Image segmentation is an important tool with wide applications in computer vision and medical image analysis, but it remains a challenging problem to this day. This talk introduces the variational model and algorithm for image segmentation developed by ourselves in recent research. The main content includes: 1) significant development of the distance regularized level set evolution (DRLSE) model in our early work, proposing a new and physically meaningful image segmentation variational model---the active and sink forward backward diffusion model, aimed at overcoming the limitations of existing image segmentation variational methods in terms of robustness and parameter tuning. Moreover, this model has strong physical intuitiveness and mathematical interpretability, and the algorithm has good universality; 2) Further improvements and extensions have been made to the variable scale region fitting (RSF) model proposed by ourselves earlier, overcoming the limitations of the original RSF model's sensitivity to initialization and poor controllability of curve evolution.