Supplementary Figure 3: Generation of equally spaced correspondence points along a contour by principal components analysis

a) The contour (black thin line) is generated by segmentation of a binary mask following¹. The first (thick black lines) and the second (dashed black line) principal components (PC) are drawn intersecting at the centroid of the contour. The two intersections for each PC with the contour is computed (black points) and are added to the set of correspondence points, p. For each two pair of points (p _i and p _i+1) generate an equal distance midpoint q (white circle) between these two points. (b) At the next level start from the midpoints q and draw a line perpendicular to the midline between p _i and p _i+1 where this line intersects the contour add that point to the set of correspondence points. Iterate the procedure for as many levels as the user wants, e.g. (c) three levels 16 points, (d) four levels 32 points. This scheme follows². 1.Suzuki, S. & be, K. Topological structural analysis of digitized binary images by border following. Computer Vision, Graphics, and Image Processing 30, 32–46 (1985). 2.Mitra, J. et al. A Thin-Plate Spline Based Multimodal Prostate Registration with Optimal Correspondences. 7–11 (2010). doi:10.1109/SITIS.2010.12.