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Image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing. However, known edge-preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times. In this paper, we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles, respectively. In this context, we propose a new method for estimating rotation angles and shear parameters based on the so-called structure tensor. Further, we show how the knowledge of appropriate diffusion tensors can be used in variational models. Numerical examples including orientation estimation, denoising and segmentation demonstrate the good performance of our methods.