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We present a level-set based technique to recover key characteristics of a defect or crack (e.g. location, length and shape) in a two-dimensional material from boundary electrical measurements. The key feature of this work is to extend the usual level-set technique for modeling volumetric objects to very thin objects. Two level-set functions are employed: the first one models the location and form of the crack, and the second one models its length and connectivity. An efficient gradient based method is derived in order to define evolution laws for these two level-set functions which minimize the least squares data misfit. Numerical experiments show the utility of this method even in the presence of a significant noise level in the measurements. A finite element method is used to simulate the electric field behavior in the presence of very thin objects.