Perception of symmetric image patterns is one of the important stages in visual information processing. However, local interference of the input image disturbs the detection of symmetry in artificial neural network based models. In this paper, we propose a noise-robust neural network model that can correct asymmetric corruptions and returns clear symmetry axes. For efficient detection of bilateral symmetry as well as asymmetry correction, our network adopts directional blurring filters. The filter responses are fed to oscillatory neurons for line extraction, which serializes the activation of multiple symmetry axes. Given an activated symmetry axis, the network estimates the difference of counterparts to generate a masking filter that covers the asymmetric parts. The network reconstructs the ideal mirror-symmetric image with complete symmetry axes by self-correction of corruptions. Through simulations on corrupted images, we verify that our network is superior to Fukushima's symmetry detection network. Our network successfully presents biologically plausible and robust symmetry perception mechanism.