If the object exceeds the field of measurement (FOM) of a given CT scanner, severe artifacts may result. In this work, we propose an adaptive detruncation (ADT) method to reconstruct images from medical CT projections which are truncated in the transaxial direction. The truncated projections are extrapolated by estimating the convex hull of the patient. The ADT method allows us not only to achieve artifact-free images in the FOM but also to extend the images beyond the FOM, and can therefore be very attractive, for example, in PET/CT scanners for attenuation correction.