Jen-Hong Tan et al.
For most cases, the edges of an eye in an ocular thermogram generate an elliptical dark ring in Isc. This dark ring is a low and relatively level region
on the 2D manifold, as illustrated in Fig. 5.2. The term I2 |
(vC(s)) represents |
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d2 |
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the total potential energy of all snake points, and the term |
Isc(vC(sn)) |
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ds |
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determines the flatness of the region of the manifold where a snake stays, |
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with respect to x-y plane. Hence, for a snake that has converged |
and stayed |
on the eye edges, it gives a minimum value for the term |
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d2 |
I |
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Isc2 (vC(s)). |
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sc |
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However, in actual practice, the problem as illustrated |
in Fig. 5.3 appears |
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Isc2 (vC(s))ds |
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occasionally. Hence, the term |
vC (s) ds |
is added to promote the selection |
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of the snake falling on the preferred region. The term |
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vC (s) |
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is input to |
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prevent the snake from growing larger than the edges of eye.
5.3.3. Locating Cornea
The cornea is assumed to be circular and since snake points vC(s) = [xC(s) yC(s)] are equi-distant, the location of its center can be calculated through
xcc = avg xC(s) . |
(5.8) |
ycc = avg yC(s) |
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Fig. 5.3. Incorrect localization of lower eyelid by snake (occasionally).
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Automated Localization of Eye and Cornea
Let the radius of cornea be rc |
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rc = rt × dX, |
(5.9) |
and define |
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dX = max xC(s) − min xC(s) |
(5.10) |
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dY = max yC(s) − min y C(s). |
(5.11) |
Consider two cases in which one of the snakes correctly localizes the eye and another snake converges only to the cornea (not visible in thermogram), as illustrated in Fig. 5.4. For a snake to correctly converge to the eye edges, the corresponding dX and dY are almost equal to the width and the height of the eye. If the corneal radius is roughly 0.25 times the width of an eye, the dX/dY for the eye would be two (assume the cornea touches the upper and lower eyelid). The rt, then, has to be 0.25 for Eq. (5.9) to be true.
In the second case, the dX/dY is one, and rt is 0.5 for the equation to be true. From these cases, we propose a formula to determine the corneal radius adaptively, based on simple interpolation.
2 − 1 |
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dXdY − 1 |
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0.25 |
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Hence,
rt = |
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− 1 (−0.25) + 0.5. |
(5.12) |
dY |
Fig. 5.4. (a) An eye correctly localized by snake and (b) an eye incorrectly localized by snake.
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