Many effective image deformation methods have been proposed in recent years, but few of them use the contours of objects as the reference of deformation. However, the contour is an important factor, and contour-based deformation can guarantee that the edge of the object after deformation is smoother compared to point-based image deformation. This article presents an image deformation method based on contours using Moving Integral Least Squares (MILS) optimisation. First, the authors set the key points in the image to create control contours as required and then adjust the positions of these points to generate the desired contours. In order to warp these contours to their new positions, the image is deformed using MILS. They derive the affine, similarity, and rigid transformations in a general framework, and users can choose different curves according to their needs. The proposed method possesses two characteristics: (i) it is able to create detail-preserving and intuitive deformations; and (ii) the solution of the deformation function has a simple closed form. They compare their method to the state-of-the-art algorithm, which is modelled by rigid transformation. Experimental results show that their deformation is more vivid.