Impact of outliers on the recovered ellipticity and position angle for the KDE (circles), PCA (squares), and robust PCA (diamonds) methods for two sets of true parameters. The colour of the points indicates the location of the outliers. The points in pink with a positive x and negative y correspond approximately to the direction of the semi-minor axis, and the points in orange with a positive x and positive y correspond approximately to the direction of the semi-major axis of the ellipse. Outliers were added within fixed quadrants relative to the cluster centre, not strictly along the ellipse axes, which leads to small asymmetries in the recovered angles when the ellipse position angle changes. The dashed green line represents the true value of the ellipticity and angle, taken to 0.15 and 45^° (top panel) and to 0.25 and 60^° (bottom panel). We note that for the Robust PCA method, only one point is visible, thus highlighting the robustness of the method. Regardless of the direction where outliers are added, the ellipticity and position angle are accurately recovered.