In recent years, deep learning has achieved good results in the semantic segmentation of medical images. A typical architecture for segmentation networks is an encoder-decoder structure. However, the design of the segmentation networks is fragmented and lacks a mathematical explanation. Consequently, segmentation networks are inefficient and less generalizable across different organs. To solve these problems, we reconstructed the segmentation network based on mathematical methods. We introduced the dynamical systems view into semantic segmentation and proposed a novel segmentation network based on Runge-Kutta methods, referred to hereafter as the Runge-Kutta segmentation network (RKSeg). RKSegs were evaluated on ten organ image datasets from the Medical Segmentation Decathlon. The experimental results show that RKSegs far outperform other segmentation networks. RKSegs use few parameters and short inference time, yet they can achieve competitive or even better segmentation results compared to other models. RKSegs pioneer a new architectural design pattern for segmentation networks.
Keywords: Runge–Kutta methods; convolutional neural network; dynamical system; semantic segmentation.