Figure 2

Graphical illustration of curvHDR gating for bivariate data. Panel (a): Polygon corresponding to a region of statistically significant high negative curvature. Panel (b): The convex hull of the polygon from (a). Panel (c): A new, larger, polygonal region obtained by growing the region from (b) using the notion of 'sphere rolling' (in this bivariate case it is 'circle rolling') around inner polygon. Approximate circle rolling is achieved by taking normal vectors of equal length from the centre of each edge of the inner polygon. The size of the outer polygon is chosen so that the ratio of its area to the inner polygon is a pre-specified growth factor G. Panel (d): The bivariate measurements are subsetted according to inclusion inside the polygon from (c). Panel (e): A kernel density estimate is obtained using only the subsetted data from (d). Panel (f): The final gate corresponds to a high density region contour of the kernel density estimate from (e), in this case the τ = 0.1 highest density region.