The core (defined in the accompanying paper by Morse) provides a means for characterizing the middle/width behavior of a figure, that is, an object or component thereof, directly from the image intensities and in a way insensitive to detail. The figures in question are either complete objects, contained subobjects, object protrusions, or object intrusions. The core provides the ability to claim regions of the image as including either the boundary information of an object or its protrusion or intrusion cores. The angulation in scale space, spatial position, and scale of a figure's core allows one to move from the core to a boundary at the scale of the figure. The core of protrusion and intrusion subfigures of the figure in question will intersect this boundary at the scale of the core. Moreover, if each point on the boundary at the scale of the core is blurred in proportion to the scale of the corresponding point on the core, a collar is formed within which the boundary of the figure can be found. We show how to find the collar and how stably to find the boundary, given the collar, even in noisy or blurred objects. This ability leads to an accurate, robust, automatic method of object area computation, and the generalization of this approach to 3D also provides the basis for efficient surface rendering and volume rendering.