT-Bridge Editor. Highlighted regions allow inspection of local geometry and surrounding structure.

Intermediate reverse-bridge states and segmentation constraints across multiple examples. — Intermediate bridge states The paper shows the reverse bridge trajectory from the structural condition toward the image domain, ordered from right to left.

04 / Experiments

Does the synthetic data help?

We compare Real-only, Synth-only, and Real+Synth training using the same detector backbones and evaluation splits. All reported detection results below are measured on real images.

ARCADE

Public benchmark. Detectors are trained with real images, synthetic images, or their union, and evaluated on the same held-out real test split. Mean ± standard deviation over three runs.

ARCADE · Downstream stenosis detection · Higher is better
Detector	Training data	mAP@0.5 ↑	F1 ↑
YOLOv8	Real-only	0.525 ± 0.009	0.664 ± 0.009
YOLOv8	Synth-only	0.662 ± 0.008	0.737 ± 0.008
YOLOv8	Real+Synth	0.727 ± 0.006	0.775 ± 0.007
DINO-DETR	Real-only	0.508 ± 0.010	0.645 ± 0.010
DINO-DETR	Synth-only	0.615 ± 0.012	0.697 ± 0.011
DINO-DETR	Real+Synth	0.720 ± 0.007	0.766 ± 0.008
Grounding DINO	Real-only	0.276 ± 0.012	0.453 ± 0.014
Grounding DINO	Synth-only	0.330 ± 0.015	0.505 ± 0.015
Grounding DINO	Real+Synth	0.418 ± 0.011	0.564 ± 0.013
RTMDet	Real-only	0.545 ± 0.008	0.687 ± 0.009
RTMDet	Synth-only	0.625 ± 0.010	0.726 ± 0.010
RTMDet	Real+Synth	0.675 ± 0.007	0.749 ± 0.008

Multi-center

Internal dataset collected across three centers. Evaluation uses held-out real images with the same detector suite and training settings. Mean ± standard deviation over three runs.

Multi-center · Downstream stenosis detection · Higher is better
Detector	Training data	mAP@0.5 ↑	F1 ↑
YOLOv8	Real-only	0.654 ± 0.011	0.725 ± 0.010
YOLOv8	Synth-only	0.582 ± 0.014	0.648 ± 0.013
YOLOv8	Real+Synth	0.731 ± 0.008	0.779 ± 0.007
DINO-DETR	Real-only	0.638 ± 0.010	0.710 ± 0.009
DINO-DETR	Synth-only	0.565 ± 0.013	0.635 ± 0.012
DINO-DETR	Real+Synth	0.725 ± 0.007	0.768 ± 0.008
Grounding DINO	Real-only	0.385 ± 0.012	0.532 ± 0.014
Grounding DINO	Synth-only	0.312 ± 0.016	0.485 ± 0.015
Grounding DINO	Real+Synth	0.442 ± 0.010	0.588 ± 0.011
RTMDet	Real-only	0.615 ± 0.009	0.695 ± 0.010
RTMDet	Synth-only	0.548 ± 0.012	0.622 ± 0.011
RTMDet	Real+Synth	0.688 ± 0.006	0.754 ± 0.007

Source: downstream detection tables in the camera-ready manuscript. Download results (CSV) · Full paper

Real+Synth has the highest mAP@0.5 and F1 for every reported detector in both settings. Synthetic-only training performs differently across datasets, highlighting the importance of evaluating on real images.

Image fidelity and generation quality

Image-quality metrics reported in the paper. FID and LPIPS: lower is better. IS and SSIM: higher is better.
Method	FID ↓	IS ↑	LPIPS ↓	SSIM ↑
Pix2PixHD	52.874	4.150	0.704	0.676
SPADE	78.636	2.831	0.600	0.577
SDEdit	46.900	3.120	0.410	0.705
SDM	39.417	2.708	0.485	0.616
SiameseDiff	34.200	2.710	0.281	0.790
OT-Bridge Editor	16.747	4.630	0.248	0.878

05 / Ablation & scope

Which constraints matter?

Path-level guidance improves boundary alignment.

GPG is compared with endpoint-only constraints and a variant without the boundary term. Boundary Dice and IoU are distinct from the image-quality metrics above.

Geometric generation-path guidance ablation; values are mean ± standard deviation as reported in the paper.
Variant	Boundary Dice ↑	Boundary IoU ↑	Final path error ↓
Endpoint only	0.765 ± 0.024	0.682 ± 0.028	2.8 ± 1.2
Without boundary term	0.582 ± 0.015	0.455 ± 0.018	12.4 ± 1.8
GPG	0.895 ± 0.008	0.812 ± 0.009	1.1 ± 0.3

Representation and preservation

The composite domain combines complementary structural cues. Removing the preservation constraint increases changes outside the edited region.

Synthetic data scale

In the reported ARCADE scaling study, gains saturate around a 1:1 synthetic-to-real ratio. More synthetic data is not uniformly more useful.

Mask sensitivity

Spatially displaced masks reduce downstream detection performance more than modest boundary jitter. Accurate localization remains important.

Scope and limitations

The experiments concern coronary angiography. Unseen centers, rare lesion morphologies, and different acquisition protocols require further study. The method is a research data-augmentation tool.

06 / Reference

Cite this work

arXiv citation · Accepted to ICML 2026

@article{li2026geometrically,
  title={Geometrically Constrained Stenosis Editing in Coronary Angiography via Entropic Optimal Transport},
  author={Li, Jialin and Zhang, Zhuo and Cao, Yue and Lan, Guipeng and Wen, Jiabao and Xiao, Shuai and Yang, Jiachen},
  journal={arXiv preprint arXiv:2605.08851},
  year={2026},
  note={Accepted to ICML 2026},
  doi={10.48550/arXiv.2605.08851},
  url={https://arxiv.org/abs/2605.08851}
}