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7.5Quantitative Analysis and Evaluation of Linear Structure Detection Methods

7.5.1 Methodology of Evaluation

The performance of the dual-model detector and the other methods described in Sect. 7.2 is obtained by validating the extracted nerve fibers in comparison with an expert manual delineation using CCMetrics.4 Only the raw response of each method is taken into account without any further postprocessing operations or shade correction methods as shown in Fig. 7.9. Binary images are obtained by a simple uniform thresholding operation that is followed by a thinning operation to achieve a one-pixel-wide skeleton image.

To be consistent in this comparison of different methods, the detection algorithm did not include any pixel classifications. Responses from techniques with multiscale analysis, such as LinOp, Hessian, DTCWT, and Monogenic Signal, were considered by taking the maximum magnitude of all levels.

Three measures have been used to quantify the evaluation: the false-positive (FPR), the true-positive (TPR), and the equal-error rate (EER), which is the average of optimal FPR and false-negative rate at minimal difference between both. A receiver operating characteristic (ROC) analysis was conducted by comparing the generated skeleton at different threshold intervals of the methods’ responses with the manually delineated ground-truth. A tolerance of ±3.141 μm (3 pixels) was allowed in determining coincidence between the ground-truth and the detected nerve fibers.

The peak signal to noise ratio (PSNR) in (7.18) is also used to evaluate the performance of all methods.

MAXI
PSNRdB = 20 log √e	(7.18)

The PSNR is computed with respect to the mean squared error e, which is the mean square difference between the detected nerve fibers and the ground-truth manual delineation. MAXI is the maximum possible intensity (fixed) and e is the mean square error. The practical implementations of the Hessian, the DTCWT, and the Monogenic Signal were obtained from public domain sources [44–46], while the rest were implemented by our research group.

4CCMetrics is a purpose built interactive graphical interface which helps in the analysis undertaken by experts to manually delineate nerve fibers in CCM images.

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Fig. 7.9 Example response images for all different detection methods. The responses were taken as a raw output from the detector without any postprocessing and converted to binary images and then to skeleton images for fair comparison

7.5.2 Database and Experiment Setup

The evaluation has been conducted on a database of 525 CCM images captured using the HRT-III5 microscope from 69 subjects (20 controls and 49 diabetic patients). The pixel size is 1.0417 μm and the field of view is 400 × 400 μm2 of

5Heidelberg Engineering Inc. modified to acquire corneal confocal images.

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Fig. 7.10 The receiver operating characteristic (ROC) curves of all five detectors. The dual-model performance of detecting nerve fibres has clearly outperformed the other methods

the cornea. For each individual, several fields of view are selected manually in the centre of the cornea from the Bowman’s layer showing recognizable nerve fibers.

Using the neuropathy disability score (NDS) [47], 48 patients were categorized into four groups according to severity of neuropathy (nonneuropathic: 0 ≤ NDS ≤ 2(n = 26), mild: 3 ≤ NDS ≤ 5(n = 9), moderate: 6 ≤ NDS ≤ 8(n = 10) and severe:

9≤ NDS ≤ 10(n = 3).

7.5.3Nerve Fiber Detection Comparison Results

The superior performance of the dual-model is borne out by the ROC curves of Fig. 7.10 in which the dual-model shows improved detection at all operation points. The EER and PSNR values for all the methods are presented in the box-plots in Fig. 7.11 and Table 7.1. Each data point in Fig. 7.11 corresponds to the evaluation on one of the 525 CCM images in the database.

The dual-model shows lower EER and higher PSNR than all other methods (Table 7.1). These improvements are statistically significant (p ≈0 using three different nonparametric tests). The table also shows that the standard deviations of both EER and PSNR are low for the dual-model, which indicates a more stable and robust behavior.

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Fig. 7.11 The box-plots of the EER (left) and the PSNR (right) are shown for all methods. The box-plots indicate the upper and the lower quartiles as well as the median (the bar) of the EER and PSNR values respectively; whiskers show the extent of the rest of the data while crosses indicate outliers for (a) dual-model, (b) LinOp, (c) 2D Gabor, (d) Hessian, (e) DTCWT, and (f) Monogenic

Table 7.1 A comparison of mean EER and PSNR and their standard deviations for all five detection methods; the dual-model has achieved the lowest EER and the highest PSNR

		EER(%)			PSNR(dB)
		μ	σ		μ	σ
Dual-model	17.79		10.58	19.0774		2.16
LinOp	22.65		10.76	18.5132		2.09
2D Gabor	24.15		10.74	18.8042		2.11
Hessian	23.14		11.53	17.9269		2.27
DTCWT	34.17		10.43	17.0045		2.23
Monogenic	26.50		12.58	18.1084		2.20

The closest performance to the dual-model has been achieved by LinOp, which has 4.86% greater EER on average. The performance of the Hessian methods is also similar with an average EER of 23.14% (Table 7.1). The poorest performance is obtained with the DTCWT and Monogenic Signal, as these are general-purpose methods. The dual-model has also shown a superior performance in terms of achieving higher PSNR values for the response images. As shown in the box-plot (Fig. 7.11), the average PSNR of the dual-model is 19.08 dB, while all PSNR groups have means smaller than the dual-model as indicated by Table 7.1, which shows a summary of the comparison. The closest PSNR is at 18.80 dB.

7.5.4 Evaluation of Clinical Utility

Of the several features listed in Sect. 7.3.3, which may be used to quantify the nerve fibers, NFL has been shown to be the most discriminating, and it is that feature that

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Fig. 7.12 The scatter plot of the manually and the automatically computed NFL metrics. There is clearly a very strong correlation (r = 0.93)

Table 7.2 A comparison of the manual and the automated analysis; unlike manual analysis, the automated analysis is insensitive to observer variability and can be much quicker

	Manual	Automated
p-value(×10−8)	0.03	2.03
Coefficient of variation	0.34	0.29
Observer variability	Yes	No
Processing time	5–10 min	≈ 5 s

we use to compare automatic detection with expert manual analysis (ground-truth). NFL is measured as the total number of pixels in the nerve fiber skeleton after the postprocessing of Sect. 7.4.4.

Figure 7.12 shows a scatter plot of manual vs. automatic measurements of NFL. There is clearly a strong correlation (r = 0.93) indicating that the automated system is successfully identifying the correct nerve fibers. The coefficient of variation cv = σ /μ of the manual analysis is 0.34, reducing for the automated analysis to 0.29, which indicates more reliability and robustness of the results (Table 7.2).

The box-plots in Fig. 7.13 shows NFL measured manually and automatically for the stratified group of subjects. There is a strong similarity between the manual and the automated analysis. However, the scale of the NFL has slightly changed from