目的 在脑部肿瘤图像的分析过程中，准确分割出肿瘤区域对于计算机辅助脑部肿瘤疾病的诊断及治疗过程具有重要意义。然而，由于脑部图像常存在结构复杂、边界模糊、灰度不均以及肿瘤内部存在明暗区域的问题，使得肿瘤图像分割工作面临严峻挑战。为了克服上述困难，更好地实现脑部肿瘤图像分割，提出一种基于稀疏形状先验的脑肿瘤图像分割算法。方法 首先，研究脑部肿瘤图像的配准与形状描述，并以此为基础构建脑部肿瘤的稀疏形状先验约束模型；继而，将该稀疏形状先验约束模型与区域能量描述方法相结合，构建基于稀疏形状先验的能量函数；最后，对能量函数进行优化及迭代，输出脑部肿瘤区域分割结果。结果 本文使用脑胶质瘤公开数据集BraTS2017进行算法测试，本文算法的分割结果与真实数据之间的平均相似度达到93.97%，灵敏度达到91.3%，阳性预测率达到95.9%。本文算法的实验准确度较高，误判率较低，鲁棒性较强。结论 本文算法能够结合水平集方法在拓扑结构描述和稀疏表达方法在复杂形状表达方面的优势，同时由于加入了形状约束，能够有效削弱肿瘤内部明暗区域对分割结果造成的影响，从而更准确和稳定地实现脑部肿瘤图像分割。

Objective In the process of analyzing brain tumor images, accurate segmentation of brain tumors is crucial to the diagnosis and treatment of computer-aided brain tumor diseases. Magnetic resonance imaging (MRI) is the primary method of brain structure imaging in clinical applications, and imaging specialists commonly outline tumor tissues from MRI images manually to segment brain tumors. However, manual segmentation is laborious, especially when the brain image has a complex structure and the boundary is blurred. The brain tumor area in the image might have bright or dark blocks that are marked in magenta. These areas may cause holes in the result or excessive shrinkage of the contour. Moreover, due to the limitation of the imaging principle and the complexity of the human tissue structure, this technique usually encounters problems, such as uneven intensity distribution and overlapping of tissues. The segmentation effect of traditional methods based on thresholds, geometric constraints, or statistics is poor and adds challenges to tumor image segmentation. To overcome these difficulties and realize improved segmentation, the common characteristics of the brain tumor's shape are studied to construct a sparse representation-based model and propose a brain tumor image segmentation algorithm based on prior sparse shapes. Method The Fourier-Melli method is utilized to implement image registration, and the shape description of brain tumor images is studied. A prior sparse shape constraint model of brain tumors is proposed to weaken the influence of light and dark areas inside the tumor on the segmentation results. The K-means method is used to cluster the data in the mapping matrix into several classes and calculate the average of each group separately to be used as a predefined sparse dictionary, and the sparse coefficients are updated through the orthogonal matching method. Then, the prior sparse shape constraint model is combined with the regional energy to construct the energy function. The following steps are implemented to initialize the contour. First, the fast bounding box (FBB) algorithm is used to obtain the initial rectangular contour region of the brain tumor, and the region centroid is adopted as the seed of the region growing method. The initial value of the level set function is then generated. The optimization and iteration details of the energy function utilizing the relationship between the high-level sparse constraint and the underlying energy function are also provided in this paper. Result To verify the feasibility of the proposed algorithm, this study uses the multimodal glioma dataset from the MICCAI BraTS2017 challenge, which contains brain MRI images of patients suffering from brain glioma, to test the algorithm. The dice similarity coefficient, sensitivity, and positive predictive positivity value (PPV) are selected as technical indicators to further evaluate the accuracy of the brain tumor segmentation results. We compare the algorithm with other image segmentation algorithms. The algorithm proposed by Joshi et al. uses wavelet transform to preprocess an MRI image, roughly segments the image through a contour-based level set method, and filters the shape and size of the results from the previous step by utilizing the soft threshold method. The algorithm proposed by Zabir et al. uses the K-means method to determine the initial tumor location points and calculates the initial value of the DRLSE level set by utilizing the region grown method. The algorithm proposed by Kermi et al. uses FBB to determine the approximate location of the brain tumor then utilizes the region growing method and geodesic active contour model for brain tumor segmentation. The algorithm proposed by Mojtabavi et al. outlines the initial contours of brain tumors artificially. It defines a level set function combined with region-and edge-based approaches then iteratively optimizes the energy function using the fast-marching method. In addition, to further verify the influence of the shape constraint terms on the segmentation results, the shape constraint terms are shielded during the testing of the algorithm for comparison. Experimental results show that the proposed algorithm can accurately and stably extract brain tumors from images. The average similarity between the segmentation result and the real data of the algorithm, the sensitivity, and the positive prediction rate reach 93.97%, 91.3%, and 95.9%, respectively. The proposed algorithm is more accurate and has a lower false positive rate and stronger robustness than other algorithms of the same type. Conclusion A novel image segmentation algorithm based on sparse shape priori is proposed to describe the shape of brain tumors and construct the sparse shape constraint model of brain tumors. Then, the energy function is constructed by combining the level set constraint method, and the relationship between the high-level sparse constraint and the low-level energy function is used to derive the target contour. The difficulty in this work is selecting the appropriate variational level set model according to the image features and the appropriate shape priori model for dealing with the complex and changeable shape of brain tumors to ensure that the complexity of the algorithm is reduced while retaining a significant amount of shape details. Compared with other algorithms, the proposed algorithm combines the advantages of the level set method in topological structure description and the sparse expression method in complex shape expression. The algorithm has good robustness and can accurately segment brain tumors. In our future work, we will further study the problem of multi-modal brain tumor segmentation to make better use of information from MRI data.