Surface reconstruction with volume preservation

The marching cubes (MC) algorithm is widely used for converting volume data into surface data. It generates surfaces with the connected intersection points with a level or value equal to a given threshold. The resulting surfaces are iso-surfaces. However, it will be shown that local volume is not preserved in the conversion. Consequently, the resulting shape is not necessarily close to the original shape. We present a new approach to the problem. Instead of a single threshold value for the entire image we adjust thresholds locally so that local volume becomes approximately equal to the corresponding voxel value. First, a detailed explanation is given using a 2D image. Then, for a 3D case a technique to analytically compute volume in various cases of forming iso-surfaces is developed. We will demonstrate the advantage of our algorithm using several artificial and real examples.