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Table 5.2. Summary of results on the proposed algorithm.

5.4. Results

The results of the proposed algorithm are tabulated in Table 5.2. Two hundred and sixty-nine thermograms were collected from 135 subjects. The localization was said to be “correct” if the cornea located by the algorithm fell approximately at the center of the eye and its diameter value was close to the height of the eye. This algorithm showed a success rate of 84%; Fig. 5.5 illustrates some of these results.

Table 5.3 shows a tabulation of the number of incorrect localizations of the eye and cornea with respect to the age group. The rate of failure was 2.6 times greater in the normal subjects who were more than 35 years old compared to the younger peers.

5.5. Discussion

In this work, human intervention on starting contours was replaced by the minimization of the target-tracing function. The genetic algorithm searches for the minimum of the target-tracing function. In most cases, it took less than one minute for the genetic algorithm to get the minimum of the targettracing function on a PC equipped with an Intel core dual processor.

The population size for each generation in a genetic algorithm is set to 15 individuals. The criteria to stop it from further continuation are: (i) no improvement in the fitness function (target-tracing function) (Eq. (5.7)) for three consecutive generations, (ii) no improvement in the fitness function for 100 seconds, and (iii) the number of generations has reached 18.

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Fig. 5.5. Sample results from the localization of the eye and cornea.

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Table 5.3. Number of incorrect localization by age groups.

The movement of snake toward minima in this study is highly dependent on σ1, the standard deviation of the Gaussian blur function. Larger values in that term result in an over-smoothened image, giving a GVF force field that will shrink a snake into the cornea-sclera region instead of sticking to the eye edges. On the contrary, a smaller value in the term gives a rougher image, and the resulting GVF force field often provides unnecessary friction to the snake movement.

Equations (5.9)–(5.12) were proposed for the determination of the corneal center and radius. They were to evaluate the snake points returned from the target-tracing function and adaptively decide the corneal center and the corresponding radius. However, in practice, these equations require extra attentions in two extreme cases.

First, in cases where the corneal diameter is calculated through Eqs. (5.9) and (5.12) is larger than the dY obtained in Eq. (5.11), the corneal radius is set to dY/2. Second, the corneal radius is often too small when dX/dY is larger than 2.3. In this case, the radius value is again approximately set to dY/2.

From Table 5.3, it is apparent that the failure rate of this algorithm was higher in normal subjects older than 35 years. Observations revealed that the facial temperature profile of subjects older than 35 years is more complex than that of the young. This extra complexity hampers the target-tracing function from correctly selecting the snake that most closely delineates the eye edges.

For subjects who have an epicanthic fold (or “double eyelid”), the algorithm may not localize the eye and cornea accurately. This type of error is included in the category of “incorrect localization.” The snake occasionally stays on the epicanthic fold instead of on the actual eyelid. The corneal

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radius in this case will be larger, and the area of OST acquisition will cover part of the eyelashes.

Literature covers a number of automated methods developed for ocular detection. Asteriadis et al. utilized edge-related geometrical information of an eye and its surrounding area to locate the eye.34 The variance projection function (VPF) was developed and applied to the similar application with encouraging results.35 Furthermore, the computational complexity in their method is relatively low.

Feng et al.36 detected an eye window based on the extraction of multicues from a gray level, and the precise iris and eye corner were located by VPF and eye variance filter. This method has been tested on 930 face images by the MIT AI laboratory, and the accuracy was 92.5%. Jee et al. detected eye pairs using edge detection, binary information, and support vector machines, and achieved an accuracy of more than 92%.37 That system is fast and reliable, and can be used for face detection.

Research has also been performed in the tracking of eye movements in a sequence of images. For example, the time-adaptive self-organizing map (TASOM)-based active contour models (ACMs) tracks eye movements.38 This method detected the boundaries of the human ocular sclera and tracked its movements. Eye features, such as the iris center or eye corners, were located using information regarding the iris edge. It showed a good performance in general and a better performance than that of the gradient vector field snake-based method.

The above-mentioned algorithm works well for optical facial images, but may not work for IR thermal images. In many cases, the lower eyelid is not clearly discernible in thermogram images. The eyelash, rather than the eyelid, defines the boundary for the upper eyelid. Moreover, the boundary defining iris and cornea are almost absent in nearly all thermograms. Therefore, we propose this automated algorithm, by snake and target-tracing function, to locate the eye and cornea in an IR thermogram.

5.6. Conclusion

IR thermography is a possible alternative approach for the diagnosis of ocular diseases. In this study, we have proposed a method to identify a cornea automatically using a snake and target-tracing function. This algorithm can

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