A new method has been developed for interpreting the shadows of arbitrarily shaped surfaces by segmenting and labeling the shadow boundary. The method is based on the fact that a linear projection of any light ray (the ray is assumed to originate at a single, distant source) across a shadow either enters or exits the shadow at its boundary. Hence, junctures of entry and exit segments form vertices that can be found directly for any given direction of illumination and view. Entry-exit vertices that are extremes of the boundary (which is normal to the axis of light) can be identified as junctures of specific profiles of the shadow-making object. These junctures, in turn identify the segments connected to them. The method assumes successful lower level extraction of shadow boundaries. When one object occludes part of another object's shadow, critical junctures occur, but these sometimes are not entry-exit vertices. These hidden junctures create ambiguities that must be dealt with in the context of neighboring segments. Certain a priori knowledge is helpful in this situation. The method may require knowledge of the surface or the object. The entry-exit method also provides a new link between the tasks of shadow boundary extraction and shape inference in the overall process of shadow interpretation. In conjunction with existing methods for the other tasks, the entry-exit method makes it possible to interpret arbitrarily shaped shadows.