Establishing optimal correspondence across object populations is essential to statistical shape analysis. Minimizing the description length (MDL) is a popular method for finding correspondence. In this work, we extend the MDL method by incorporating various local curvature metrics. Using local curvature can improve performance by ensuring that corresponding points exhibit similar local geometric characteristics that can't always be captured by mere point locations. We illustrate results on a variety of anatomical structures. The MDL method with a combination of point locations and curvature outperforms all the other methods we analyzed, including traditional MDL and spherical harmonics (SPHARM) correspondence, when the analyzed object population exhibits complex structure. When the objects are of simple nature, however, there's no added benefit to using the local curvature. In our experiments, we did not observe a significant difference in the correspondence quality when different curvature metrics (e.g. principal curvatures, mean curvature, Gaussian curvature) were used.