Shape registration is very fundamental for shape analysis problems, especially for abnormality detection in medical applications. In virtual colonoscopy, CT scans are typically acquired with the patient in both supine and prone positions. The registration of these two scans is desirable so that the user can clarify situations or confirm polyp findings at a location in one scan with the same location in the other, thereby improving polyp detection rates and reducing false positives. However, this supine-prone registration is challenging because of the substantial distortions in the colon shape due to the patient’s change in position. In this work, we present an efficient algorithm and framework for performing this registration through the use of conformal geometry and Ricci flow to guarantee that the registration is a diffeomorphism (a one-to-one and onto mapping). The taeniae coli and colon flexures are automatically extracted for each supine and prone surface, employing the colon geometry. The two colon surfaces are then divided into several segments using flexures, and each segment is cut along a taenia coli and conformally flattened to the rectangular domain using Ricci flow. Corresponding feature points between supine and prone are found and used to adjust the conformal flattening to be quasi-conformal, such that the features become aligned.We present multiple methods of visualizing our results, including 2D flattened rendering, corresponding 3D endoluminal views, and rendering of distortion measurements. We demonstrate the efficiency and efficacy of our registration method by illustrating matched views on both the 2D flattened colon images and in the 3D volume rendered colon endoluminal view. We analytically evaluate the correctness of the results by measuring the distance between features on the registered colons.
