We describe a new neural-network technique developed for an automated recognition of solar filaments visible in the hydrogen H-alpha line full disk spectroheliograms. This technique allows neural networks learn from a few image fragments labelled manually to recognize the single filaments depicted on a local background. The trained network is able to recognize filaments depicted on the backgrounds with variations in brightness caused by atmospherics distortions. Despite the difference in backgrounds in our experiments the neural network has properly recognized filaments in the testing image fragments. Using a parabolic activation function we extend this technique to recognize multiple solar filaments which may appear in one fragment.