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In this paper, a new decomposition method is introduced that splits the image into geometric (or cartoon) and texture parts. Following a total variation based preprocesssing, the core of the proposed method is an anisotropic diffusion with an orthogonality-based parameter estimation and stopping condition. The quality criterion is defined by the theoretical assumption that the cartoon and the texture components of an image are orthogonal to each other. The presented method has been compared with other decomposition algorithms through visual and numerical evaluation to prove its superiority.