发表机构
Harbin Institute of Technology（哈尔滨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对医学图像分割中边界定位和结构保持难题，提出几何正则化流匹配框架GR-FM，利用SDF和双调和及Eikonal约束，在多个数据集上实现稳定高效的分割。
AI 中文摘要
医学图像分割在精确边界定位和复杂结构保持方面仍然具有挑战性，因为目标区域通常表现出弱边界、细粒度结构和不规则形状，而高质量图像和精确标注通常有限。现有的基于流匹配的生成式分割方法主要学习状态空间中的速度场，但缺乏对恢复表示的空间正则性和距离场属性的显式约束。这一局限性可能导致空间振荡、边界位移和细结构中的不连续性。为解决这些问题，我们提出了一种图像条件几何正则化流匹配框架，称为GR-FM，该框架将分割表述为从初始分布到目标隐式表示分布的连续概率传输过程。GR-FM不直接建模二元掩码，而是采用SDF来描述目标结构，其中每个像素由到对象边界的符号距离表示，从而产生连续几何场。随后采用流匹配和常微分方程来实现确定性和高效的分布传输。训练目标进一步包含双调和正则化项和Eikonal约束，以增强恢复表示的空间平滑性、结构一致性和距离场特性。此外，我们分析了在几何约束下的连续传输过程，并研究了零水平集的演化。在MoNuSeg、GlaS和DRIVE数据集上进行的实验表明，GR-FM在区域重叠和边界精度方面均取得了有竞争力的性能，减少了性能变化，并仅用少量积分步骤即可保持稳定的分割结果。
英文摘要
Medical image segmentation remains challenging in terms of accurate boundary localization and complex-structure preservation, as target regions often exhibit weak boundaries, fine-grained structures, and irregular shapes, while high-quality images and precise annotations are usually limited. Existing generative segmentation approaches based on Flow Matching mainly learn velocity fields in the state space but lack explicit constraints on the spatial regularity and distance-field properties of the recovered representation. This limitation may lead to spatial oscillations, boundary displacement, and discontinuities in fine structures. To address these issues, we propose an image-conditioned Geometrically Regularized Flow Matching framework, termed GR-FM, which formulates segmentation as a continuous probability transport process from an initial distribution to a target implicit representation distribution. Instead of directly modeling binary masks, GR-FM adopts the SDF to describe the target structure, where each pixel is represented by its signed distance to the object boundary, resulting in a continuous geometric field. Flow Matching and ordinary differential equations are then employed to achieve deterministic and efficient distribution transport. The training objective further incorporates a biharmonic regularization term and an Eikonal constraint to enhance the spatial smoothness, structural consistency, and distance-field characteristics of the recovered representation. Moreover, we analyze the continuous transport process under geometric constraints and investigate the evolution of the zero level set. Experiments conducted on the MoNuSeg, GlaS, and DRIVE datasets demonstrate that GR-FM achieves competitive performance in both region overlap and boundary accuracy, reduces performance variation, and maintains stable segmentation results with only a small number of integration steps.
