Colonography is an important screening tool for colorectal lesions. This paper presents a method for establishing spatial correspondence between prone and supine inner colon surfaces reconstructed from CT colonography. The method is able to account for the large deformations and torsions of the colon occurring through movement between the two positions. Therefore, we parameterised the two surfaces in order to provide a 2D indexing system over the full length of the colon using the Ricci flow method. This provides the input to a non-rigid B-spline registration in 2D space which establishes a correspondence for each surface point of the colon in prone and supine position. The method was validated on twelve clinical cases and demonstrated promising registration results over the majority of the colon surface.