Figure 2.

Persistent homology and leaf serrations. A, Point cloud representing the contour of a leaflet. B, A coarse approximation (in black) of the contour (in gray) using an elliptical Fourier transform. C, A color map of a signed distance function from the contour to the Fourier approximation, positive sign for points outside the contour (more red), negative sign for points inside the contour (more blue). D, The Euler characteristic (the number of connected components minus the number of holes) curve. The Euler characteristic is plotted against traversal of the signed distance function. Shown are example leaves depicting the number of connected components (dark magenta) at the indicated positions in the curve (magenta dotted lines).