Before revision:  In this paper, we introduce a new type of geodesic metrics that encodes the edge-based anisotropy features, the region-based homogeneity penalization and asymmetric enhancement. In contrast to the original isotropic dual-front model, the use of the asymmetric enhancement can reduce the risk of shortcuts or leakage problems especially when the initial curves are far away from the target boundaries  .
After revision:  In this paper, we introduce a type of asymmetric quadratic metrics dual-front model, the use of the asymmetric enhancement can reduce the risk of shortcuts or leakage problems especially when the initial curves are far away from the target boundaries .