Volumetric colon wall unfolding using harmonic differentials

Volumetric colon wall unfolding is a novel method for virtual colon analysis and visualization with valuable applications in virtual colonoscopy (VC) and computer-aided detection (CAD) systems. A volumetrically unfolded colon enables doctors to visualize the entire colon structure without occlusions due to haustral folds, and is critical for performing efficient and accurate texture analysis on the volumetric colon wall. Though conventional colon surface flattening has been employed for these uses, volumetric colon unfolding offers the advantages of providing the needed quantities of information with needed accuracy. This work presents an efficient and effective volumetric colon unfolding method based on harmonic differentials. The colon volumes are reconstructed from CT images and are represented as tetrahedral meshes. Three harmonic 1-forms, which are linearly independent everywhere, are computed on the tetrahedral mesh. Through integration of the harmonic 1-forms, the colon volume is mapped periodically to a canonical cuboid. The method presented is automatic, simple, and practical. Experimental results are reported to show the performance of the algorithm on real medical datasets. Though applied here specifically to the colon, the method is general and can be generalized for other volumes.