We exploit the mathematical modeling of the border completion problem in the visual cortex to design convolutional neural network (CNN) filters that enhance robustness to image occlusions. We evaluate our CNN architecture, BorderNet, on three occluded datasets (MNIST, Fashion-MNIST, and EMNIST) under two types of occlusions: stripes and grids. In all cases, BorderNet demonstrates improved performance, with gains varying depending on the severity of the occlusions and the dataset.