Demonstration of efficient transfer learning in segmentation problem in synchrotron radiation X-ray CT data for epoxy resin

ABSTRACT Synchrotron radiation X-ray computed tomography (CT) provides information about the three-dimensional electron density inside a sample with a high spatial resolution. Recently, the need to examine the internal structure of materials composed of light elements, such as water and carbon fibers in resins, has increased. Small density differences in these systems give low X-ray contrast; segmentation methods suited for this type of problem are necessary. Machine learning is typically used to analyze CT data, and a large amount of training data is required to train a machine learning model. Conversely, transfer learning, which uses existing learning models, can develop a learning model using only a small amount of training data. In this study, the synchrotron radiation X-ray CT images of an epoxy resin containing water have been analyzed using transfer learning as the validation of a method for analyzing low-contrast CT data with high accuracy. Circular domain structures in the resin have been observed using the X-ray CT method, and statistical information about these structures has been successfully obtained by transfer learning-based analysis. Here, transfer learning is performed using twelve slices within an X-ray CT 3D image, demonstrating that low-contrast synchrotron CT data can be segmented with a small amount of training data. GRAPHICAL ABSTRACT IMPACT STATEMENT Segmentation of domains in polymer resins in low-contrast synchrotron radiation CT was demonstrated using a transfer learning method with a low computational cost and a small amount of training data.


Introduction
X-ray computed tomography (CT) can visualize the three-dimensional (3D) internal structure of materials and is used for nondestructive measurements in various fields, including medical and industrial.The X-ray CT method can obtain the internal physical quantities of materials such as the linear absorption coefficient (LAC).Refraction index decrement (RID) is also obtainable by combining X-ray CT with the X-ray phase contrast imaging method.Therefore, attempts have been made to examine internal structures, such as water, liquid CO 2 , and air in meteorites and rocks, using X-ray CT [1,2].As the LAC and RID depend on the density and constituent elements, the image contrast between rock and liquid differs.Meanwhile, X-ray CT measurements on polymers have also been reported [3][4][5].Epoxy resins are thermosetting resins obtained from epoxy compounds and curing agents and are extensively used as adhesives and encapsulants for semiconductor devices.Generally, the sorption and diffusion of water molecules into epoxy resins during manufacturing degrade adhesive strength and semiconductor device quality [6].Therefore, it is important to understand the dynamics of water in epoxy resins.Although the density difference between the epoxy resin and water is small (1.1-1.4 g/cm 3 ), their CT image contrast is expected to differ because of the slight difference in density.Because the difference in their CT image contrast can be expected to be slight, it is necessary to consider a technique for acquiring CT data with high efficiency and analyzing low-contrast CT data.
In the field of synchrotron radiation measurements, technological advances in light sources and detectors, as well as automated measurements, have increased measurement efficiency and speed.This allows more samples to be measured quickly, and a large amount of measurement data can be acquired in a single beamtime.In particular, the X-ray CT method based on synchrotron radiation can acquire high-resolution 3D data dependent on the LAC inside the samples in less than 10 min per sample.It is crucial to analyze experimental data efficiently because high-resolution experimental data can be obtained in a short time.
In recent years, analysis such as image and spectral analyses using machine learning (ML) has been performed in various fields of both basic and applied research [7][8][9][10][11][12].Many analyses based on ML intend to automate and improve the efficiency of analysis by delegating tasks previously performed by humans to artificial intelligence.In analysis tasks that remove specific regions from images, such as segmentation of CT data, visual or thresholding analysis is typically used.In visual analysis, a large amount of time and human cost are wasted by checking many CT images one by one.Conversely, thresholding analysis, which can be performed automatically using a computer to process large amounts of data without wasting both time and human cost, is unsuitable for segmenting low-contrast CT images.ML-based analysis has been attracting attention, but ML requires a large amount of data for training to generate a learning model.The CT methods visualize 3D structures.There are two methods for segmenting the 3D CT data.One is to treat 3D images directly; the other is to analyze twodimensional (2D) slice images and then to connect 2D segmented images to a 3D segmented image.The former method, which uses machine learning, has been previously reported in the medical field and has demonstrated its capability in identifying organ regions [13][14][15][16].There are also several reports of direct segmentation of 3D images in the materials field [17,18].Direct segmentation of the 3D images generally demands a larger number of computation operations and a larger memory size in the computing hardware than segmenting 2D images.Therefore, it will be computationally more efficient if we can conduct segmentation only with the 2D slice images.ML is also used in various fields of synchrotron radiation X-ray CT [7,[19][20][21][22], but it is difficult to prepare training data for each field.However, if we can use transfer learning, which creates a highly accurate training model with a small amount of data by utilizing existing trained models, the amount of training data can be significantly reduced.In the field of material science, the amount of data available for learning is small due to the high cost of data acquisition and the high awareness of information confidentiality.In this respect, transfer learning is expected to have applications in the field of material science, and property prediction using transfer learning has been reported [23][24][25][26][27].In this study, the effectiveness of transfer learning in synchrotron radiation X-ray CT has been investigated using U-Net [28], which was constructed for image segmentation in the biomedical field.A transfer learning model has been constructed using twelve 2D slice images as training data.The resulting 2D segmented images were connected to construct a 3D segmented image.The results have demonstrated that the segmentation of synchrotron radiation X-ray CT images with high computational efficiency and with a small number of training data is possible.

Experimental
Epoxy resin samples were obtained by mixing hydrogenated diglycidyl ether of bisphenol A (HDGEBA) and 1,4-cyclohexanebis(methylamine) (CBMA) in a 2:1 molar ratio and subsequent curing.Figure 1(a,b) show the chemical structures of HDGEBA and CBMA and a schematic illustration of the sample preparation, respectively.The procedures of the sample preparation are described below.First, we obtained a mixture of HDGEBA, CBMA, and 8 wt% water (WCR).As a reference, a mixture of HDGEBA and CBMA, with no water, was prepared (RWCW).Molds with a size of 10 � 10 � 2 mm were fabricated with silicone rubber on a Si wafer coated with alumina at a thickness of approximately 5 nm by atomic layer deposition (ALD).The ALD instrument was made by Savannah S100 (Veeco Instruments Inc., ALD instrument, USA) .Hereafter, the alumina-coated Si wafer will be called a substrate.After stirring and degassing, each transparent mixture was poured into the molds.Finally, epoxy resin samples were obtained by curing at controlled temperatures.For both WCR and RWCW samples, the mixtures were cured at 313 K for 3 h, and only the RWCW mixture was further post-cured at 393 K for 24 h.Only one WCR sample and one RWCW sample each were prepared and used in this study.During X-ray CT and infrared spectroscopy measurements, the WCR sample peeled off the Si substrate because of the poor adhesive strength caused by water addition.X-ray CT for the RWCW sample was measured while it was adhered on the Si substrate.
The X-ray CT experiments were conducted at BL20XU of SPring-8, synchrotron radiation facility, Japan [30].The photon energy of incident light was set to 30 keV.A visible light conversion-type X-ray camera consisting of a scintillator (Gd 3 (Ga,Al) 5 O 12 (Ce), GAGG 20 µm thick), microscope objective lens, and complementary metal-oxide-semiconductor camera (Hamamatsu Photonics, detector for X-ray CT, Japan, ORCA-Flash4.0,2048�2048 pixels) was used as the detector for the X-ray CT measurements.The distance from the sample to the detector camera was set at 10 cm so that the image contrast of the sample structures can be recognized using the edge-enhance effect of X-ray refraction [31].The samples were set on a rotating stage, and 1800 X-ray transmission images were taken during 180° rotations.The field of view of the X-ray CT image was cylindrical with a diameter of 1 mm and a height of 1 mm, and the voxel size was (0.5 µm) 3 .The CT data in this paper has been adjusted for image contrast for its viewability, but no additional processing, such as treatments for ring or streak artifacts, has been performed.
We performed image analysis using Python (Version: 3.6.8)and an ML model to quantitatively estimate the circular domain number density and domain size in the bulk region and near the resin/ substrate interface of the WCR sample.The procedure for circular domain segmentation by ML is described below.A 3D CT image for the WCR sample is composed of 371 2D slice images.The twelve 2D slice images were used for the training data, and the six images, different from the training data, were used for the validation data.The 2D slice images for training and evaluation were extracted from the 3D CT data at intervals.For those twelve and six images, we manually created binary images showing the region corresponding to the domain area and used them as the ground truth.For the manual segmentation, the domain regions were carefully traced using Adobe Photoshop.Approximately 5% of the total 2D slice images for the WCR sample was used to build the learning model.The ML model adopted U-net [28], and transfer learning with ResNet [32] was performed.We created first segmentation model using Python library Segmentation Models (Version: 0.2.0) [33].ResNet50 with 50 layers was used as the encoder and ImageNet was used for its weights.A sigmoid function was used for the activation function.For the criterion, we used a Dice loss function expressed as follows using the ground truth region A and the predicted region B.
The models were developed with an Adam solver [34] with a mini-batch size of 8 and a learning rate of 0.0001 during 500 epochs based on the PyTorch (Version: 1.10.1)framework [35] and were optimized to have the highest intersection over union (IoU) score for the training data.The IoU score is expressed by the following formula.
The IoU score will be between 0 and 1, with the closer to 1 meaning that the ground truth and predicted regions match.The personal computer (PC) server used for the analysis was equipped with double Intel Xeon Gold 6238 R (2.2 GHz, 38.5 MB cache, 28 cores), 256 GB memory, and NVIDIA Tesla T4 GPU (16 GB).
The image analysis was performed using a single core and 32 GB memory.To identify the circular domains of different sizes, learned models were developed for each domain.The number of circular domains used for the learning process was 16,537 small domains and 676 large domains.Data augmentation was performed using the Python package Albumentations [36] (Version: 1.2.1), and the number of images after augmentation was 960.The IoU scores for the training data for the learned models obtained at 500 epochs were 0.834 for the large domains found near the resin/ substrate interface and 0.626 for the small domains found in the bulk region.The IoU scores for the validation data for the large and small domains were 0.910 and 0.627, respectively.Since the IoU scores for the validation data are comparable or better than those for the training data, this learned model is applicable to the segmentation of the X-ray CT data in this study.
If two identical squares overlap with a diagonal shift of only 1/9, the IoU score would decrease to about 0.65.This fact indicates that our model allows for good domain segmentation.The IoU score for the validation data tends to be lower than the score for the training data, but in our segmentation model, the IoU score for the validation data is higher than the score for the training data.In this study, six 2D slice images extracted from 3D images at intervals that were different from the training data were used as the evaluation data.We expect that the IoU score for the validation data might happen to be higher because of the smaller number of validation images compared to the training images.Note that the IoU score for large domains, which are fewer, is higher than the IoU score for small domains, which are more numerous.
Although it is expected that small domains with larger numbers can be trained more accurately, the IoU score was higher for large domains because smaller domain sizes are more sensitive to differences from the ground truth in segmentation results.Training of the large and small circular domain models was performed on the GPU, which took ,8 and ,5 h to train 500 epochs of each model, respectively.The IoU scores for the training data for each learned model at 50 epochs are 0.806 and 0.602, respectively, a 3%-4% difference from the IoU scores for the adopted model; thus, it is possible to use a learned model with a smaller number of epochs.Note that the segmentation in this study was performed using the typical hyperparameters described above, and that tuning of those parameters could improve segmentation accuracy.We also describe information on modeling large and small domains together.We have estimated IoU scores by creating a model that segments large and small domains together, using the same procedure as we have used to construct the model separately for large and small domains.The IoU scores for the training and validation data by the model obtained at 500 epochs were 0.691 and 0.672, respectively.Compared to the IoU scores when the models were created separately for large and small domains, the large domain has shown poor segmentation accuracy, whereas the small domain has shown better accuracy.As mentioned above, an IoU score of about 0.65 can be considered a good segmentation, so we can obtain good segmentation results when both domains are modeled together.Training the model for the 500 epochs has taken about 7 hours, and that has been half the total 13 hours of creating separate models for the large and small domains.There is a segmentation accuracy deterioration for large domains, but there is an advantage in segmentation with the same model in terms of the time it takes to construct the model.The image analysis shown below used the results of segmentation by the models for the separate large and small domains.Attenuated total reflection Fourier transform infrared spectroscopy JASCO (ATR-FTIR), Japan was also performed on the epoxy resin samples to confirm the presence of water in them.The ATR-FTIR details are described in the supplemental material.

Measurements
Figure 2(a) shows the experimental X-ray CT image for the bulk region of the WCR sample (at a distance of approximately 130 μm from the substrate).There are many circular domains of approximately several μm diameter inside the resin sample.Figure 2(b) shows the X-ray CT results of the WCR sample near the resin/substrate interface (at a distance of approximately 25 μm from the substrate).Circular domains were also observed near the interface between the substrate and the bulk region, but the size and number density of these domains differed from those in the bulk region of the resin.The circular domain size in the bulk region was a several μm, whereas it was as large as 10-20 μm near the resin/substrate interface.The circular domain number density near the resin/ substrate interface is lower than that in the bulk region of the resin.The experimental results of the X-ray CT measurement for the RWCW sample are depicted in Figure 2(c).In the RWCW sample, the corners of the sample were measured by X-ray CT.The resinatmosphere boundary and bubble could be observed.The circular domains of μm order observed in the WCR sample were not observed in the RWCW sample.The circular domains observed in the WCR sample were caused by the addition of water, and one can assume that the domains encapsulate the water inside.The differences in structure due to the addition or non-addition of water could be qualitatively assessed from the CT images, but some image noise and artifacts, as described below, make this difficult to assess quantitatively.The X-ray CT images in Figure 2 show ring artifacts caused by the uneven sensitivity of the detector.In the X-ray CT image in Figure 2(b), in addition to the ring artifact, artifacts with radial streaks from the domains and distorted domains can be observed.These artifacts are caused by the reflections and refractions from the sample.The sample has a plate-like shape of 10 � 10 � 2 mm 3 , which is significantly larger than the 1-mm field of view of the CT used, and the X-ray transmission varies significantly with the angle of the sample in CT measurements.
This causes many errors in general CT reconstruction calculations, as shown in Figure 2 as the image distortion of the circular domains.Three methods for reducing the number of these artifacts are to make the sample less than 1 mm cylindrical, to shorten the distance between the sample and the camera, and to measure by laminography, where the axis of rotation is tilted from the direction perpendicular to the optical axis.

Image analysis
The image analysis results for the X-ray CT image of the bulk region of the resin shown in Figure 3(a-c) have successfully extracted circular domains with different densities from the resin.Conversely, the X-ray CT image near the resin/substrate interface shown in Figure 3(d-f) is distorted by the effects of the sample surface.Although it is difficult to precisely recognize the boundary between the domains and the resin, the domains extracted by the image analysis accurately reproduced the domains observed in the experimental CT image.Compared with comparing Figure 3(b,e), the number density and size of the circular domains in the bulk region and near the resin/substrate interface are significantly different even though they have the same viewing area.From Figure 3(a,d), the estimated domain number densities in the bulk region and the region near the resin/substrate interface are 6854 and 98 mm −2 , respectively, which are nearly 70 times different.Figure 4(a-f) show the histograms of the area S, equivalent diameter ϕ, and circularity C of circular domains in the bulk region (Figure 3 and circularity are defined as ϕ ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 4S=π p and C ¼ 4πS=L 2 , respectively, where L represents the length of the circular domain perimeter.As depicted in Figure 4(a,b), the circular domain area in the bulk region is distributed below 20 μm 2 , which is below 5 μm in terms of equivalent diameter.Conversely, near the resin/substrate interface, most domains are distributed over 20 μm 2 in the domain area, which is greater than 5 μm in equivalent diameter (Figure 4(d,  e)).From the histograms, the size of the circular domains in the resin is different compared with the bulk region of the resin and the vicinity of the resin/ substrate interface.In terms of circularity, as depicted in Figure 4(c,f), the circular domains are distributed mostly at approximately 0.9 both inside the resin and near the substrate, and circularity is independent of the domain positions.The circularity is 1 for a perfect circle and approaches 0 as one moves away from the circle.That is, the domains in the sample have a nearly circular shape.This is because the surface area of the domains is minimized by a surface tension effect, and a spherical shape has the smallest surface area when the volume is constant.
Figure 5(a) shows the dependence of the volume ratio and the mean equivalent diameter of the spherical domains on the distance from the substrate.The volume ratio and mean equivalent diameter of the spherical domains are the percentage of the volume occupied by the domains in the CT data at each distance and the mean diameter at each distance assuming that the domains are perfect spheres, respectively.The Python package connected-components-3d (cc3d) [37] was used to estimate the volume ratio and the mean equivalent diameter.The 2D images after circular domain segmentation were concatenated using cc3d to form 3D data, and the centroid and  volume of each domain were estimated.The equivalent diameter of each spherical domain was defined as ϕ ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 6V=π 3 p , where V represents the volume of each domain.The 3D data were divided by 3 μm in distance from the substrate, and the volume ratio and the mean equivalent diameter at each distance were evaluated from the volume and equivalent diameter of circular domains with the centroid within the region.
The volume ratio of circular domains is 2.7% near the substrate, increases rapidly to 10.2% near 18 μm, and quickly decreases to less than 1%.The ratio increases monotonically in the 27-40-μm region and shows a plateau at 4.3% in the 40-60μm region.The ratio decreases in the region from 60 to 80 μm and is constant at approximately 3.6% in the region deeper than 80 μm.The volume ratio of domains changes up to a distance of 80 μm from the interface, but the ratio barely changes in the bulk region deeper than 80 μm.The volume ratio of domains changes up to a distance of 80 μm from the interface, but the ratio barely changes in the bulk region deeper than 80 μm.As the region from the interface to 80 μm where the volume ratio changes is a small region compared with the entire sample, the circular domain volume ratio of the entire sample can be assumed to be close to 3.6%.Comparing the amount of water added during sample preparation (8 wt%) with the ratio of circular domains occupying the sample, the volume ratio occupied by circular domains is 4.4% less than that of water.Possible reasons for this are the lack of circular domain formation due to the dissolution of water in the resin and the presence of microscopic size circular domains that cannot be detected by X-ray micro-CT.The mean equivalent diameter of the circular domains is larger than 10 μm near the substrate, whereas, in the bulk region, it is approximately 3 μm.The mean equivalent diameter changes drastically at a distance of around 20 μm from the substrate.The mean equivalent diameter is 14.2 μm in the region around 18 μm from the substrate, whereas it is 3.0 μm in the bulk region, indicating that the mean circular domain size is more than four times larger near the substrate.The resin can be divided into three regions in terms of domain volume ratio and mean equivalent diameter.The first is the region from the substrate to approximately 27 μm, where there are large, aggregated circular domains.The second is the region from 27 to 80 μm, where the circular domain size is small and almost constant, but the volume ratio varies significantly, and a plateau is observed in some regions.The third is a region deeper than 80 μm, where both the circular domain size and volume ratio are constant, corresponding to the bulk region.The first region is nearest to the resin/substrate interface, suggesting that water agglomerates near the interface and thus affects the adhesive strength.In the second region, the circular domain size does not change, but the volume ratio changes, implying that the number of circular domains varies with the distance from the substrate.The structure of the resin and water in the region near the substrate shallower than 80 μm is related to the adhesive strength.It is expected that the circular domains in the resin are defects in the adhesive resin, resulting in a decrease in adhesive strength.
Figure 5(b) shows the 3D volume rendering image of the segmented circular domains in the WCR sample, which was obtained by analyzing the circular domains in sliced 2D X-ray CT images.From the figure, there are many circular domains in the order of several μm in the bulk region, whereas domains larger than 10 μm exist only near the resin/substrate interface.Furthermore, the size and number density of circular domains change significantly around 30 μm, which corresponds to the fact that the mean equivalent diameter and volume ratio vary drastically around 30 μm.As described thus far, applying transfer learning to circular domain segmentation allows us to observe the domains in the sample and easily extract statistical information.
Training ML and deep learning models for image analysis typically involves datasets containing hundreds, thousands, or even millions of images, enabling high-accuracy image analysis [7,20,[38][39][40].We used twelve slice images in a 3D CT image for the transfer learning in this study and created data with binary images, with each image manually segmented.Despite the small size of the training data, we have successfully segmented the circular domains in the X-ray CT images with high accuracy by applying transfer learning to the trained model, as depicted in Figure 3.As the trained model could be developed using a part of the measurement data, there was no need for beamtime to acquire new data for training.In addition, the data size of the training data is small, making image analysis using transfer learning an efficient analysis method in terms of both time and data size.Analysis based on transfer learning can be performed even during beamtime by generating ground truths for a few images from experimental data.Performing accurate analysis during beamtime provides feedback on the experimental results and is useful for more effective measurements.The segmentation by transfer learning used in this study can be applied to large-scale systems such as plastic specimens used for strength testing and is expected to be applied to big data analysis.It will be of wide interest if the present segmentation method based on transfer learning can be applied to large-scale systems such as plastic specimens used for strength testing.To extend the application range, the conditions of the present model in terms of the sample types, domain morphologies, and imaging conditions need to be clarified.
Several models have been proposed for CT image segmentation in the field of material science, besides U-net, such as SegNet [41] and ResAttUnet [42].While in this study we chose U-net, which provided satisfactory accuracy at an acceptable computational cost, it is possible that other models provide better performance than U-net.A comparative study among the proposed models for this type of segmentation problem will be the subject of future work.

Refraction contrast
The effects of refraction contrast on X-ray CT images are described below.The refractive index of X-rays to matter has a value slightly less than unity.Therefore, when X-rays pass near the boundary of an object, the path is slightly deflected from the high-density side to the low-density side, contrary to visible light.When the X-ray transmission image is observed at some distance from the object, the transmitted image near the boundary of the object shows a contrast such that the transmission is lower on the high-density side than it is and higher on the low-density side due to the effect of this refraction.As a result, the CT image near the boundary has a higher contrast on the high-density side than it is and a lower one on the low-density side, forming an obvious edge-enhanced contrast created by the neighboring bright and dark lines, as observed near the resinatmosphere boundary in Figure 2(c).The refraction contrast resolution is expressed as ffi ffi ffi ffi ffi λL p , where λ denotes the wavelength of incident light, and L denotes the distance between the sample and the camera.In this study, because we used X-rays with an incident photon energy of 30 keV (λ ¼ 0:413 Å) and the sample-camera distance was set to 10 cm, the refraction contrast resolution could be estimated to be approximately 2.0 μm. Figure 6 shows the X-ray CT image, including the circular domain observed near the resin/substrate interface and its line profile.Refraction contrast is observed near the resin/domain boundary.The density of the resin sample used in this study has been estimated to be 1.116 � 0.004 g/cm 3 by a gas pycnometer using helium.The X-ray CT image contrast near the boundary between the circular domain and resin is weaker on the domain side and stronger on the resin side because the inside of the domain observed near the substrate is less dense than the resin.The refraction contrast resolution has been estimated from the experimental line profiles.The refraction contrast resolution corresponds to the full width at half maximum (FWHM) from the baseline of each refraction contrast structure (I-IV).The FWHM for each structure has been estimated to be 2.0 μm for I, 2.3 μm for II, 2.2 μm for III, and 2.0 μm for IV, respectively.It agrees well with the refraction contrast resolution estimated from the incident light energy and the sample-camera distance.Although the refraction contrast emphasizes the boundaries of regions of different densities and produces clear images, it also makes it difficult to obtain accurate boundary positions between the resin and the circular domains.The systematic error in X-ray CT images in this study is estimated to be as large as the refraction contrast resolution (,2 μm).

Prospect of multiscale X-ray CT
In this study, we have applied the synchrotron radiation X-ray CT method and ML analysis to epoxy resins.We found that the structures of μm order in the resin can be easily segmented using this method.Although the adhesive strength of epoxy resins decreases when water is introduced during the curing process, the distribution of water in the resin has not been experimentally reported thus far.Because the distribution of water in the resin can be visualized by the X-ray CT method, it is expected that the effect of water on the adhesive strength of adhesive resins can be clarified from a structural viewpoint.In addition to the X-ray micro-CT with a 1-mm field of view used in this study, the high-energy X-ray nano-CT with a narrower field of view and higher spatial resolution is also available at SPring-8 BL20XU [43,44].In this study, a large amount of water was intentionally added to the resin sample to facilitate the observation of water, but the actual amount of water in the epoxy resin is small; thus, the use of the high-energy X-ray nano-CT is essential to observe the distribution of water in the actual system.The use of multiscale CT, consisting of the X-ray micro-CT and the high-energy X-ray nano-CT, is expected to advance adhesion technology.

Summary
We performed X-ray CT measurements on WCR and RWCW samples and analyzed the measurement images using ML to validate the analysis method for low-contrast CT images such as images of a mixture of adhesive resin and water.Based on the X-ray CT measurement results, although no specific structure was observed in the RWCW sample, the circular domains derived from water were successfully observed in the WCR sample.We performed the ML-based segmentation of structures in the sample containing water to obtain statistical information about the circular domain structure.The training was successfully performed within 13 h using a PC server with NVIDIA Tesla T4 GPU (16 GB).Differences in the circular domain size and the domain number density were observed depending on the distance from the resin/substrate interface, and we found that the domains with large sizes were present only near the substrate.Considering that the adhesion strength of the adhesive resin is most related to the structure near the substrate, we proposed that the large domains present near the substrate affect the adhesion strength.In the ML-based analysis, several images of the target to be analyzed were used as training data, and there was no need to prepare new training data.We have demonstrated that ML-based analysis is useful as a simple method for analyzing lowcontrast X-ray CT images.

Figure 1 .
Figure 1.(a) Chemical structures of HDGEBA and CBMA [29].(b) Schematic illustration showing the preparation of epoxy resin samples on silicon substrates coated with Al 2 O 3 .

Figure 2 .
Figure 2. Tomographic slice images in the epoxy resin samples.(a) Bulk in the WCR sample (at a distance of approximately 130 µm from the substrate).(b) Near the resin/substrate interface in the WCR sample (at a distance of approximately 25 µm from the substrate).(c) in the RWCW sample.
(a)) and near the substrate (Figure 3(d)).The equivalent diameter 3. (a) X-ray CT image of the bulk region of the WCR sample.The circular domains extracted by image analysis are indicated by solid lines.(b) X-ray CT image magnified within the square frame in (a).(c) Same as (b), but excluding the solid lines representing the domains.(d) Same as (a), but showing the X-ray CT image near the resin/substrate interface of the WCR sample.(e) X-ray CT image magnified within the square frame in (d).(f) Same as (e), but excluding the solid lines representing the domains.

Figure 4 .Figure 5 .
Figure 4. (a) Histogram of the area of the circular domains in the bulk region of the WCR sample.(b) Histogram of the equivalent diameters of the circular domains in the bulk region of the WCR sample.(c) Histogram of the circularity of the circular domains in the bulk region of the WCR sample.(d) Histogram of the area of the circular domains near the resin/substrate interface of the WCR sample.(e) Histogram of the equivalent diameters of the circular domains near the resin/substrate interface of the WCR sample.(f) Histogram of the circularity of the circular domains near the resin/substrate interface of the WCR sample.

Figure 6 .
Figure 6.(a) X-ray CT image of the circular domains near the resin/substrate interface.(b) line profile along the solid line in (a).