Synthetic Labelled Images

We created a set of 4 artificial images of size $256 \times 256$, labelled house, clown, house2 and clown2, illustrated in Fig. 1. All 4 contain 5 corresponding structures: roof (hat) of intensity 87; shadow (hair) of intensity 39; wall (face) of intensity 127; windows (eyes and mouth) of intensity 215; and background of intensity 255.

  

Figure 1: Artificial images: ( left-right) clown, house, clown2, house2

We applied unmodified (UF) and modified (MF1-3) fluid to register the house to the clown images, with the house door defined as normal, weakly-deformable, passive or motionless to compare the ability of the algorithms to reduce or prohibit deformation. Figures 2 and 3 show the results.

  

Figure 2: Progress of the UF registration of house to clown image

To measure the deformation of the door, we applied to a grid image the same deformation as that of the source, and noted the locations of gridpoints in the door region before and after registration. For each registration, we inserted these into a thin-plate spline and computed its bending energy as given by [7]. The results were: UF (target: clown) 1.018; MF3 (target: clown) 0.065; MF3 (target: clown2) 0.058; MF1 (target: clown2) 0.045; MF2 (target: clown2) 0. Fig. 3 (bottom) shows the final deformations of the door regions in the grids.

  

Figure 3: Registration of S = house2 to T = clown/clown2, restricting deformation of the door. ( Columns, left-right): UF ( T = clown); MF3 (T = clown); MF3 (T = clown2); MF1 (T = clown2); MF2 (T = clown2). ( Rows, top-bottom): Deformed S; T - deformed S; original S - deformed S; door regions of corresponding deformed grids.