Traditional image processing methods employing partial differential equations (PDEs) offer a multitude of meaningful regularizers, along with valuable theoretical foundations for a wide range of image-related tasks. This makes their integration into neural networks a promising avenue. In this paper, we introduce a novel regularization approach inspired by the reverse process of PDE-based evolution models. Specifically, we propose inverse evolution layers (IELs), which serve as bad property amplifiers to penalize neural networks of which outputs have undesired characteristics. Using IELs, one can achieve specific regularization objectives and endow neural networks' outputs with corresponding properties of the PDE models. Our experiments, focusing on semantic segmentation tasks using heat-diffusion IELs, demonstrate their effectiveness in mitigating noisy label effects. Additionally, we develop curve-motion IELs to enforce convex shape regularization in neural network-based segmentation models for preventing the generation of concave outputs. Theoretical analysis confirms the efficacy of IELs as an effective regularization mechanism, particularly in handling training with label issues.

翻译：传统图像处理方法采用偏微分方程（PDE）提供了大量有意义的正则化器，并为广泛的图像相关任务奠定了宝贵的理论基础。这使其与神经网络的融合成为一个极具前景的研究方向。本文提出一种受PDE演化模型逆过程启发的新型正则化方法。具体而言，我们引入了逆演化层（IELs），其作为不良特性放大器，用于惩罚输出具有不期望特性的神经网络。通过使用IELs，可以实现特定的正则化目标，并赋予神经网络输出以相应PDE模型的特性。我们聚焦于使用热扩散IELs的语义分割任务进行实验，结果表明其在缓解噪声标签影响方面的有效性。此外，我们开发了曲线运动IELs，以在基于神经网络的分割模型中强制实施凸形状正则化，从而防止生成凹形输出。理论分析证实了IELs作为一种有效正则化机制的功效，特别是在处理具有标签问题的训练时。