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This paper presents a new technique to reduce the storage cost of high quality 3D video. In 3D video, a sequence of 3D objects represents scenes in motion. Every frame is composed by one or several accurate 3D meshes with attached high fidelity properties such as color and texture. Each frame is acquired at video rate. The entire video sequence requires a huge amount of free disk space. To overcome this issue, we propose an original approach using Reeb graphs, which are well-known topology based shape descriptors. In particular, we take advantage of the augmented multiresolution Reeb graph properties to store the relevant information of the 3D model of each frame. This graph structure has shown its efficiency as a motion descriptor, being able to track similar nodes all along the 3D video sequence. Therefore we can describe and reconstruct the 3D models of all frames with a very low-cost data size. The algorithm has been implemented as a fully automatic 3D video compression system. Our experiments show the robustness and accuracy of the proposed technique by comparing reconstructed sequences against challenging real ones.