A methodology based on mathematical morphology is proposed for efficient recognition of two-dimensional (2D) objects or shapes. It is based on the introduction a shape descriptor called the morphological autocorrelation transform (MAT). The MAT of an image is composed of a family of geometrical correlation functions (GCFs) which define its morphological covariance in a specific direction. The MAT is translation-, scale-, and rotation-invariant. It is shown that in most situations, a small subset of the MAT suffices for image representation. The characteristics and performance of a shape recognition system based on the MAT are investigated and analyzed. Computational complexity of the proposed morphological-based recognition system is examined. It is shown that shape properties, such as area, perimeter, and orientation, are readily derived from the MAT representation, and that the proposed system is well suited for shape representation and classification.