图像语义目标的可靠分割是指算法在分割图像中语义目标的同时给出分割结果的不确定性度量。如何在语义目标分割过程中引入各种不确定性，对其建立概率推理模型，量化分割结果的不确定性，从而减少由不确定因素带来的风险是现代人工智能、计算机视觉领域的研究热点。本项目关注数据与模型参数的不确定性，结合随机偏微分方程和深度神经网络技术，实现图像语义目标的可靠分割。首先，采用随机偏微分方程将不确定性引入分割过程，更准确地刻画现实世界的空-时噪声和模型不确定性。其次，设计由随机偏微分方程驱动的深度神经网络，通过有监督或弱监督的方式确定随机微分方程的参数，同时赋予这种网络良好的物理可解释性。最后，引入贝叶斯概率框架，建立不确定性在深度随机微分方程网络中传播的概率模型，量化分割结果的不确定性。该项目是对基于偏微分方程的图像分割方法的继承和发展，同时也是对研究深度神经网络可解释性的有益尝试。

Semantic objects segmentation means that departing semantic objects from images, which are with the associated uncertainty quantification. It is about how to embed the process of uncertainty quantification into models of semantic objects segmentation, design the probability inference model, and quantify the uncertainty to reduce the potential risk. It has increasingly became the hot topic in the field of artificial intelligence and computer vision. Focus on the uncertainty of image data and parameters of models, our project attempts to realize semantic objects segmentation with uncertainty quantification by leveraging stochastic differential equations and deep neural networks together. Firstly, based on stochastic differential equations, we involve the uncertainty into segmentation to accurately depict spatial-time noise and the uncertainty of parameters. Secondly, we design a new neural network driven by stochastic differential equations. The parameters of stochastic partial differential equations are learnt in the manner of supervised learning. Once the parameters is set, we could give the associated neural networks a good interpretability. Last, employing Bayesian probability to model the propagation of uncertainty in the neural network driven by stochastic differential equations, we provide the uncertainty quantification of segmentation results. Our project is the inheritance and expansion of the segmentation based on partial differential equations, and it is also a profitable attempt to study the interpretability of general deep neural networks.