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 lines.
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 lines.
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 is self-intersecting.
[4], 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 lines.
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 [5] used the curvature of
isophotes to design a voting system for eye and pupil localization.