Level Set Method Based On Partial Differential Equation Network

In recent decades,with the development of computer technology and the popularization of the Internet,the scale of digital image takes on an explosive growth trend.Image segmentation is an important technology for people to understand and analyze massive digital images.As a kind of unsupervised image segmentation method based on Partial Differential Equation(PDE),Level Set Method(LSM)has attracted wide attention for its advantages of flexible processing of image topology changes.However,traditional LSMs are difficult to be used on a large scale in practical projects because of the low segmentation efficiency on complex natural images,limited application scenarios and the manual adjustment of parameters.Inspired by the curve evolution theory and based on the neural network,we designed the partial differential equation networks,and achieved the supervised level set based image segmentation.The specific work is as follows.(1)Focusing on the problem of manual adjustment of parameters,we designed a partial differential equation network based on Transfer Learning(TL)and changed level set method into supervised method.The partial differential equation network uses convolution operators to extract image features and forms a library of candidate basis functions.The network represents a PDE via the linear combination of these candidate differential basis,and takes the single-layer regression network as the basic unit.The initialized network structure and parameters are transferred from the source domain.The Sequential Threshold Ridge Regression(STRidge)algorithm is used to learn the time series data to be characterized in each layer of the network.The coefficients of each differential term in the equation are obtained,and then the PDE obtained by numerical method is solved to realize the curve evolution.The proposed network learns the desired PDE from data set based on transfer learning,the parameters are updated and optimized on the entire data set.It avoids the manual adjustment of PDE parameters,and improves the training efficiency,long-term prediction ability as well as segmentation accuracy.(2)In order to improve the segmentation performance of level set method on complex natural images,we proposed a more practical partial differential equation network based on Attention Mechanism(AM)and symbolic network.Considering that final resolution of PDE corresponds to the segmentation result,and utilizing attention mechanism to adjust weights of training data close to final solution,the proposed network improves the ability of estimation of final resolution,and furthermore improves the segmentation accuracy.Additionally,symbolic network is employed to combine candidate functions in library and features extracted from images together in order to represent more complicated PDE,which greatly extends the scope of application of our network.To sum up,based on the traditional level set method,we proposed two data-driven partial differential equation networks on which supervised image segmentation methods based on level set are realized.The partial differential equation networks learn the level set evolution equation from training data without manual parameter adjustment,and improves the effectiveness of image segmentation method.The thesis extends the traditional level set method from the unsupervised to the supervised,which is innovative and contributes to the practical application of PDE based methodologies.