Colon Flattening with Discrete Ricci Flow

We present a novel colon flattening algorithm using the discrete Ricci flow. The discrete Ricci flow is a powerful tool for designing Riemannian metrics on surfaces with arbitrary topologies by user-defined Gaussian curvatures. Moreover, the discrete Ricci flow deforms the Riemannian metric on the surface conformally and minimizes the global distortion, which means the local shape is well preserved. Two numerical methods, the gradient descending method and Newton’s method, for computing the discrete Ricci flow have been implemented. Both methods are accelerated with CUDA on the GPU. The flattened 2D rectangular mesh of the colon is rendered using volumetric ray-casting method with pseudo color to produce electronic biopsy images.