br A database containing pattern cells selected by a
A database containing 1577 pattern Necrostatin 1 selected by a medical expert was used in the experiments. The cell pattern data were acquired from 39 fields of view, obtained from nine patients with detected breast cancer.
Fig. 5. Exemplary fields of view of analyzed images: left column – variety of illu-mination, middle column – different cell packing densities in field of view, right column – different types of cell overlapping.
where x, y, and z represent the following cell areas: x is the com-mon part of both cells, y is the test cell reconstructed only by our system, and z is the cell marked only by the expert. The results representing the average reconstruction accuracy for each field of view are presented in Table 1 (column 3). Column 4 displays the accuracy levels obtained for the same FISH images when using the classical method (watershed algorithm), without the reconstruction procedure.
The average accuracy of the cell area estimation in our method was 85.17%, compared with the manual segmentation by the med-ical expert, which is fully acceptable in practice. For the classical method (without reconstruction), the obtained accuracy was only 48.60%. It can be observed that most papers report their results in a much simpler form, as the ratio of the number of segmented cells to their true number in the image (omitting the comparison of the cell area). For example, Reljin et al. (2017) declared the de-fined relative error to be within the limit of +9% to −13% in a set of 100 images, while papers inspired mainly by Raimondo et al. (2005) presented relative errors within the limit of +21% to −33% for the same set. Additional experiments were conducted on the next 50 FISH images, applying the above definition of segmenta-tion quality. We found that the relative error varied from +3% to −9% in the analyzed set of 50 FISH images.
An illustration of different stages of the reconstruction process is provided in Fig. 6. Part A of the figure presents the original cell nucleus, part B displays the result of the watershed algorithm ap-plication, part C indicates the cell boundary identified by an expert, part D displays the cell selected by the automatic system as the closest to the original deformed cell, and part E represents the re-sults of the automatically reconstructed cell and expert selections, superimposed onto one another to depict the differences between these two contours.
Fig. 7 presents the comparative results concerning the bound-aries of nine exemplary cells obtained by the standard approach (red color) and the outline of the proposed reconstruction proce-dure (white color).
Standard nuclei segmentation techniques, which are directly based on the watershed method, are particularly susceptible to two types of distortion: (1) the brightness values of the blue channel changing discontinuously within the cell, and (2) the stroma over-lapping the cell. Both types of distortions are visible in Fig. 7. Our reconstruction procedure allowed for obtaining corrected results compatible with the expert decisions. r> Graphs indicating the influence of the cell and stroma overlap-ping are depicted in Fig. 8. These graphs represent the change in which the reconstruction accuracy with the percentage degree of the cell being overlapped by another cell (left figure) and by the stroma (right figure). The blue line depicts the details of the ac-
Results representing accuracy of reconstruction of cell areas.
Field of view Number of cells Acc [%] (proposed reconstruction method) Acc [%] (without reconstruction)
Fig. 6. Illustration of different stages of reconstruction process.
curacy at different degrees of cell overlapping, while the red line indicates the linearized trend line.
It can be observed that, irrespective of the type of overlapping, the accuracy changes exhibited a decreasing tendency at the in-creasing overlapping area. At an overlapping degree exceeding 40%, the accuracy began to decrease more rapidly. The study ended at
Fig. 7. Exemplary graphical results of reconstruction procedure for nine test cells:
red color – watershed method, white color – proposed reconstruction procedure.
60% of cell overlapping, as at values higher than 60%, the results could be questionable from a medical point of view.
Numerical parameterization of the overlapping phenomena is another important factor for medical experts, because it allows for deciding in an objective manner whether a given cell should be considered or omitted in the analysis.
Table 2 presents a summary of the study on the overlapping level for 20 cells of different shapes and sizes, all in the area range of 34 to 52 μm2, which were found in one selected field of view