Congratulations to Professor Ani Eloyan and PhD Student Kun Meng who were published in the April 2021, Volume 83, Issue 2 of the Journal of the Royal Statistical Society!
With increasing availability of medical imaging data, estimation of high-dimensional objects observed in these images is of interest. For example, when looking at a computed tomography image from a cancer patient, a radiologist can see the cancer tumor. Our aim in this work is to automatically estimate the tumor surface and identify the points located inside the tumor using several points on the tumor surface given by the radiologist. Successful estimation approaches require a rigorous modeling framework for characterizing such high-dimensional objects. In this paper, we propose the framework of principal manifolds for modeling high-dimensional objects including a model complexity selection, and show that the proposed approach performs well even in settings where data are contaminated by noise. In addition, our proposed approach is computationally efficient and generalizable to settings other than cancer imaging.