We describe how inflation, the act of mapping a 2D silhouette to a 3D region, can be applied in two disparate problems to offer insight and improvement: silhouette part segmentation and image-based material transfer. To demonstrate this, we introduce Puffball, a novel inflation technique, which achieves similar results to existing inflation approaches – including smoothness, robustness, and scale and shift-invariance – through an exceedingly simple and accessible formulation. The part segmentation algorithm avoids many of the pitfalls of previous approaches by finding part boundaries on a canonical 3-D shape rather than in the contour of the 2-D shape; the algorithm gives reliable and intuitive boundaries, even in cases where traditional approaches based on the 2D Minima Rule are misled. To demonstrate its effectiveness, we present data in which subjects prefer Puffball's segmentations to more traditional Minima Rule-based segmentations across several categories of silhouettes. The texture transfer algorithm utilizes Puffball's estimated shape information to produce visually pleasing and realistically synthesized surface textures with no explicit knowledge of either underlying shape.