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The paper proposes a new morphological reversible contour/edge representation algorithm for the representation of 2D binary shapes of digital images. The concise representation algorithm uses representative lines of different sizes and types to cover all the significant features of the binary contour/edge image. These well-characterized representative line segments, which may overlap among different types, take minimum representative points than that of most other prominent shape representation algorithms including MST and MSD. The new algorithm is computationally efficient than most other algorithms in the literature and is also capable of approximating edge images. The approximated outputs produced by the proposed algorithm by using minimal number of representative points are more natural to the original shapes than that of MST and MSD.