B. The Proximity Function
The displacement functionis connected with the prox-
imity of image pixels.
The proximity is the distance between adjacent pixels after
image warping. This value is inverse to the density value. If the
proximity functionis less than 1, then the area is densified
at the point . If the proximity is greater than 1, then the grid is
rarefied. For an unwarped image.
The constraint (1) leads to non-negativity of the proximity
function. Also high values of the proximity function should be
avoided, because it will be hard to perform interpolation in rar-
efication areas if the rarefication is too strong.
We use the proximity functionto calculate the displace-
ment function:
C. Edge Model
The choice of the displacement function is based on the as-
sumption that the blurred edgecan be approximated by