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In this paper, we describe a novel 3D subdivision strategy to extract the surface of binary image data. This iterative approach generates a series of surface meshes that capture different levels of detail of the underlying structure. At the highest level of detail, the resulting surface mesh generated by our approach uses only about 10 percent of the triangles in comparison to the Marching Cube (MC) algorithm, even in settings where almost no image noise is present. Our approach also eliminates the so-called "staircase effect," which voxel-based algorithms like the MC are likely to show, particularly if nonuniformly sampled images are processed. Finally, we show how the presented algorithm can be parallelized by subdividing 3D image space into rectilinear blocks of subimages. As the algorithm scales very well with an increasing number of processors in a multithreaded setting, this approach is suited to process large image data sets of several gigabytes. Although the presented work is still computationally more expensive than simple voxel-based algorithms, it produces fewer surface triangles while capturing the same level of detail, is more robust toward image noise, and eliminates the above-mentioned "staircase" effect in anisotropic settings. These properties make it particularly useful for biomedical applications, where these conditions are often encountered.