Fig. 4.

This digit a ‘0’, shown in (a) should consist of one connected component with one loop, corresponding to one long red bar and one long green bar in the barcode diagram. The network is given as an input the highly corrupted version of this digit, shown in (b). The digit reconstructed by the original network, (c), is misclassified as an ‘8’. Its barcode diagram, (d) has three green bars: an incorrect topology for a ‘0’. After applying the topological prior to the reconstruction, the network output (e) is correctly classified as a ‘0’. Its barcode diagram, (f) shows the correct topological features of a ‘0’ digit.