Shadows provide information that allows inferences to be made about the three-dimensional nature of objects. Essential to those inferences is the ability to identify segments of the shadow boundary that correspond to various portions of the object that has cast the shadow. Entry-exit vertices, that are extremes of the boundary, and tangent to the projection of the light beams, can be identified as junctions of specific segments of the shadow boundary. The authors restrict the analysis to smooth convex bodies, and prove that points of discontinuity of the derivative on the shadow boundary form another set of vertices. These two types of junctions are discussed extensively, and combined into a labeling scheme that can segment the boundary into logically consistent pieces. The authors discuss the possible ambiguities that may arise during the labeling process due to occlusion of one object by another, and show that there is no ambiguity in the cases of occlusion of shadows and of shadows that fall on other objects.>