The Chan-Vese model is very popular for image segmentation. Technically, it combines the reduced Mumford-Shah model and level set method (LSM). This segmentation problem is solved interchangeably by computing a gradient descent flow and expensively and tediously re-initializing a level set function (LSF). Though many approaches have been proposed to overcome the re-initialization problem, the low efficiency for this segmentation problem is still not solved effectively. In this paper, we first investigate the relationship between the L1-based total variation (TV) regularizer term of Chan-Vese model and the constraint on LSF and then propose a new technique to solve the re-initialization problem. In detail, four fast projection methods are proposed, i.e., split Bregman projection method (SBPM), augmented Lagrangian projection method (ALPM), dual split Bregman projection method (DSBPM), and dual augmented Lagrangian projection method (DALPM). These four methods without re-initialization are faster than the existing approaches. Finally, extensive numerical experiments on synthetic and real images are presented to validate the effectiveness and efficiency of these four proposed methods.