As the number of people affected by diseases in the gastrointestinal system is ever-increasing, a higher demand on preventive screening is inevitable. This will significantly increase the workload on gastroenterologists. To help reduce the workload, tools from computer vision may be helpful. In this paper, we investigate the possibility of constructing 3D models of whole sections of the human colon using image sequences from wireless capsule endoscope video, providing enhanced viewing for gastroenterologists. As capsule endoscope images contain distortion and artifacts non-ideal for many 3D reconstruction algorithms, the problem is challenging. However, recent developments of virtual graphics-based models of the human gastrointestinal system, where distortion and artifacts can be enabled or disabled, makes it possible to ``dissect'' the problem. The graphical model also provides a ground truth, enabling computation of geometric distortion introduced by the 3D reconstruction method. In this paper, most distortions and artifacts are left out to determine if it is feasible to reconstruct whole sections of the human gastrointestinal system by existing methods. We demonstrate that 3D reconstruction is possible using simultaneous localization and mapping. Further, to reconstruct the gastrointestinal wall surface from resulting point clouds, varying greatly in density, Poisson surface reconstruction is a good option. The results are promising, encouraging further research on this problem.