An automated chorio-scleral interface (CSI) detection algorithm based on polarization sensitive optical coherence tomography (PS-OCT) is presented. This algorithm employs a two-step scheme based on the phase retardation variation detected by PS-OCT. In the first step, a rough CSI segmentation is implemented to distinguish the choroid and sclera by using depth-oriented second derivative of the phase retardation. Second, the CSI is further finely defined as the intersection of lines fitted to the phase retardation in the choroid and sclera. This algorithm challenges the current back-scattering intensity based CSI segmentation approaches that are not fully based on anatomical and morphological evidence, and provides a rational segmentation method for the morphological investigation of the choroid. Applications of this algorithm are demonstrated on in vivo posterior images acquired by a PS-OCT system with 1-μm probe.
© 2012 Optical Society of America
The choroid is an internal layer of the eye with several basilic functions. It accounts for most of the ocular blood flow , providing metabolic support to the retinal pigment epithelium (RPE) and the inner retina . The choroid also plays a roll in the absorption of excess light penetrating the retina and the RPE and stabilizing the temperature of the macula . Its thickness is related to several ocular pathological parameters, e.g., the intraocular pressure, perfusion pressure , and endogenous nitric oxide production . The morphological investigation of the choroid is of significant interest in the diagnosis and study of ocular diseases such as glaucoma  and age-related macular degeneration . However, the choroid defies the conventional optical imaging methods because of the strong light scattering and absorption characteristics of the RPE. Indocyanine green angiography [8–10], which relies on near-infrared wavelength, allows visualization of choroidal vessels, but it does not provide depth-resolved information. Ultrasonography is another approach used for choroidal examination , but its resolution is limited by a trade-off between detection depth and resolution.
Optical coherence tomography (OCT) [12, 13], which provides noninvasive and cross-sectional images with micrometric resolution, has been a common imaging method in ophthalmology [14–16]. The OCT technique has been dramatically improved in terms of imaging speed and resolution in the past two decades since its invention [17, 18]. The branch of Fourier-domain OCT (FD-OCT), including spectral-domain OCT and swept-source OCT, provides up to 20MHz scanning speed [17, 19], as well as enhanced sensitivity and signal to noise ratio (SNR) [20–22]. The increased acquisition speed to time domain OCT (TD-OCT) allows repeated 2D imaging of the retina, providing the possibility of speckle reduction and SNR improvement by averaging OCT images. Recently, the enhanced depth imaging (EDI) OCT technique has been developed and utilized to study the cross-sectional structure and measure the thickness of the choroid [23, 24]. Another approach to obtaining a choroid image using OCT, the application of a 1-μm wavelength probe, is rapidly being developed for its high penetration ability in the posterior segment of the eye [25–29].
Most retinal segmentation algorithms are achieved by using back-scattering intensity information obtained by conventional OCT . This intensity based segmentation relies on image contrast properties of each retinal layer, which have been widely investigated by comparing OCT images and histological studies. Various methods have been developed for the robust and fully automated segmentation of retinal OCT images. Hee et al. proposed the first segmentation method in TD-OCT based on intensity variation . Since then, various methods have been developed for the segmentation of OCT images. Recently reported automated segmentation can provide robust segmentation of several sub-layers in the retina with superior precision to manual segmentation [32, 33]. However, when it comes to the choroid, there is a lack of morphologic knowledge. Its thickness would become significantly reduced when cut off from its blood supply. This makes it difficult to acquire knowledge of the chorio-scleral interface (CSI) in morphology in vitro, and hence it has been impossible to define the CSI in an OCT image based on histological knowledge. Most of the current OCT studies about choroidal morphology are based on manual segmentation. Ophthalmologists manually and empirically identify CSI. However, to the best of our knowledge, no clear morphological or anatomical evidence supports the empirical manual segmentation of CSI. Recently, Kajić et al. reported an automated choroidal segmentation approach using a statistical model , but the training data for the construction of this model was still obtained by manual segmentation of intensity OCT images.
Polarization sensitive OCT (PS-OCT) is a functional extension of OCT providing intensity tomography and birefringence tomography simultaneously [35–38]. Tissues consisting of organized microstructure or collagen alter the polarization status of light, reflected as a phase retardation change or other birefringent parameters. Several studies have reported retinal imaging using PS-OCT. The phase retardation and birefringence of the retinal nerve fiber layer has been well investigated [39, 40]. Götzinger et al. reported a functional segmentation of RPE using depolarization information obtained by PS-OCT .
Birefringent properties of the choroid and sclera have a clear difference . The sclera represents a strong birefringence because of its high concentration of of collagen, and hence the phase retardation should increase along the penetration. Meanwhile, despite of a small amount of collagenic components in the choroid, the choroidal birefringence is so low that it is negligible for the PS-OCT system with a typical birefringence sensitivity. And hence the phase retardation can be reasonably considered as constant in the choroid . This has been validated by high penetration PS-OCT using a 1-μm probe reported by Yamanari, et al. . The depth-resolved birefringence properties measured by PS-OCT can be utilized as a contrast source for the segmentation of these tissues.
In this paper, we present an automated segmentation algorithm to detect the CSI based on phase retardation tomography obtained by PS-OCT. The segmentation algorithm consists of two steps: Firstly, a rough segmentation is achieved by model analysis and a dynamic programming algorithm in the phase retardation image to initialize further respective phase retardation analysis in choroid and sclera. Next, linear regressions are applied to both layers near the rough segmentation results, and the CSI is determined by the intersection of the two fitted lines. Finally, a back-scattering based error detection and correction algorithm is performed to avoid the segmentation error caused by large vessels. Several results of this algorithm are presented to verify the efficiency of CSI detection.
2.1. Acquisition of phase retardation image
In this study, we employed a full-range Jones matrix PS-OCT system with a 1-μm probe beam for the polarization sensitive measurement . The principle and setup of the Jones matrix PS-OCT has been reported in detail elsewhere [43–46]. In this system, the Jones matrix detection is achieved by modulating the incident light using an electro-optic modulator (EOM). It creates modulation-multiplexed two orthogonal polarization states. This polarization modulation results in two multiplexed OCT spectra with different carrier frequencies, i.e., a null-frequency and the same frequency with the polarization modulation. Both of the multiplexed spectra are then detected by polarization diversity detectors consisting of horizontal and vertical detectors. The OCT signals corresponding to the two carrier frequencies are numerically demultiplexed after detection. Since the OCT signals are multiplexed both by the carrier frequency and the polarization diversity detection, we finally obtain 4 OCT signals simultaneously. And then the cumulative Jones matrices of a sample are obtained by assigning the 4 OCT signals to each element of the Jones matrices. High-penetration Jones matrix tomography can be obtained from the posterior segment of eye by this PS-OCT system, and successive signal processing provides the corresponding phase retardation tomography.
Image quality is critical for biomedical image segmentation, especially for computer-assisted segmentation tasks. Speckle noise and a limited SNR are two of the main issues resulting in difficulty with segmentation. As reported in recent research, the signal to noise issue introduces both systematic and random errors in phase retardation measurement in the Jones matrix PS-OCT . Usually, the SNR of an optical signal back-scattered from the CSI is low. It results in randomness and a low contrast in phase retardation tomography. This prevents an accurate quantitative analysis of phase retardation, leading to the failure of phase retardation information based CSI segmentation. To improve the quality of the phase retardation images, we measured several B-scans repeatedly in a same position of the eye, and performed the Jones matrices averaging described in .
Figure 1 shows intensity and phase retardation images resolved from a single Jones matrix B-scan and averaged Jones matrix B-scan. Figure 1(c) reveals that the averaging strongly reduced the speckle noise in intensity image and improves the SNR. It is also shown in Fig. 1(d) that an enhanced phase retardation contrast appears around the CSI.
2.2. Two-step segmentation based on phase retardation
Since the sclera is a collagenous tissue and the choroid is not, the birefringence properties in choroid and sclera are quite different. In this work, the CSI is determined as the boundary between areas with different phase retardation properties. We use the gradient of phase retardation to represent the birefringence. The segmentation approach consists of two steps. A rough segmentation is implemented in advance for the initialization of subsequent phase retardation analysis. Then, depth-oriented linear regressions are applied to the phase retardations in both the roughly segmented choroid and the sclera for an exact segmentation.
2.2.1. Rough segmentation
The second step of our algorithm is based on the depth-oriented slope fitting of the phase retardation which is applied to the choroid and sclera separately. Therefore, the interface of these layers should be roughly identified in advance. The purpose of the rough segmentation from the first step is to determine the ranges of linear regressions for the second-step of our algorithm.
Since the amount of birefringence is low in the retina and choroid, we model the phase retardation in the choroid as a small constant value, i.e., a linear line with a slope of zero in depth. On the other hand, sclera has a strong birefringence, and hence we model the scleral birefringence as a linear line with a positive slope in depth. In this model, the CSI is detected as a local maximum of the second derivative of the phase retardation in depth. In our implementation the second derivative is obtained by a discrete operator of [−1 0 0 0 0 2 0 0 0 0 −1], which is equivalent to a wide kernel first derivative operator of [ −1 −1 −1 −1 −1 1 1 1 1 1] and the successive standard first derivative operator of [−1 1]. The wide kernel operator is used to enhance the derivative value and improve the SNR of the second derivative. This second derivative possesses a local maximum at the CSI, while minor fluctuations of the phase retardation are filtered out. The location of the local maximum is utilized as the first estimation of the CSI in the next procedure.
In our implementation, we first reduced the speckle noise using a rectangular averaging filter (size: 30 × 10 pix = 100 μm (lateral) × 79 μm (axial)) in the phase retardation images. This moving average significantly reduces the speckle in a phase retardation image as shown in Fig. 2(a). Then, the second derivative of the despeckled phase retardation was obtained along penetration in each A-line using the protocol described above. The distribution of the second derivative is shown in Fig. 2(b). A local maximum band can be observed around the expected CSI.
However, in Fig. 2(b), the CSI is not the only layer detected as local maximum. The strongest signal appears around the inner limiting membrane. To identify the CSI, the region of interest should be limited. This is achieved by segmentation of the choroid/RPE interface using the back scattering intensity information. The RPE complex is known as a set of hyper-reflective layers within retinal OCT images, while the choroid has a lower intensity signal than the RPE complex. Here we first adopt the same method as  for RPE estimation. Then, the interface of the choroid and RPE is assigned to the pixels with minimum negative gradients beneath the RPE estimation in the intensity OCT image blurred by using a Gaussian filter with a standard deviation of 3 × 3 pixels. The yellow line in Fig. 2(c) indicates the RPE/choroid boundary segmented using this method. We shift this boundary 5 pixels (40 μm) towards the choroidal side to exclude the RPE from the region of interest. All of the pixels anterior to the choroid/RPE interface as well as other pixels with a negative second derivative value or an intensity lower than twice of noise floor are set to 0. Then, the second derivative information is normalized in each A-line. Here we use d(i, j) to denote the normalized second derivative of the j-th pixel in the i-th A-line.
To obtain a continuous curve as the CSI estimation, we applied a graph searching method using dynamic programming based on the second derivative information. The dynamic programming method has been used in several automated segmentations of retinal layers in intensity OCT images, providing a robust solution to shortest path or minimum cost problems without an initialization of start and end points [32, 50, 51]. To apply the graph searching method, we first classify all pixels into either a potential CSI or a false CSI. The pixels meeting the condition of d(i, j) ≥ 0.5 are classified as potential CSI and the others are classified as false CSI. Furthermore, the node costs of these two types of pixels are assigned as
The node cost of potential CSI slope is shown in Fig. 2(c) with a rainbow color-map superimposed on an intensity image, where transparent is assigned to the node cost of 2. In this definition, the node cost at a potential CSI ranges from 0 to 1, lower than half of the node cost in a false slope position. This setting can effectively limit the segmented CSI within the potential CSI band, isolating it from the fake patches of local maximum in the second derivative distribution.
The minimum cost from the first A-line to node (i, j) in this dynamic programming algorithm is represented as
The optimal solution is defined by searching the path with minimum cost from the leftmost A-line to the rightmost A-line. A 50-pixel (3.3% of the transversal range) median filter is also applied to reject minor segmentation error. This solution is shown with a red line in Fig. 2(d).
2.2.2. Slope fitting in phase retardation
The gradient of phase retardation reveals birefringence properties in the tissue. Phase retardation increases rapidly with penetration in the sclera due to the presence of birefringent components, while remaining almost a constant in the choroid. The boundary of these two layers should appear as an inflection in the phase retardation model. The exact segmentation to the CSI is achieved by slopes fitting to cumulative phase retardation in the choroid and sclera as described in following paragraphs.
The phase retardation model in the choroid and sclera is illustrated in Fig. 3. In this model, we assumed constant phase retardation in the choroid. An average of the phase retardation is obtained between the RPE/choroid boundary and the initial estimation of the CSI for each Aline, where the RPE/choroid boundary was segmented by using the intensity image as described before, and the initial estimation of the CSI was obtained by the method described in 2.2.1. This averaging is equivalent to a linear regression to the phase retardation in the choroid by a regression line with zero. Linear regressions are applied to the 7-pixel (55-μm) regions in the sclera close to the initial estimation of the CSI. Since the initial segmentation might lack accuracy, we do 11 trials with the start point of this linear regression from −5 pixels to +5 pixels (−40 μm to +40 μm) to the initially estimated CSI, and select the regression with the maximum gradient as the phase retardation slope in the sclera. This operation is for excluding the choroidal and scleral regions with aliasing of the phase retardation from the linear regression since these two regions have low phase retardation that minimize the gradient. The CSI of each A-line is defined as the intersection of these two lines as shown in Fig. 3(a). Finally, the CSI is acquired by smoothing the intersections in the B-scan direction by a 50-pixel median filter as exemplified in Fig. 4(b), while Fig. 4(a) shows the CSI estimation before smoothing.
2.3. Error correction
A large blood vessel in the choroid or sclera can disturb this phase retardation information based CSI detection. The anterior boundary of a blood vessel is sometimes detected as the CSI by this algorithm. One reason might be the unreliable measurement of the phase retardation in the blood vessels. The back scattering signal from blood is very weak, so the SNR inside of a blood vessel is relevantly low. As it was revealed in Ref. 47, measured phase retardation would approach around 2/3 π as the effective SNR decreases. This erroneous high phase retardation would mimic the phase retardation in the sclera. The collagen in the vessel wall can also be a factor that misleads our phase retardation oriented CSI segmentation.
To eliminate the segmentation error around a large vein, an additional optimization algorithm based on an intensity image is applied. Identification of blood vessel’s position around the CSI is required in error correction. This is achieved by the analysis of intensity information beneath the CSI obtained in the two-step segmentation process described in Section 2.2. The intensity inside the blood is rather weak due to the low back scattering from blood. A moderate intensity can be observed in the sclera near the CSI, and the intensity constantly decreases along penetration in the intensity images acquired by PS-OCT. Note that this feature is only warranted in polarization-independent intensity OCT images, which are free from the birefringence artifact that exists in standard OCT images [26, 52]. We distinguish the segmentation error by evaluating the distance between the segmented CSI and the pixel with maximum intensity beneath it in each A-line. If this distance is higher than a threshold, e.g. 5 pixels, the CSI would be corrected to the maximum intensity position, which indicates the posterior boundary of a blood vessel. In the end, a median filter with the width of 25 A-lines is utilized to reject the false correction that can happen in a single A-line.
Figure 5 shows an example of an intensity based segmentation error correction. As indicated by white arrows, the phase retardation based segmentation result is located within blood vessels in some regions. It is clear that the phase retardation failed in segmentation of the CSI. These errors can be detected and corrected by the intensity based process described above. The corrected segmentation result shown with a yellow line in Fig. 5 provides a more reasonable estimation of the CSI around the vessel regions.
We employed a 1-μm probe polarization sensitive swept source OCT to obtain phase retardation and back-scattering images. The setup and parameters of this system have been described in Ref. 43 in detail. In vivo multiple B-scan imaging has been performed in healthy eyes. The macular region of the retina is imaged with 1,500 A-lines per frame and 64 frames are repeatedly acquired in a 5-mm horizontal area centered at the fovea. The probe power on the cornea was 0.81 mW.
The axial motion was detected and canceled by a custom-made correlation based algorithm. In this algorithm, a B-scan frame is selected as a reference. The cross-correlation functions between an A-line in the reference frame and the A-lines in the corresponding transversal location in the other frames are calculated. These correlation functions provide the axial displacement of each A-line respect to the reference frame. The outliers in the detected displacement within a frame were eliminated by applying medial filtering with a kernel size of 100 A-lines. The intra-frame-motion respect to the reference frame was then corrected by using the predicted displacement for each frame. After this motion correction, the image correlations between the reference frame and all of the motion corrected frames were calculated, and the most highly correlated 15 frames were selected. An averaged Jones matrix B-scan was yielded from the 15 frames and the reference frame by using the Jones matrix averaging algorithm .
Six subjects without marked posterior disorder were involved in this study. Six eyes of three subjects were first measured. A high similarity between the two eyes of the same subject was observed. Hence, only one eye from each remaining subject was scanned. Finally, six eyes of the six subjects were involved in the following study.
An example of phase retardation based segmentation is shown in Fig. 6. This B-scan is acquired from a myopic eye of an adult subject. In the region indicated with an ellipse in Fig. 6(a), the tissue appears as a homogeneous intensity feature. No structrural information indicates the location of the CSI, so it is difficult to determine whether the CSI is smooth or abruptly convex in this region. In the same region in Fig. 6(b), a clear difference in birefringence property can be visualized through phase retardation information. The real CSI can be detected as shown in Fig. 6 using the 2-step algorithm described in Section 2.2. The phase retardation based method provides more reliable CSI segmentation than the intensity based method.
In several previous studies about choroidal thickness, the choroidal thickness was manually determined at only a few representative locations, and the distribution of choroidal thickness is evaluated based on the thickness at these locations [53, 54]. This method is based on the assumption that the CSI is smooth. However, the phase retardation based segmentation results challenge this assumption. In Fig. 5, it is clear that the CSI appears to deviate around the large blood vessels in the thin choroid. Figure 7 also gives an example of rough CSI. The CSI segments marked with yellow circles appear as convex patterns, contradicting the assumption of a smooth CSI. According to the phase retardation image shown in Fig. 7(b), the convex distributions of the phase retardation are also found in these regions, and the phase retardation based segmentation accurately represents them. This unsmooth CSI obtained by the phase retardation based segmentation was clearly observed in 3 out of 6 subjects.
Abnormal CSI segmentation associated with a low birefringence region beneath the fovea was sometimes obtained. Figure 8 shows an example. It is clear that there is a region with abruptly low phase retardation around the CSI near the fovea. This phase retardation distribution was found in three out of six subjects, either with myopia or hyperopia. Since this CSI segmentation algorithm is based on the phase retardation information, the segmented CSI can be given as a concave shape. However, a corresponding concave structure cannot be found in the intensity image (Fig. 8(a)). One potential reason for this could be the alteration of the birefringence property in the sclera at the foveal region. However, neither the phase retardation nor the intensity information can provide indisputable evidence to identify the CSI. Further study including an in vitro histological study may be required to correctly understand this issue.
In measurements of one subject out of six, the penetration depth is quite limited in the choroid. The results are shown in Fig. 9. Both the intensity and phase retardation images are poor in the posterior choroidal region. Reasons for this might be a very thick choroid or strong light absorption. The low quality of phase retardation measurement leads to the failure of CSI segmentation. Even so, the algorithm still provided a reasonable CSI segmentation at the left part of the B-scan, i.e., at the nasal region. Further development and optimization of the PS-OCT hardware will provide higher signal intensity for these cases, and may solve this issue.
The repeatability of this method was also evaluated as follows. We first selected 16 B-scan frames from the 64 frames in a single dataset by the correlation based algorithm. An averaged Jones matrix image was created from these 16 frames. The RPE and the CSI were segmented from this averaged Jones matrix image, and the choroidal thickness distribution was defined as the distance between the RPE and the CSI. And then, another 16 frames were selected from the residual 48 frames by the same correlation algorithm, and the same operations including the averaging, segmentation, and calculation of choroidal thickness were performed. Namely, the segmentation was performed twice with two independent OCT images corresponding to the same location of the eye. Finally, the standard deviation of the difference of the choroidal thicknesses along the transversal direction was obtained. This standard deviation would provide a measure of repeatability of the segmentation algorithm.
We performed this evaluation with 4 datasets obtained from 4 subjects which show reasonable phase retardation distributions. The standard deviations of the difference of the choroidal thickness were 14.1 μm, 17.1 μm, 10.8 μm and 8.2 μm. These standard deviations correspond to 1- to 2-pixel depth of our PS-OCT image. And hence, the repeatability of our system is believed to be reasonable.
In the Jones matrix PS-OCT, both the accuracy and precision of phase retardation measurement rely on effective SNR . An effective SNR is mainly determined by the lowest SNR channels in the Jones matrix measurement. In our system, two of the four channels use a phase modulated probe beam achieved by an electro-optic modulator. The SNR in the modulated channels are more than 10-dB lower than that in non-modulated channels. Hence, the effective SNR level is limited to a relatively low range, raising both systematic and random error in the phase retardation measurement. This is one of the main issues that degrade phase retardation analysis and segmentation. We believe optimization of the PS-OCT system can promote segmentation accuracy and reduce the failure rate of the segmentation.
In this work, phase retardation image quality is enhanced by averaging several Jones matrix B-scans. Jones matrix averaging is very sensitive to eye motion among B-scans since the complex Jones matrix elements can counteract each other in the case of a mismatch. We did not implement transversal motion compensation to save calculation time, only choosing a group of B-scans with less transversal eye motion from a set of B-scans. So there is a trade-off between noise reduction and signal preservation related to the number of B-scans in Jones matrix averaging. Increasing the B-scans number can reduce the noise level, but degrade the accuracy in phase retardation measurement. The optimal phase retardation image quality is limited by this trade-off. There are three possible solutions to this issue. An optimized PS-OCT system can acquire Jones matrix B-scans with high effective SNR, so fewer B-scans are required for noise reduction. Increasing the scanning speed can restrain the eye motion effect by shortening the acquisition time. A timesaving and effective motion compensation algorithm or extra motion tracking hardware [55, 56], might be able to further increase the averaged phase retardation image quality.
Although the choroid is a phase retardation preserving layer, a moderate increase in phase retardation was sometimes observed in the choroid along the depth. This could be because of a systematic error caused by the decreasing effective SNR. A Monte-Carlo-based phase retardation estimator can restrain systematic error introduced by noise . However, this method requires an accurate effective SNR value for each pixel. The Jones matrix averaging is a complex averaging process. Although the Jones matrices have a non-correlated global phase to each other, the global-phase is cancelled before the complex averaging , a small amount of residual global phase results in an out-of-phase summation of the signals and degrades the effective SNR. Since this signal degradation is not fully predictable, the Monte-Carlo-based phase retardation estimator can not always provide a correct estimation of the phase retardation. Therefore, we did not apply the Monte-Carlo-Based estimator in this study. Further optimization of PS-OCT hardware will improve the sensitivity, and will eliminate the necessity of Jones matrix averaging. The Monte-Carlo-Based estimator could be a powerful aid to phase retardation based CSI segmentation for an improved future version of PS-OCT.
In current status, an image with 1,500 (lateral) × 300 (axial) pixels requires around 12 seconds for the pre-processing and 10 seconds for segmentation with an algorithm implementation written in LabVIEW (LabVIEW 2011 for 64-bit Windows 7) on Intel CORE i7 CPU Q720 at 1.60 GHz with 8-GB RAM. The pre-processing includes motion cancellation, Jones matrix averaging, and phase retardation calculation, and the time consumptions are nearly equally distributed in these three processes. Among the sub-processes in the segmentation process, the rough segmentation is the most time consuming process, it takes around 7 seconds. We expect to shorten the pre-processing time by taking the advantage of a graphics processing unit (GPU) in the future, since the pre-processing can be heavily parallelized according to its mathematical properties. Although we are currently using a multi-core CPU, the program has not been well parallelized. The segmentation speed can also be optimized by proper usage of multiple CUP cores.
We have developed an algorithm for automated and functional detection of the CSI based on phase retardation information obtained by PS-OCT. The choroid and sclera were modeled by linear incremental phase retardation along the depth. Segmentation was achieved by a two-step algorithm based on a phase retardation image followed by fine correction based on the corresponding intensity image. The first step of the two-step algorithm used the second derivative of the phase retardation image and a graph-search algorithm, and provided an initial estimate of CSI for the second step. The second step defined the CSI based on the difference of the phase retardation slopes of the choroid and sclera. Phase retardation tomography represents the depth-resolved birefringence properties in the sample, offering functional information above structure to recognize tissues. The phase retardation based CSI segmentation algorithm provides a reliable method for an investigation of CSI morphology. Currently, the number of subjects examined is six. Further study with a larger number of subjects and a larger variety of eyes including several refraction errors and several diseases would be important to strengthen the reliability of the algorithm.
This study is partially supported by the Japan Science and Technology Agency through the contract of the development program of advanced measurement systems.
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