Abstract — When present, fractures tend to dominate fluid flow though rock bodies, and characterizing fracture networks is necessary for understanding these flow regimes. X-ray computed tomography (CT) has long been successfully used to image fractures in solid samples, but interpretation of CT data is complicated by the inevitable blurring that occurs when fractures are thin compared to the data resolution. This issue is particularly acute when attempting to quantify fine fractures in scans of larger samples, as typically required for characterizing flow systems on a meaningful scale. A number of methods have been proposed to account for CT blurring, but do not include the ability to account for material inhomogeneity and fracture orientation. We here propose an improved method for fracture measurement that consists of characterizing the blurring as a point-spread function (PSF), and using it, in combination with a calibration for the CT number for void space, in an iterative procedure to reconstruct the fracture and material configuration; we call this the inverse PSF (IPSF) method. Tests on CT scans of homogeneous natural samples show that the IPSF method provides more precise results than others. Further testing demonstrates that it can also recover accurate measurements in heterogeneous materials, although particularly severe inhomogeneities may lead to a locally noisy signal. The accuracy, generality, and adaptability of the IPSF method make it very well suited for characterizing fractures and fractures surfaces in natural materials. The principles behind the IPSF method also apply to the reverse problem of measuring thin features that are denser than their surroundings, such as veins or membranes, when they have one dimension that is small compared to CT data resolution.