Establishing a correspondence between a stored model and an object in the world is a valuable process. This relationship can be performed in a "global" manner -- employing correlation techniques -- or in a "piecewise" manner -- where component matching is used. In this paper we describe the merits of establishing a piecewise correspondence between a stored model, which is a complete, viewpoint independent description, and the viewpoint dependent description that is obtained from sensing an object in the world. Piecewise correspondence is the matching of object components to model components in a unique manner. In general there will exist object components for which there are no stored model components, and model components for which there are no visible object components. This matching problem can be expressed as a Double subgraph isomorphism, where we search for the maximal subset that is common to both the model graph and the object graph and thus determine a partial match. The determination of a piecewise correspondence makes certain Image understanding tasks possible since it is known which object components are missing. Their location and type may then be hypothesized by the image understanding system. For features missing due to image processing limitations, the location of the feature in the image is determined, and the image is reexamined in an expectation-driven manner with more sensitive thresholds. If the feature is missing due to occlusion, then the sensor is repositioned so that the hypothesis can be tested from a new viewpoint. Sensor repositioning is computed first in the model-centered framework and then transformed via the established correspondence to the object-centered framework. Sensor repositioning may also serve to disambiguate object matching when a poor initial view is given. The ability to advise feature extraction routines to reprocess a section of an image, or to redirect the sensor view for hypothesis verification and disambiguation are all steps toward Image understanding. These capabilities are driven by the establishment of a piecewise correspondence between a viewed scene and a stored model. Presented in this paper is a computer vision system which performs these tasks and which will soon be incorporated into a full robotic system.