A novel interpolation-based model for the computation of the Gray Level Co-occurrence Matrix (GLCM) is presented. The model enables GLCM computation for any real-valued angles and offsets, as opposed to the traditional, lattice-based model. A texture directionality estimation algorithm is defined using the GLCM-derived correlation feature. The robustness of the algorithm with respect to image blur and additive Gaussian noise is evaluated. It is concluded that directionality estimation is robust to image blur and low noise levels. For high noise levels, the mean error increases but remains bounded. The performance of the directionality estimation algorithm is illustrated on fluorescence microscopy images of fibroblast cells. The algorithm was implemented in C++ and the source code is available in an openly accessible repository.