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We present a novel image interpolation method based on variational models with both smoothing and orientation constraints. By introducing the orientation constraint, we simplify the nonlinear PDE problem into a series of problems with explicit solutions. In our model, the gradient directions for the interpolated pixels are first estimated using a modified orientation diffusion method. Using these estimated gradient directions adaptive directional interpolation is carried out. An effective numerical implementation of the adaptive directional interpolation is presented for the case of upsampling by factors of two. This implementation had very low complexity and is well suited for real-time applications.