Multi-dimensional Neural Network for fingerprint matching
Based on my skim of the paper, I suspect that this is just a standard neural network (in which the entire image is fed into the neural network as an input, one input line per pixel in the image), and they have invented a fancy-sounding name for a standard use of neural networks.  You could of course contact the authors to ask them this question, but that's what it looks like to me.

To replicate their work, I suggest you read Section 5.1 very carefully and use the descriptions there to replicate their work.