The α-Embracing Contour
Manuel Abellanas · 2008
Every notion of depth induces a stratification of the plane in regions of points with the same depth with respect to a given set of points. The boundaries of these regions, also known as depth-contours, are an appropriate tool for data visualization and have already been studied for some depths like Tukey depth [5, 9, 10, 11] and Delaunay depth [3, 8]. The contours also have applications in quality illumination as is the case of good α-illumination [2]. The first α-depth contour is also known as the α-embracing contour. We prove that the first α-depth contour has linear size and we give an algorithm to compute it that runs in O(n2 log n) time and O(n2) space.