An integrated framework for analyzing three-dimensional shape differences: Evaluating prostate morphometry

Three-dimensional (3D) morphometric features of anatomical objects may provide important information regarding disease outcome. In this paper we develop an integrated framework to quantitatively extract and analyze 3D surface morphology of anatomical organs. We consider two datasets: (a) synthetic dataset comprising 640 super quadratic ellipsoids, and (b) clinical dataset comprising 36 prostate MRI studies. Volumetric interpolation and shape model construction were employed to find a concise 3D representation of objects. For the clinical data, a total of 630 pairwise registrations and shape distance computations were performed between each of 36 prostate studies. Graph embedding was used to visualize subtle differences in 3D morphology by non-linearly projecting the shape parameters onto a reduced dimensional manifold. The medial axis shape model used to represent the shape of super quadratic ellipsoids was found to have a large Pearson´s correlation coefficient R² = 0.805 with known shape parameters. For the prostate gland datasets, spherical glands were found to aggregate at one end of the manifold and elliptical glands were found to aggregate at the other extrema of the manifold. Our results suggest our framework might discriminate between objects with subtle morphometric differences.