The paper "Fast Global Minimization of the Active Contour/Snake Model" by Xavier Bresson, Selim Esedoğlu, Pierre Vandergheynst, Jean-Philippe Thiran, and Stanley Osher addresses the issue of local minima in the active contour/snake model, a widely used variational model for image segmentation. The authors propose a novel approach to determine a global minimum of the active contour model by unifying image segmentation and image denoising tasks into a global minimization framework. They integrate three well-known models: the snake model, the Rudin–Osher–Fatemi (ROF) denoising model, and the Mumford–Shah segmentation model. The paper establishes the existence of a global minimum for the active contour model through theoretical theorems and proofs. Numerically, a dual formulation of the minimization problem is introduced, which allows for fast global minimization of the snake energy. This method avoids the time-consuming re-initialization steps in the level set approach. The effectiveness of the proposed algorithms is demonstrated through applications on synthetic and real-world images, including texture and medical images, showing superior performance compared to other segmentation models.The paper "Fast Global Minimization of the Active Contour/Snake Model" by Xavier Bresson, Selim Esedoğlu, Pierre Vandergheynst, Jean-Philippe Thiran, and Stanley Osher addresses the issue of local minima in the active contour/snake model, a widely used variational model for image segmentation. The authors propose a novel approach to determine a global minimum of the active contour model by unifying image segmentation and image denoising tasks into a global minimization framework. They integrate three well-known models: the snake model, the Rudin–Osher–Fatemi (ROF) denoising model, and the Mumford–Shah segmentation model. The paper establishes the existence of a global minimum for the active contour model through theoretical theorems and proofs. Numerically, a dual formulation of the minimization problem is introduced, which allows for fast global minimization of the snake energy. This method avoids the time-consuming re-initialization steps in the level set approach. The effectiveness of the proposed algorithms is demonstrated through applications on synthetic and real-world images, including texture and medical images, showing superior performance compared to other segmentation models.