It has long been hypothesized that the human visual system achievs robust shape and object recognition by breaking the shapes it encounters into simpler parts. The compact descriptions of these parts and their structural arrangement are stored in memory, so that the same shape or object can be recognized in multiple configurations and from other viewpoints. And indeed, humans do appear to consistently break shapes into parts, even when the shapes are unrecognizable, such the shape to the right. But if these parts are located without identifying the object, how are the parts chosen?
Many have tried to answer this question over the last several decades, most with methods based on the two-dimensional curvature of the silhouette's contour. These methods, however, are plagued with inconsistencies and ambiguities. A simpler and more robust approach is presented to us by Puffball inflation. Finding part boundaries is much easier on a three-dimensional shape than on a two-dimensional shape; because Puffball turns a two-dimensional shape into a three dimensional shape, it also provides us with a simple approach to finding part boundaries. The process is shown in the figure on the left. Figure A shows a simple shape. If we inflate the shape using Puffball, we see that the inflated shape has two sharp creases (Figure B); these creases correspond to the part-boundaries of the 2D shape. Locating points along the top of the inflation where the concave curvature is high marks the centers of these two creases (Figure C); and extending these points across the shape gives two perceptually intuitive part boundaries.
Puffball part segmentation offers numerous advantages over previous approaches. Like Puffball, it is simple and intuitive, scale-invariant, robust to perturbations, and can be run on any input. It also reliably identifies a wide variety of part boundary types, some of which were thought to be generated by separate processes. The result of Puffball part segmentation on the nonsense shape from above is shown to the right; as you can see, Puffball part segmentation does an excellent job of replicating the most intuitive part boundaries in the shape.