Unique visualization of multiply oriented lattice structures using a continuous wavelet transform

The application of continuous wavelet transformation in the phase field crystal model has yielded excellent results for the crystal lattice orientation and grain boundaries with different misorientation angles [H.M. Singer, I. Singer, Phys. Rev. E 74 (2006) 031103]. However, we show here that the orientation map from this simple method cannot distinguish symmetric orientations using a single convolution template. By introducing additional rotational templates, the grain orientation can be uniquely visualized in two and three dimensions.