Before revision:  We extract two kinds of persistent featuresfrom binary segmentation maps, namelysparse PI features and amplitude features,  by applying persistent homology to  filtrations of the cubical complexes of segmentation mapsgenerated using height functions in multiple directions .
After revision:  We extract two kinds of persistent featuresfrom binary segmentation maps, namelysparse PI features and amplitude features, by applying persistent homology to multi-directional height function-based filtrations of the cubical complexes of segmentation mapsgenerated using height functions in multiple directions .