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The use of mode-dependent transforms for coding directional intra prediction residuals has been previously shown to provide coding gains, but the transform matrices have to be derived from training. In this paper, we derive a set of separable mode-dependent transforms by using a simple separable, directional, and anisotropic image correlation model. Our analysis shows that only one additional transform, the odd type-3 discrete sine transform (ODST-3), is required for the optimal implementation of mode-dependent transforms. In addition, the four-point ODST-3 also has a structure that can be exploited to reduce the operation count of the transform operation. Experimental results show that in terms of coding efficiency, our proposed approach matches or improves upon the performance of a mode-dependent transforms approach that uses transform matrices obtained through training.