We present an automatic kidney segmentation method using ultrasound images. This method employs a coarse-to-fine approach to tackle the challenge of unclear and fuzzy boundaries. Four key innovations are introduced to enhance the segmentation process's accuracy and efficiency. First, an automatic deep fusion training network serves as a coarse segmentation strategy. Second, we propose an explainable mathematical mapping formula to better represent the kidney contour. Third, by utilizing the characteristics of the principal curve, a neural network automatically refines curve shapes, thus reducing model errors. Finally, we employ an intelligent searching polyline segment method for automatic kidney contour segmentation. The results show that our method achieves high accuracy and stability in segmenting kidney ultrasound images. This work's contributions include the deep fusion training network, intelligent searching polyline segment method, and explainable mathematical mapping formula, which are applicable to other medical image segmentation tasks. Additionally, this approach uses a mean-shift clustering model, supplanting standard projection and vertex optimization steps.