Limited angle acquisition is a well-known challenge in computed tomography reconstruction because the lack of data generates severe geometric artifacts in reconstructed images. Recently, directional total variation (DTV) regularization has shown promising results for this kind of problem but it requires fine-tuning of a global directional hyperparameter in addition to the regularization weight. In this work, we propose a new regularization, called local directional total variation (LDTV), which is a DTV based on local directional weights determined from tomographic incompleteness maps. We evaluated LDTV and compared it to state-of-the-art algorithms on simulated twodimensional acquisitions of the Forbild head phantom with a source trajectory made of two orthogonal arcs of 60°each. The reconstructed images show that the LDTV regularization performs better in this geometry for both noiseless and noisy data.