Automated Nuclear Lamina Network Recognition and Quantitative Analysis in Structured Illumination Super-Resolution Microscope Images Using a Gaussian Mixture Model and Morphological Processing

: Studying the architecture of nuclear lamina networks is signiﬁcantly important in biomedicine owing not only to their inﬂuence on the genome, but also because they are associated with several diseases. To save labor and time, an automated method for nuclear lamina network recognition and quantitative analysis is proposed for use with lattice structured illumination super-resolution microscope images in this study. This method is based on a Gaussian mixture model and morphological processing. It includes steps for target region generation, bias ﬁeld correction, image segmentation, network connection, meshwork generation, and meshwork analysis. The e ﬀ ectiveness of the proposed method was conﬁrmed by recognizing and quantitatively analyzing nuclear lamina networks in ﬁve images that are presented to show the method’s performance. The experimental results show that our algorithm achieved high accuracy in nuclear lamina network recognition and quantitative analysis, and the median face areas size of lamina networks from U2OS osteosarcoma cells are 0.3184 µ m 2 .


Introduction
The nuclear lamina, which only has a thickness of~14 nm [1,2], is a complex protein network that organizes major nuclear structures [3][4][5], and is composed of nuclear lamins [6]. The architectures of nuclear lamina networks are significantly important to biomedicine because of their influence on the genome, and they are also associated with several diseases [7]. More detailed information about the importance of understanding nuclear lamina network structure is written in Appendix A. The architecture of a nuclear lamina network can be imaged by taking advantage of the advances in super-resolution light microscopy [7][8][9][10][11][12][13]. One popular tool used for this microscopy is the structured illumination super-resolution microscope [7,[13][14][15]. After acquiring the structured illumination super-resolution microscope images of a nuclear lamina network, nuclear lamina network recognition and quantitative analysis are required to obtain quantitative information on the architecture of the

Methods
This section describes our automated image processing procedure for nuclear lamina network recognition and quantitative analysis. A flowchart illustrating the proposed algorithm is shown in Figure 1. It includes five steps: pre-processing, image segmentation, network connection, meshwork generation, and meshwork analysis. First, the target region, which contains the lamina, is generated, and bias field correction is applied to this region. Second, the lamina network is segmented via GMM segmentation. Third, network connection is performed by using the morphological closing operation. Fourth, the meshwork is generated by morphological-dilation-based processing. Finally, the geometrical parameters of the meshwork are calculated. resolution light microscopy [7][8][9][10][11][12][13]. One popular tool used for this microscopy is the structured illumination super-resolution microscope [7,[13][14][15]. After acquiring the structured illumination super-resolution microscope images of a nuclear lamina network, nuclear lamina network recognition and quantitative analysis are required to obtain quantitative information on the architecture of the network [7,13]. Although this can be performed manually, considerable labor and time is required, and the process is also subjective and inaccurate due to the discontinuity of the network in the image. Therefore, several studies have attempted to develop computer vision methods for nuclear lamina network recognition and quantitative analysis [7,13]. The mainstream computer vision method for achieving this goal is based on steerable filters and graph theory [7]. Current available methods can recognize and quantitatively analyze nuclear lamina networks without great errors; however, the results are not very accurate by the judgement of human vision. Thus, it is necessary to design an effective algorithm for nuclear lamina network recognition and quantitative analysis. One efficient method is to use existing high-accuracy image processing methods or their combinations that have not yet been applied in the domain of the nuclear lamina network recognition and quantitative analysis.
Herein, we propose, to the best of our knowledge, the first nuclear lamina network recognition and quantitative analysis algorithm using a Gaussian mixture model (GMM) [16], which is the most common image segmentation algorithm based on finite mixture models [17][18][19], and morphological processing [20][21][22][23]. To confirm the effectiveness of our proposed method, it was used to process five nuclear lamina networks, all of which yielded successful results. The results are presented in this paper.

Methods
This section describes our automated image processing procedure for nuclear lamina network recognition and quantitative analysis. A flowchart illustrating the proposed algorithm is shown in Figure 1. It includes five steps: pre-processing, image segmentation, network connection, meshwork generation, and meshwork analysis. First, the target region, which contains the lamina, is generated, and bias field correction is applied to this region. Second, the lamina network is segmented via GMM segmentation. Third, network connection is performed by using the morphological closing operation. Fourth, the meshwork is generated by morphological-dilation-based processing. Finally, the geometrical parameters of the meshwork are calculated.

Target Region Generation
To facilitate further image processing, we identified the nuclear lamina region as the target region. First, we segmented the original image with a threshold. Second, we applied the morphological closing and opening operations sequentially to the threshold-segmented image by using OpenCV's morphologyEx function in Python. With these morphological closing and opening operations, we filled small holes and removed small objects from the segmented image. Third, we filled all holes inside the segmented regions to eliminate any residual holes in the segmented regions. Finally, the largest connected region was identified as the target region. An example of target region generation on a representative image, performed using this method, is shown in Figure 2. As shown in the figure, the nuclear lamina region was successfully identified.

Target Region Generation
To facilitate further image processing, we identified the nuclear lamina region as the target region. First, we segmented the original image with a threshold. Second, we applied the morphological closing and opening operations sequentially to the threshold-segmented image by using OpenCV's morphologyEx function in Python. With these morphological closing and opening operations, we filled small holes and removed small objects from the segmented image. Third, we filled all holes inside the segmented regions to eliminate any residual holes in the segmented regions. Finally, the largest connected region was identified as the target region. An example of target region generation on a representative image, performed using this method, is shown in Figure 2. As shown in the figure, the nuclear lamina region was successfully identified.

Bias Field Correction
To obtain high accuracy segmentation results in the next step, we corrected the image intensity non-uniformity of the nuclear lamina network by using the bias field correction algorithm [24]. An intensity bias field image was created by applying a Gaussian filter with 15-pixels length standard deviation to original image: The original image was corrected by dividing the bias field image within the target region generated in the previous step:

Target region
Bias field corrected image( x, y ) An example of bias field correction on a representative image, performed using this method, is shown in Figure 3. As shown in the figure, the intensity of the nuclear lamina network image is much more uniform after bias field correction.

Bias Field Correction
To obtain high accuracy segmentation results in the next step, we corrected the image intensity non-uniformity of the nuclear lamina network by using the bias field correction algorithm [24]. An intensity bias field image was created by applying a Gaussian filter with 15-pixels length standard deviation to original image: The original image was corrected by dividing the bias field image within the target region generated in the previous step: An example of bias field correction on a representative image, performed using this method, is shown in Figure 3. As shown in the figure, the intensity of the nuclear lamina network image is much more uniform after bias field correction.
An example of bias field correction on a representative image, performed using this method, is shown in Figure 3. As shown in the figure, the intensity of the nuclear lamina network image is much more uniform after bias field correction.

Image Segmentation
After preprocessing, we segmented the bias field-corrected image to obtain a rough nuclear lamina network structure using a GMM segmentation algorithm [16]. First, we resized the bias field-corrected image to 30% height and width using OpenCV's resize function in Python to save the computational time. Second, we applied the GMM algorithm to the resized image with two mixture components and five iterations, which provide lowest computation time and acceptable segmentation accuracy. Third, we selected the minimum mean value µ and the corresponding standard deviation σ. Finally, we segmented the bias field-corrected image using the following threshold: An example of image segmentation on a representative image, performed using this method, is shown in Figure 4. As shown in the figure, the nuclear lamina network structure is well segmented.

Image Segmentation
After preprocessing, we segmented the bias field-corrected image to obtain a rough nuclear lamina network structure using a GMM segmentation algorithm [16]. First, we resized the bias fieldcorrected image to 30% height and width using OpenCV's resize function in Python to save the computational time. Second, we applied the GMM algorithm to the resized image with two mixture components and five iterations, which provide lowest computation time and acceptable segmentation accuracy. Third, we selected the minimum mean value μ and the corresponding standard deviation σ. Finally, we segmented the bias field-corrected image using the following threshold: An example of image segmentation on a representative image, performed using this method, is shown in Figure 4. As shown in the figure, the nuclear lamina network structure is well segmented.

Network Connection
To close the gaps in the nuclear lamina network structure in the segmented image, we applied network connection to the segmented image. This was implemented by applying the morphological closing operation to the segmented image by using OpenCV's morphologyEx function in Python. An example of network connection on a representative image patch performed using this method is shown in Figure 5. As shown in the figure, the nuclear lamina network structure in the segmented image is well connected after network connection.

Network Connection
To close the gaps in the nuclear lamina network structure in the segmented image, we applied network connection to the segmented image. This was implemented by applying the morphological closing operation to the segmented image by using OpenCV's morphologyEx function in Python. An example of network connection on a representative image patch performed using this method is shown in Figure 5. As shown in the figure, the nuclear lamina network structure in the segmented image is well connected after network connection.
To close the gaps in the nuclear lamina network structure in the segmented image, we applied network connection to the segmented image. This was implemented by applying the morphological closing operation to the segmented image by using OpenCV's morphologyEx function in Python. An example of network connection on a representative image patch performed using this method is shown in Figure 5. As shown in the figure, the nuclear lamina network structure in the segmented image is well connected after network connection.

Meshwork Generation
After network connection, we generated the meshwork of the network. First, we generated an initial marked image by setting the foreground of the network-connected image to zero, and we

Meshwork Generation
After network connection, we generated the meshwork of the network. First, we generated an initial marked image by setting the foreground of the network-connected image to zero, and we assigned a unique number to each independent connected region in the background of the network-connected image. Second, we iteratively applied the morphological dilation operation to the marked image by using OpenCV's morphologyEx function in Python. This morphological dilation operation dilates the marked image by one pixel from the edge in each iteration. The meshwork is generated where the marked regions connect. After that, dilation is no longer performed on the marked image in locations where the meshwork has been generated. The process of morphological dilation iteration stopped when the marked image was filled with dilated regions. An example of meshwork generation on a representative image patch, performed using this method, is shown in Figure 6. As shown in the figure, the marked regions are gradually enlarged, and meshwork is generated.
Photonics 2020, 7, x FOR PEER REVIEW 5 of 10 assigned a unique number to each independent connected region in the background of the networkconnected image. Second, we iteratively applied the morphological dilation operation to the marked image by using OpenCV's morphologyEx function in Python. This morphological dilation operation dilates the marked image by one pixel from the edge in each iteration. The meshwork is generated where the marked regions connect. After that, dilation is no longer performed on the marked image in locations where the meshwork has been generated. The process of morphological dilation iteration stopped when the marked image was filled with dilated regions. An example of meshwork generation on a representative image patch, performed using this method, is shown in Figure 6. As shown in the figure, the marked regions are gradually enlarged, and meshwork is generated.

Meshwork Geometrical Parameters Calculation
After meshwork generation, we calculated the meshwork geometrical parameters, defined in [13], considering the junctions, edges, and faces. The faces are determined by the results of the morphological dilation during meshwork generation. The junction pixels must satisfy two conditions: first, the pixels should be located on the meshwork; second, there should be at least three different faces around the pixels. The edges were created because of meshwork segmentation by junctions. An example of junction-marking results on a representative image patch, performed using this method, is shown in Figure 7. As shown in the figure, the junctions were successfully determined. After determining faces, junctions, and edges, we calculated their geometrical parameters by using a pixel-counting method.

Meshwork Geometrical Parameters Calculation
After meshwork generation, we calculated the meshwork geometrical parameters, defined in [13], considering the junctions, edges, and faces. The faces are determined by the results of the morphological dilation during meshwork generation. The junction pixels must satisfy two conditions: first, the pixels should be located on the meshwork; second, there should be at least three different faces around the pixels. The edges were created because of meshwork segmentation by junctions. An example of junction-marking results on a representative image patch, performed using this method, is shown in Figure 7. As shown in the figure, the junctions were successfully determined. After determining faces, junctions, and edges, we calculated their geometrical parameters by using a pixel-counting method.
conditions: first, the pixels should be located on the meshwork; second, there should be at least three different faces around the pixels. The edges were created because of meshwork segmentation by junctions. An example of junction-marking results on a representative image patch, performed using this method, is shown in Figure 7. As shown in the figure, the junctions were successfully determined. After determining faces, junctions, and edges, we calculated their geometrical parameters by using a pixel-counting method.

Results
The U2OS osteosarcoma cell line was purchased by the Stem Cell Bank, Chinese Academy of Sciences. The U2OS cells were cultivated in McCoy's 5A medium modified (Thermo Fisher; USA) supplemented with 1% penicillin G and streptomycin (Shenggong; China) as well as 10% fetal bovine serum (Thermo Fisher; Australia) at 37 °C in a 5% (v/v) CO2 environment. Cells were fixed with 4% paraformaldehyde. After blocking in blocking buffer (containing 5% bovine serum albumin, 0.1% Triton X-100 in PBS) for 30min at room temperature, the slides were incubated with primary antibodies against lamin A (1:100, Abcam), then with anti-rabbit IgG conjugated with Alexa Fluor 488(1:2000, Abcam). Finally, nuclear lamin A network, which is used for our nuclear lamina network recognition and quantitative analysis, were viewed under a ZEISS Elyra 7 (Germany) with Lattice

Results
The U2OS osteosarcoma cell line was purchased by the Stem Cell Bank, Chinese Academy of Sciences. The U2OS cells were cultivated in McCoy's 5A medium modified (Thermo Fisher; USA) supplemented with 1% penicillin G and streptomycin (Shenggong; China) as well as 10% fetal bovine serum (Thermo Fisher; Australia) at 37 • C in a 5% (v/v) CO2 environment. Cells were fixed with 4% paraformaldehyde. After blocking in blocking buffer (containing 5% bovine serum albumin, 0.1% Triton X-100 in PBS) for 30min at room temperature, the slides were incubated with primary antibodies against lamin A (1:100, Abcam), then with anti-rabbit IgG conjugated with Alexa Fluor 488 (1:2000, Abcam). Finally, nuclear lamin A network, which is used for our nuclear lamina network recognition and quantitative analysis, were viewed under a ZEISS Elyra 7 (Germany) with Lattice SIM superhigh resolution microscope [25] equipped with alpha Plan-APO 100x/1.46 Oil DIC VIS objective lens.
The typical computational times for processing an image of 1024 × 1024 pixels using our automated approach are as follows: 0.209 s for target region generation, 0.101 s for bias field correction, 80.0 s for image segmentation, 0.0105 s for network connection, 12.4 s for meshwork generation, and 22.3 s for meshwork analysis. These computational times were obtained using a system with an Intel Core i5-9400 CPU operating at 2.90 GHz, an NVIDIA GeForce GTX 1660 Ti graphics card, and 16.0 GB RAM. The image denoising program was written in MATLAB (64-bit) and CUDA 10.0, while the other programs were written in Python (64-bit).
To confirm the effectiveness of our method, images from five nuclear lamina networks were obtained. Our method successfully recognized and quantitatively analyzed these nuclear lamina networks in the five datasets. The recognition results are shown in Figure 8. Based on the performance results, it is clear that our algorithm achieves high recognition accuracy with these five samples according to visual inspection by human. Further, the quantitative analysis of faces areas size of these five samples are shown in Figure 9. The median face areas of these five samples ranged from 0.2627 to 0.4248 µm 2 , and the median face areas of all these five samples is 0.3184 µm 2 , which has the same magnitude of order with other research [26] that used different kind of cells.
obtained. Our method successfully recognized and quantitatively analyzed these nuclear lamina networks in the five datasets. The recognition results are shown in Figure 8. Based on the performance results, it is clear that our algorithm achieves high recognition accuracy with these five samples according to visual inspection by human. Further, the quantitative analysis of faces areas size of these five samples are shown in Figure 9. The median face areas of these five samples ranged from 0.2627 to 0.4248 μm 2 , and the median face areas of all these five samples is 0.3184 μm 2 , which has the same magnitude of order with other research [26] that used different kind of cells.

Discussion
As mentioned earlier, one efficient method for nuclear lamina recognition and quantitative analysis is to use existing high-accuracy image processing methods or their combinations that have not yet been applied in this domain. Thus, we presented modified versions of three popular methods [27][28][29] as promising solutions for performing nuclear lamina network recognition and quantitative

Discussion
As mentioned earlier, one efficient method for nuclear lamina recognition and quantitative analysis is to use existing high-accuracy image processing methods or their combinations that have not yet been applied in this domain. Thus, we presented modified versions of three popular methods

Discussion
As mentioned earlier, one efficient method for nuclear lamina recognition and quantitative analysis is to use existing high-accuracy image processing methods or their combinations that have not yet been applied in this domain. Thus, we presented modified versions of three popular methods [27][28][29] as promising solutions for performing nuclear lamina network recognition and quantitative analysis.

Conclusions
In this study, an automated method for nuclear lamina network recognition and quantitative analysis was proposed. A GMM and morphological processing were the primary approaches used in our method for analyzing lattice structured illumination super-resolution microscope images. The effectiveness of our approach was confirmed based on the results of target region generation, bias field correction, image segmentation, network connection, meshwork generation, and meshwork analysis. Further, the performance of our method was empirically tested by recognizing and quantitatively analyzing nuclear lamina networks in five images that are presented. The experimental results show that our algorithm can achieve high accuracy in nuclear lamina network recognition and quantitative analysis, and the median face areas size of lamina networks from U2OS osteosarcoma cells are 0.3184 µm 2 , which has the same magnitude of order with other research [26] that used different kind of cells. Our proposed method would be helpful for standard nuclear lamina network recognition and quantitative analysis.