Effective training of deep image segmentation models is challenging due to the need for abundant, high-quality annotations. Generating annotations is laborious and time-consuming for human experts, especially in medical image segmentation. To facilitate image annotation, we introduce Physics Informed Contour Selection (PICS) - an interpretable, physics-informed algorithm for rapid image segmentation without relying on labeled data. PICS draws inspiration from physics-informed neural networks (PINNs) and an active contour model called snake. It is fast and computationally lightweight because it employs cubic splines instead of a deep neural network as a basis function. Its training parameters are physically interpretable because they directly represent control knots of the segmentation curve. Traditional snakes involve minimization of the edge-based loss functionals by deriving the Euler-Lagrange equation followed by its numerical solution. However, PICS directly minimizes the loss functional, bypassing the Euler Lagrange equations. It is the first snake variant to minimize a region-based loss function instead of traditional edge-based loss functions. PICS uniquely models the three-dimensional (3D) segmentation process with an unsteady partial differential equation (PDE), which allows accelerated segmentation via transfer learning. To demonstrate its effectiveness, we apply PICS for 3D segmentation of the left ventricle on a publicly available cardiac dataset. While doing so, we also introduce a new convexity-preserving loss term that encodes the shape information of the left ventricle to enhance PICS's segmentation quality. Overall, PICS presents several novelties in network architecture, transfer learning, and physics-inspired losses for image segmentation, thereby showing promising outcomes and potential for further refinement.

翻译：深度图像分割模型的有效训练因需要大量高质量标注而具有挑战性。生成标注对人工专家而言既费时又费力，尤其在医学图像分割领域。为简化图像标注流程，我们提出物理信息引导轮廓选择（PICS）——一种不依赖标注数据的可解释物理信息快速图像分割算法。PICS借鉴了物理信息神经网络（PINNs）和主动轮廓模型（蛇形算法）的思想。该算法采用三次样条函数而非深度神经网络作为基函数，因此计算快速且轻量化。其训练参数具有物理可解释性，可直接表征分割曲线的控制节点。传统蛇形算法通过推导欧拉-拉格朗日方程并进行数值求解来最小化基于边缘的损失泛函，而PICS则绕过欧拉-拉格朗日方程直接最小化损失泛函，成为首个采用区域基损失函数替代传统边缘基损失函数的蛇形变体。PICS创新性地使用非稳态偏微分方程（PDE）建模三维（3D）分割过程，通过迁移学习实现加速分割。为验证有效性，我们在公开心脏数据集上应用PICS进行左心室三维分割，同时引入一种保持凸性的新损失项以编码左心室形状信息，从而提升PICS分割质量。总体而言，PICS在网络架构、迁移学习和物理启发损失函数设计上均展现出创新性，为图像分割提供了具有显著潜力和优化前景的解决方案。