Supine and prone colon registration is challenging due to the change in the patient's position and the consequent severe distortion of the colon shape. We propose a novel method for colon registration in the cylinder domain. Our method uses Teichmüller Map (T-Map) to match the prescribed feature points in supine and prone positions.In addition, we propose a scheme of virtual boundaries for categorizing feature points as constraints for T-Map. We validate our proposed method on a dataset of 40 colon data and demonstrate the superiority of our method over the planar domain-based method.