**Purpose**:
To evaluate different segmentation methods in analyzing Schlemm's canal (SC) and the trabecular meshwork (TM) in ultrasound biomicroscopy (UBM) images.

**Methods**:
Twenty-six healthy volunteers were recruited. The intraocular pressure (IOP) was measured while study subjects blew a trumpet. Images were obtained at different IOPs by 50-MHz UBM. ImageJ software and three segmentation methods—*K*-means, fuzzy C-means, and level set—were applied to segment the UBM images. The quantitative analysis of the TM-SC region was based on the segmentation results. The relative error and the interclass correlation coefficient (ICC) were used to quantify the accuracy and the repeatability of measurements. Pearson correlation analysis was conducted to evaluate the associations between the IOP and the TM and SC geometric measurements.

**Results**:
A total of 104 UBM images were obtained. Among them, 84 were adequately clear to be segmented. The level-set method results had a higher similarity to ImageJ results than the other two methods. The ICC values of the level-set method were 0.97, 0.95, 0.9, and 0.57, respectively. Pearson correlation coefficients for the IOP to the SC area, SC perimeter, SC length, and TM width were −0.91, −0.72, −0.66, and −0.61 (*P* < 0.0001), respectively.

**Conclusions**:
The level-set method showed better accuracy than the other two methods. Compared with manual methods, it can achieve similar precision, better repeatability, and greater efficiency. Therefore, the level-set method can be used for reliable UBM image segmentation.

**Translational Relevance**:
The level-set method can be used to analyze TM and SC region in UBM images semiautomatically.

^{1}Elevated intraocular pressure (IOP) is harmful to the optic nerve and can aggravate glaucoma. Therefore, IOP is the most widely used parameter for evaluating and monitoring glaucoma.

^{2}IOP is balanced by the production and outflow of the aqueous humor. Most studies on glaucoma pathogenesis have focused on outflow resistance. The trabecular meshwork (TM) and Schlemm's canal (SC) pathway account for 75% to 80% of the whole outflow,

^{3}making it an important area for study.

^{4}showed that an acute IOP elevation can reduce the SC area and alter the TM configuration in human and animal eyes.

^{5}Yan et al.

^{6}demonstrated that aerobic exercise can cause TM and SC expansion, which lowers IOP. These findings suggest that TM-SC tissue configurations may determine aqueous outflow and IOP regulation. This conclusion also applies to patients with glaucoma. Swain et al.

^{7}reported that SC is collapsed in most patients with primary open-angle glaucoma (POAG). Moreover, clinical studies have shown that canaloplasty is an effective and safe procedure to lower IOP in patients with POAG.

^{8}Cagini et al.

^{9}

^{,}

^{10}determined that canaloplasty is not as successful in eyes that exhibit an irreversible collapse of outflow pathways. These findings suggest that morphologic changes of TM-SC in patients with glaucoma can lower IOP and improve the disease.

^{11}

^{,}

^{12}The latter can be used in almost all kinds of patients, even those who have a cloudy cornea or arcus senilis and cannot be examined with OCT.

*K*-means clustering

^{13}and fuzzy C-means clustering (FCM).

^{14}In previous studies, UBM image segmentation was performed freehand or partly assisted by image analysis software.

^{6}

^{,}

^{15}

^{–}

^{18}Among them, ImageJ software (National Institutes of Health, Bethesda, MD) was the most commonly used. However, manual segmentation is time-consuming and depends on the experience of the technician. Moreover, UBM images are usually corrupted with intensity inhomogeneities, which make TM and SC segmentation an inherently difficult task.

^{19}Recently, level-set methods have been proposed to deal with images with intensity inhomogeneity, such as the local intensity clustering method

^{20}

^{,}

^{21}and the edge-based method.

^{22}These approaches have been successfully applied to segment magnetic resonance images of the breast, X-ray images of bones, ultrasound images of the prostate,

^{20}and infrared breast thermography.

^{23}

^{24}These segmentation methods were further verified in UBM images obtained under different IOPs. With these segmentation results, quantitative analysis of the TM-SC region was done and compared.

^{24}One eye of each participant was randomly selected for the UBM examination using a 50-MHz UBM (Suoer SW-3200L; Suowei Co., Tianjin, China). The IOP of the other eye before and during the trumpet blowing was measured using the Icare Pro tonometer (Tiolat Oy, Helsinki, Finland). According to the results of our preexperiment and previous studies,

^{6}the SC detection rate at the inferior quadrant is the highest. Thus, all the images were obtained from the inferior quadrant of the eye at four time points: before trumpet blowing, 10 seconds after the start of blowing (IOP increasing period), immediately after blowing cessation (IOP peak time), and 10 seconds after blowing cessation. All examinations were conducted by the same ophthalmologists and under the same illumination conditions using identical equipment.

*K*-Means Clustering

*K*-means

^{13}is a fast and simple clustering algorithm that is used to classify an image into a specific number of disjointed clusters. The general idea is to identify

*K*centroids, one for each cluster, and then associate each data point to the nearest centroid.

^{25}Let Ω be the image domain,

*I*(

*x*): Ω →

*R*be the observed image, and

*x*,

*y*represent the pixel coordinates. In a previous study,

^{26}segmentation of image

*I*(

*x*) into

*K*clusters was achieved by minimizing the following equation:

*j*and its cluster centroid,

*c*, and

_{j}*M*is the pixel number of the image.

^{27}and later improved by Bezdek et al.

^{14}This algorithm is widely used in data clustering and image segmentation.

^{28}

^{,}

^{29}By introducing the possibility of partial memberships to clusters, this algorithm attempts to partition every pixel into a collection of fuzzy cluster centroids by minimizing the following objective function:

*u*is the fuzzy membership degree of pixel \(I(x_i^{(j)})\) and cluster centroid

_{ij}*c*, which satisfies

_{j}*u*∈ [0, 1], and \(\sum\limits_{i = 1}^M {{u_{ij}}} = 1,{\rm{ }}j = 1,2, \cdots ,K\). In addition, parameter

_{ij}*m*(

*m*> 1) is a constant that determines the fuzziness of the resulting partitions.

*I*can be modeled as

*J*(

*x*) is the real image,

*B*(

*x*) is the bias field that accounts for the intensity inhomogeneity, and

*n*(

*x*) is the noise term.

^{30}The bias field

*B*(

*x*) is assumed to change slowly, and the value

*B*(

*x*) can be considered approximately constant in a neighborhood of

*O*= {

_{y}*x*||

*x*−

*y*| ≤ ρ},

*B*(

*x*) ≈

*B*(

*y*) for

*x*∈

*O*. Real image

_{y}*J*reflects an intrinsic property of the imaging objects, which can be assumed to be a piecewise constant. Moreover,

*J*takes approximately

*N*distinct constant values

*c*

_{1},

*c*

_{2},⋅⋅⋅

*c*in disjointed regions Ω

_{N}_{1},Ω

_{2},⋅⋅⋅Ω

_{N}, where \(\Omega = \cup _{i = 1}^N{\Omega _i}\) and Ω

_{i}∩Ω

_{j}= Ø for

*i*≠

*j*. Thus, the intensities of points in each subregion Ω

_{i}∩

*O*can be approximated as follows:

_{y}*O*can be classified into

_{y}*N*distinct clusters with centers

*m*≈

_{i}*B*(

*y*)

*c*:

_{i}*K*-means method is used to classify the local intensities in

*O*. Then, clustering criterion function ε

_{y}_{y}of

*y*in Ω can be written as

*k*(

*y*−

*x*) is the Gaussian kernel function, which is selected as a truncated Gaussian function defined by

^{25}

*a*is a normalization constant, such that ∫

*k*(

*u*)

*du*= 1, and σ is the standard deviation of the function. The smaller the value of ε

_{y}, the better the classification of

*y*in Ω. Therefore, the optimal partition of the entire domain Ω can be realized by joint-minimizing ε

_{y}, which can be written as the following local clustering criterion function:

*R*be a level-set function, and function ε can be written as the function of Φ = (φ

_{1},φ

_{2},⋅⋅⋅φ

_{k}),

*c*= (

*c*

_{1},

*c*

_{2},⋅⋅⋅

*c*) and the bias field

_{N}*b*:

*e*(

_{i}*x*) = ∫

*k*(

*y*−

*x*)|

*I*(

*x*) −

*B*(

*y*)

*c*|

_{i}^{2}

*dy*and the membership functions

*m*=1 for

_{i}*y*∈ Ω

_{i}, and

*m*= 0 for

_{i}*y*∉Ω

_{i}. For the case of two phases, the membership functions are defined by

*m*

_{1}(φ) =

*H*(φ) and

*m*

_{2}(φ) = 1 −

*H*(φ). The energy function in the two-phase level-set formulation is defined by

*L*(φ) and

*R*(φ) are the regularization terms. Energy minimization is achieved by an iterative process. By minimizing this energy, the level-set method

_{p}^{30}can segment the image and estimate the bias field that can be applied for bias correction. When the above energy function

*F*(φ,

*c*,

*b*) obtains the minimum value or the maximum number of iterations is reached, the iteration is terminated.

*t-*test was used to compare the mean differences when the measurement data were obtained by ImageJ and the three segmentation methods (

*P <*0.05 was considered statistically significant).

^{31}

^{,}

^{32}The relative error and the interclass correlation coefficient (ICC) were employed to quantify the accuracy and repeatability of the three methods.

^{33}Because systematic differences are part of the measurement error, a two-way random-effects model was used to calculate the ICC.

^{34}

*K*-means, FCM, and level set were used to obtain the boundary curves of the different gray regions in the UBM images. The segmentation results are shown in Figures 3 to 6.

*K*-means methods are discontinuous. Some interference occurs between the TM and SC, which makes identifying the TM area difficult. The SC region segmented using the level-set method has a clear outline, and the TM region boundary can be easily identified. It is obvious that the level-set method produces more accurate segmentation results than the other two methods.

*P*= 0.663,

*P*= 0.071,

*P*= 0.755, and

*P*= 0.117 for SC area, SC perimeter, SC length, and TM width, respectively). There were no statistically significant differences in the SC area and SC perimeter measurements between the

*K*-means method and by ImageJ (

*P*= 0.103 and

*P*= 0.901 for SC area and SC perimeter, respectively), while the differences for the SC length and TM width between the two methods were statistically significant (

*P*< 0.001 for SC length and TM width). There was no statistically significant difference between the SC area measured by the FCM method and the corresponding result measured by ImageJ (

*P*= 0.662), while the differences in the SC perimeter, SC length, and TM width between the two methods were statistically significant (

*P*= 0.032,

*P*< 0.001, and

*P*< 0.001 for SC perimeter, SC length, and TM width, respectively).

*K*-means methods. Among the four parameters measured by the ImageJ and three segmentation methods, the SC area was the most consistent parameter.

*K*-means and FCM methods for segmenting the TM-SC region, only the level-set method was used to perform the correlation analysis. The correlations among the SC area, SC perimeter, SC length, TM width, and IOP were analyzed using the Pearson correlation coefficient and linear regression analysis. The results are shown in Figure 8. It can be observed that, as the IOP increases, the SC area, perimeter, and length tend to decrease. The TM width likewise decreases. Pearson correlation coefficients for IOP to the SC area, SC perimeter, SC length, and TM width are −0.91, −0.72, −0.66, and −0.61, respectively. Thus, a negative correlation relationship between the IOP and the geometrical measurement of TM and SC can be inferred.

^{6}

^{,}

^{15}

^{–}

^{18}However, manual outlining is a time-consuming and tedious task. In this article, we showed that the level-set method can be used to extract the TM-SC region from the UBM image and useful features can be obtained from the segmentation. Compared with manual segmentation, the level-set method produced similar segmentation results while providing better repeatability and efficiency. In addition, the level-set method had higher accuracy than the classical FCM and

*K*-means methods.

^{4}

^{,}

^{5}The reason for TM-SC region collapse may be the compression force caused by acute IOP elevation to the elastic structure. Assuming that accurate measurements of the TM and SC response to IOP fluctuation in patients in vivo are realized, mathematical models can be used to calculate the TM stiffness, which has recently been shown to be associated with resistance to outflow.

^{35}

^{–}

^{37}Among the four measurement indicators in this study, the Pearson correlation coefficient for IOP to the SC area is the highest. Thus, we may speculate that the SC area can be used as a sensitive indicator for measuring the TM-SC region.

**X. Wang**, None;

**Y. Zhai**, None;

**X. Liu**, None;

**W. Zhu**, None;

**J. Gao**, None

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