Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.

翻译：图像分割仍是一个未解决的问题,特别是当相关对象的强度因强度不均(也称为偏差字段)而出现重叠时,相关对象的密度就会发生重叠。对于具有强度不均匀的分层图像,建议了一个偏差校正嵌入的级别设置模型,该模型的不均匀性分别由正正方形主要函数(IEOPF)估算。在拟议模型中,偏差的顺差由特定一组正方形主要函数的线性组合估计。随后定义了不均匀的强度组合能量,并引入了由级别集函数描述的组群成员功能,将能量改写为拟议模型的数据术语。类似于流行的定级方法,也包含一个整齐化术语和弧长术语,分别用于规范并平滑动定级设定函数。在拟议模型中,该模型随后扩展为多通道和多阶段模式,分别用于分层图像和多对象图像。该模型在文献和公共脑韦布和IBSR模型中广泛使用的合成图像和真实性图像中进行了广泛测试,以重写为拟议模型数据集的数据术语的精确性,实验结果和比较方法展示。