We present an interactive image deformation method which preserves the local shapes of salient objects in the concerned image during the deformation. The proposed method falls into the moving least squares (MLS) framework, but notably differs from the original MLS deformation method. First, a saliency-related distance is developed to replace the original Euclidean distance in the weight definition. Second, the original affine matrix is decomposed into a single rotation matrix and a symmetric matrix by using a singular value decomposition, then the free parameters of these matrices are interpolated according to the saliency information. Furthermore, for the line-based MLS deformation, the closed-form solution of weight cannot be found directly when using the proposed saliency-based distance. To address this problem, we propose a method using an exponential transformation to regulate the weight where the regulation factor is also correlated to saliency information. All these revisions lead a saliency-sensitive mapping which creates a deformation change in the nonvital parts of image while preserving the local shapes of salient parts. Experimental results show that the proposed deformation outperforms the original MLS deformation in terms of visual performance.