We have used least-median-of-squares (LMS) regression to analyze gray-scale images of optical fiber ends. This regression is a form of robust regression that ignores outlying data points. We fitted ellipses to the images of each of two fiber ends by using LMS and least-sum-of-squares regression. The two methods yielded nearly identical results on a pristine fiber end, but the LMS method was far superior on a damaged fiber end, even though we made no effort to filter the outlying data points.