Abstract  The integration of representation and recognition of rigid solid objects is becoming increasingly important in computer-aided design (CAD), computer-aided manufacturing (CAM), computer graphics, computer vision, and other fields that deal with spatial phenomena. The mathematical framework used for modeling solid objects is mathematical morphology, which is based on set-theoretic concept. The mathematical characteristics of these operators are investigated in order to achieve a formal theory. Using mathematical morphology as a tool, our theoretical research aims at studying the representation schemes for the dimension and tolerance of the geometric structure. Object features can be also extracted by using the mathematical morphology approach. Through a distance transformation, we can obtain the shape number, significant points database, and skeleton. We have also developed the object recognition, localization, and corner and circle detection algorithms.