We tested on an edge map computed from a local homogeneity measurement, which is a potential replacement for the traditional gradient-based edge map in level-set segmentation. In existing level-set methods, the gradient information is used as a stopping criteria for curve evolution, and also provides the attracting force to the zero level-set from the target boundary. However, in a discrete implementation, the gradient-based term can never fully stop the level-set evolution even for ideal edges, leakage is often unavoidable. Also the effective distance of the attracting force and blurring of edges become a trade-off in choosing the shape and support of the smoothing filter. The proposed homogeneity measurement provides easier and more robust edge estimation, and the possibility of fully stopping the level-set evolution. The homogeneity term decreasing from a homogenous region to the boundary, which dramatically increases the effective distance of the attracting force and also provides additional measurement of the overall approximation to the target boundary. Therefore, it provides a reliable criteria of adaptively changing the advent speed. By using this term, the leakage problem was avoided effectively in most cases compared to traditional level-set methods. The computation of the homogeneity is fast and its extension to the 3D case is straightforward.