C-arm images suffer from pose dependant distortion, which needs to be corrected for intra-operative quantitative 3D surgical guidance. Several distortion correction techniques have been proposed in the literature, the current state of art using a dense grid pattern rigidly attached to the detector. These methods become cumbersome for intra-operative use, such as 3D reconstruction, since the grid pattern interferes with patient anatomy. The primary contribution of this paper is a framework to statistically analyze the distortion pattern which enables us to study alternate intra-operative distortion correction methods. In particular, we propose a new phantom that uses very few BBs, and yet accurately corrects for distortion. The high dimensional space of distortion pattern can be effectively characterized by principal component analysis (PCA). The analysis shows that only first three eigen modes are significant and capture about 99% of the variation. Phantom experiments indicate that distortion map can be recovered up to an average accuracy of less than 0.1 mm/pixel with these three modes. With this prior statistical knowledge, a subset of BBs can be sufficient to recover the distortion map accurately. Phantom experiments indicate that as few as 15 BBs can recover distortion with average error of 0.17 mm/pixel, accuracy sufficient for most clinical applications. These BBs can be arranged on the periphery of the C-arm detector, minimizing the interference with patient anatomy and hence allowing the grid to remain attached to the detector permanently. The proposed method is fast, economical, and C-arm independent, potentially boosting the clinical viability of applications such as quantitative 3D fluoroscopic reconstruction.