窄带法是水平集图像分割的一种常见的加速方法.传统窄带仍然存在冗余的计算区域；传统窄带法与LATE （Local Approximation of Taylor Expansion）水平集模型结合时，图像分割效率反而可能下降.针对这些问题，本文提出了一种基于LATE水平集图像分割模型的矩形窄带法.在每次LATE水平集迭代之前，对水平集做如下窄带处理.首先找出水平集的所有过零点；然后对过零点做活动约束，剔除不活动的过零点，有效缩小窄带范围；再对活动约束的过零点生成矩形窄带；对重叠的矩形窄带进行合并优化，使得矩形窄带总面积尽可能小.最后，在矩形窄带范围内求解水平集微分方程，更新水平集，完成本次迭代.在水平集演化的不同阶段，对传统窄带法的窄带面积与本文矩形窄带面积进行了比较.随着迭代次数增加，矩形窄带面积与传统窄带法的窄带面积之比逐渐减小到0，说明矩形窄带法有效地减少了冗余计算量.针对不同程度的灰度不均匀图像，本文方法与LATE方法、结合LATE模型的直接窄带法、以及结合LATE模型的DTM窄带法进行了比较.直接窄带法和DTM窄带法的分割速度反而慢于LATE方法.对灰度严重不均匀的图像，直接窄带法和DTM窄带法的分割质量受到了较大影响.本文方法在保持较好分割效果的条件下，分割速度快于LATE方法.本文的矩形窄带方法有效地降低了算法复杂度，提高了图像分割效率.
The narrow-band method is a common acceleration method for level set image segmentation. The traditional narrow-band still has redundant computational regions; When the traditional narrow-band method is combined with the LATE (Local Approximation of Taylor Expansion) level set model, the image segmentation efficiency may be reduced. In order to solve these problems, a rectangular narrow-band method based on LATE level set image segmentation model is proposed in this study. The level set is subjected to the following narrow-band processing before each LATE level set iteration. First, find out all the points of zero crossings of the level set; second constrict the points of zero crossings by the activity constraints, eliminate the inactive points of zero crossings, and effectively reduce the area of the narrow-band, then generate a rectangular narrow-band for the points of zero crossings by the active constraints, optimize the overlapping rectangular narrow-band so that the total area of the rectangular narrow-band is as small as possible. Finally, the level set differential equation is solved in the narrow-band of the rectangle, and the level set is updated to complete this iteration. In the different stages of the level set evolution, the area of the traditional narrow-band and the rectangular narrow-band of this study are compared. As the number of iterations increases, the ratio of the area of rectangular narrow-band to the area of traditional narrow-band is gradually reduced to zero, indicating that the rectangular narrow-band method effectively reduces the amount of redundancy calculation. For images with different degrees of intensity inhomogeneity, the proposed method is compared with the LATE method, the direct narrow-band method, and the DTM narrow-band method. The direct narrow-band method and the DTM narrow-band method have lower segmentation efficiency than the LATE method, and the segmentation quality is greatly affected for some images with severe intensity inhomogeneity. Under the condition of maintaining good segmentation effect, the segmentation speed of the proposed method is faster than that of LATE method. The rectangular narrow-band method in this study effectively reduces the complexity of the algorithm and improves the efficiency of image segmentation.