In this work, we present effective methods for detecting and representing invariant features of three dimensional (3-D) objects from single images. Our methods are independent of the viewpoint position, and can be used in the recognition process of 3-D objects. ne invariant features are; shapes of the object surfaces, organization of the surfaces within the object, and the new feature which is shapes of privileged surfaces (PS) of the object. Also we explain the way these features are represented and matched against stored model of the object. Our work is built around the knowledge based approach and depends on the fact that while it is true that the appearance of a 3-D object may change completely as it is viewed from different viewpoints, it is also true that many aspects of the object projection remain invariant over large ranges of viewpoints. This approach is different from the other approach that derives or calculates depth information and orientations of surfaces using more than one image of the object, or the approach that statistically detects and matchs the object features. The main contribution of our work is the introduction of privileged surface of 3-D object which plays an important role in the recognition process. Also we introduce heuristic methods for detecting shapes of surfaces, object organization, object & model representations and matching. The idea of matching privileged surfaces reduces the ambiguity that may arise due to limited visibility of the object surfaces (existence of hidden surfaces) when matching features of both the image and the model. Also matching privileged surfaces reduces the need of detecting and matching orientations of surfaces. This approach has been applied to 3-D objects which are bounded by planar surfaces. However, the work can be extended in a straightforward manner to support 3-D objects that are bounded by curved. surfaces.