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We propose a level set based variational approach that incorporates shape priors into Chan-Vese's model for the shape prior segmentation problem. In our model, besides the level set function for segmentation, as in Cremers' work, we introduce another labelling level set function to indicate the regions on which the prior shape should be compared. Our model can segment an object, whose shape is similar to the given prior shape, from a background where there are several objects. Moreover, we provide a proof for a fast solution principle, which was mentioned by F. Gibou et al., and similar to the one proposed in [B. Song et al., (2002)], for minimizing Chan-Vese's segmentation model without length term. We extend the principle to the minimization of our prescribed functionals.