br Each patch of the tested image T
Each patch of the tested image T subjected to reconstruc-tion was compared to different patches of the pattern image P, and this process resulted in a set of potential coordinates of the best matches: (x1,y1), (x2,y2), …, (xz,yz). These coordinates defined the position at which the upper left corner of the test image T should be located inside pattern image P. The additional param-eters γ 1,…γ z, representing the rotation angle, and e1, e2, …, ez, representing the enlargement level of the tested image T, were also calculated in this phase. In general, n pattern Necrostatin1 and m test cells generated n × m comparisons, each generating z results. Therefore, n × m × z possible reconstructions had to be analyzed. This is a very large number; however, it could be significantly reduced by consid-ering the sensitivity and similarity measures. The similarity μ and sensitivity v defined by (3) and (4), respectively, were determined for each possible combination in the reconstruction procedure. The combinations meeting the condition v > 0.9 were finally consid-ered for reconstruction, while the other candidates were rejected.
In the next phase, each test image T(i) for 0 < i < m was ro-tated by a given angle γ i. As a result of the rotation, the new im-age, containing empty fragments located in the background (as a side effect of the rotation process) was obtained. These empty ele-ments were filled with the average values of the neighboring back-ground. Thereafter, each image was scaled using the enlargement value ei. Finally, the test image was superimposed onto the corre-sponding pattern images, using the coordinates xi,yi, and the sim-ilarity measures were calculated for all image pairs. The final re-constructed cell was represented by the pattern of the maximum similarity value.
As a result, we obtained a reconstruction of the highest sim-ilarity level of T(i) to the selected pattern image P. The result of the complete algorithm was the set of h reconstructed cells. The number was h < n, because not every cell was subject to recon-struction. A simplified three-step diagram presenting the general cell reconstruction process is illustrated in Fig. 4.
In summary, the cell reconstruction procedure illustrated in
Fig. 4 can be presented as the sequence of the following steps:
• Initial image segmentation using any standard procedure; for example, the watershed procedure. • Scaling of each segmented cell to the proper size ρ.
• Preparation of cells forming the pattern P and tested set T.
◦ The yellow-green stroma pixels are removed in the entire field of view
Fig. 4. Simplified diagram representing full process of cell nuclei reconstruction.
◦ The gene biomarkers pixels are removed in the cells
• Application of PatchMatch procedure to each cell of T.
• Comparison of the tested cell T to the possible candidates of the pattern cells in P searching for the best match.
• Determination of the sensitivity and similarity of each pair of T and P cells.
• Selection of pairs satisfying the condition of assumed sensitivity and similarity values.
• Reconstruction of the analyzed T cell based on its highest sim-ilarity to the cell from P set.
4. Numerical experiments
4.2. Testing results
Another database containing nine fields of view (one field for each patient) was used to assess the effectiveness of the proposed algorithm. An additional 200 randomly selected cells were manu-ally marked by an expert to assess the quality of the reconstruction method. The cells selected for testing were deformed to different degrees, as illustrated in Fig. 5. To evaluate the proposed method, the cells reconstructed by our automatic system were compared to the cells manually identified by the expert.
The entire reconstruction procedure was implemented in MATLAB (2018). The accuracy measures for both results (expert and automatic system) were defined according to the following for-mula:
The image data used in the work were obtained in the registra-tion process of microscopic tissue preparations at the Department of Pathology of the Military Institute of Medicine, Warsaw, Poland. Tissue samples were obtained by means of fine-needle biopsy or the excision of tissues in breast cancer tumor surgery. The images were created in fluorescence technology and by using an Olympus BX61 microscope with a DP 72 camera. The immersion lens UP-lanSApo 100× Oil was used for image acquisition (100× lens mag-nification, 10× internal magnification and enlargement of camera adaptation, 1000× total magnification). All images were registered at a resolution of 2070 × 1548 pixels.
The analyzed images were of different qualities. The brightness range of the pixels was very wide, and the density and location of the nuclei were inhomogeneous within the field of view. The number of cells/nuclei in the analyzed images varied from several dozens to several hundreds in one field of view. The ratio of the image area covered by cells to the entire field of view changed from 60% to almost 100%. In many cases, the boundary between the nucleus and background was blurred, while several cells were partly overlapped. The saturation of the nuclei colors within the examined images also differed. Selected parts of the exemplary fields of view exhibiting such diversities are presented in Fig. 5: left column – variety of illumination, middle column – different cell packing densities in field of view, right column – different types of cell overlapping.