Variational Partial Differential Equations And Deep Learning Fused Medical Image Segmentation Methods

Intelligent diagnoses and treatments are current national strategical objectives,which require the interdisciplinary and integration of modern medicine,mathematics,biology,and information science.Precise analysis of medical images is the foundation and prerequisite to achieving intelligent diagnoses and treatments,which highly depends on mathematical modeling,algorithms,and theoretical analysis.Medical image segmentation is one of the core techniques in medical image analysis,which aims to delineate the region of clinical interest from medical images,such as organs,lesions and the surrounding tissues.It has wide applications in clinical practice,such as quantitative analysis of organs and lesions,diagnosis and progress evaluation of lesions,surgical planning,and serving as the preconditions of registration and 3D reconstruction.From the perspective of methodology,variational partial differential equation models and deep learning methods are two widely used segmentation approaches.Variational model-based approaches model the image segmentation task as an energy functional minimization problem,which can explicitly represent the edge,the prior,and the global information of objects.However,these methods are sensitive to hyper-parameters and can not automatically learn features from data.Existing variational models can be classified as edge-based,region-based,and hybrid models according to the image information in the energy functional.Deep learning-based approaches directly learn the end-to-end mapping between images and annotations,which can automatically learn object features from a number of training samples.However,these methods lack to capture the object global information and the interpretability,and rely on the large training set.In this dissertation,we propose several more precise,robust,and efficient segmentation methods and algorithms by fusing the advantages of the two kinds of approaches to address the main problems in medical image segmentation.The contributions of this dissertation include four aspects:1.We propose a geodesic active contour guided level set function regression deep network by fusing the edge-based variational model and the deep learning method,which aims to address the shortage that convolutional neural networks(CNN)can not effectively capture the object global information.Using CNN directly regresses the object level set function can embed the relationships of the object voxels in the learning process,where the network can be more sensitive to small segmentation errors.In addition,by introducing the energy functional of geodesic active contours into the loss function,the network can minimize the energy function in an end-to-end way,which can guide the segmentation result to the real object boundary.Extensive segmentation experiments on four public CT and MR image datasets showed that our method achieves better segmentation performance than the other six state-of-the-art methods,especially on reducing the boundary errors and outliers.2.We propose a region-scalable fitting model regularized semi-supervised learning framework for COVID-19 infection segmentation in CT images by fusing the region-based variational model and the deep learning method,which can exploit unlabelled data to boost segmentation performances.Existing semi-supervised methods usually leverage the unlabelled data by generating pseudo labels.However,the pseudo labels can be inaccurate and degrade the network performance in the following learning process.To address this problem,we introduce the region-scalable fitting(RSF)active contour model to refine the pseudo labels,which can improve the quality of pseudo labels.We use the iterative convolution-thresholding method to solve the RSF model,which is more efficient than the conventional level set method.Extensive experiments on our benchmark dataset and a large scale dataset with 860 cases showed that the proposed method can obtain better infection segmentation results than the method without using unlabelled data and stateof-the-art semi-supervised methods without optimizing the pseudo labels.In addition,we built a statistical atlas with 860 early COVID-19 CT cases and found that the dorsal and posterior basal segments of the left and right lower lobe are the commonly infected areas.3.We propose a characteristic function-based representation to geodesic active contours(GAC)and derive an efficient algorithm termed the iterative convolution-thresholding method(ICTM),which aims to address the high computation burden of the level set method.Compared with the level set-based representation,our characteristic functionbased model has fewer hyper-parameters and does not require additional regularization terms.In addition,our ICTM is simpler and much more efficient than the level set method because the main operations in ICTM only include simple convolution and thresholding while the level set method needs to solve partial differential equations in each iteration.We also analyze the convergence of the ICTM and prove that the total energy continuously decays during the iteration process which is independent of the free parameter.Extensive experiments,on synthetic,ultrasound,CT,and MR images demonstrate that our method not only obtains comparable or even better segmentation results(compared to the level set method)but also achieves acceleration by several times to dozens of times.4.We propose a new hybrid variational model with the edge term,the region term,and the prior term for the head and neck tumor segmentation in PET/CT images by fusing the hybrid variational model and the deep learning method,which can improve the segmentation performance by exploring and using complementary information of different image modalities.Specifically,we first introduce a multi-channel 3D U-Net to segment the tumor with the concatenated PET and CT images.Then,we estimate the segmentation uncertainty by model ensembles and define a segmentation quality score to select the cases with high uncertainties.Furthermore,we develop a hybrid active contour model to refine the high uncertainty cases.The model energy functional includes the CT imagebased edge term,the PET image-based region term,and the probability map-based prior term.We also design an iterative convolution-thresholding method to solve the hybrid active contour model and give the convergence analysis.Our method ranked second in the MICCAI 2020 head and neck international segmentation challenge with an average Dice Similarity Coefficient(DSC)of 0.752,which is not statistically significant with the first place(DSC 0.759)and significantly better than the others(DSC ? 0.735).