With the material processing freedoms of additive manufacturing (AM), the ability to characterize and control material microstructures is essential if part designers are to properly design parts. To integrate material information into Computer-aided design (CAD) systems, geometric features of material microstructure must be recognized and represented, which is the focus of this paper. Linear microstructure features, such as fibers or grain boundaries, can be found computationally from microstructure images using surfacelet based methods, which include the Radon or Radon-like transform followed by a wavelet transform. By finding peaks in the transform results, linear features can be recognized and characterized by length, orientation, and position. The challenge is that often a feature will be imprecisely represented in the transformed parameter space. In this paper, we demonstrate surfacelet-based methods to recognize microstructure features in parts fabricated by AM. We will provide an explicit computational method to recognize and to quantify linear geometric features from an image.