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In this work we present a fast, content-adaptive approach for three-dimensional (3D) mesh representation of volumetric images. A rigorous error bound is derived for a 3D mesh representation of a volumetric image based on the theory of function interpolation. From this result, a computationally efficient algorithm is proposed for adaptive placement of mesh nodes (hence mesh elements) in the 3D image domain according to the image content. Experimental results demonstrate that a highly compact and accurate representation of volumetric images can be achieved at low computational cost by the proposed algorithm.