where u is the observed noisy image, sign is a sign function, and [u.sub.NN] is the second directional derivative of the image along a local normal direction to the isophote
The diffusion intensity is high when the curvature is large and decreases along with the isophote
Let the unit coordinate vectors in the O-xy system be i and j, then, any point in the space could be expressed by a vector r=xi+yj, which becomes r=[xi]p+[eta]q in the O-[xi][eta] system, where [xi] and n are the two components in the isophote
and gradient directions respectively, and p and q are the two orthogonal unit vectors:
By using third-order PDE model, the algorithm allows for the curvature of isophote
Kim, "GA-based image restoration by isophote
constraint optimization," EURASIP Journal on Advances in Signal Processing, vol.
Now, for a little more precision on the expected behaviour of [PSI](s), we decompose divergence part in terms of the tangent and normal directions to the isophote
An image can be thought of as a collection of curves with equal value, the isophotes
. At extrema an isophote
reduces to a point, at saddle points the isophote
, who proposed a method in which the information is propagated in the occluded area, through isophote
lines that cross the edges.
That is, we break it into the tangential (T) and normal (N) directions to the isophote
By measuring the phase of Venus using such isophote
contours on all three dates, I found a discrepancy of about 2 percent from prediction.
Valenti and Gevers  used the curvature of isophotes
to design a voting system for eye and pupil localization.