We propose a method for automatic detection of the foveal center in optical coherence tomography (OCT). The method is based on a pixel-wise classification of all pixels in an OCT volume using a fully convolutional neural network (CNN) with dilated convolution filters. The CNN-architecture contains anisotropic dilated filters and a shortcut connection and has been trained using a dynamic training procedure where the network identifies its own relevant training samples. The performance of the proposed method is evaluated on a data set of 400 OCT scans of patients affected by age-related macular degeneration (AMD) at different severity levels. For 391 scans (97.75%) the method identified the foveal center with a distance to a human reference less than 750 um, with a mean (+- SD) distance of 71 um +- 107 um. Two independent observers also annotated the foveal center, with a mean distance to the reference of 57 um +- 84 um and 56 um +- 80 um, respectively. Furthermore, we evaluate variations to the proposed network architecture and training procedure, providing insight in the characteristics that led to the demonstrated performance of the proposed method.