The adjacent cells with two or more overlapping. Recently,

The basic way to
automatically identify cells is to use intensity-based segmentation techniques
such as Otsu-based methods 2-4 or Watershed transformation 5. The initial
Otsu method was applied to binarization of various images, but it was improved
by the binarization technique that is invariant to the brightness through local
binarization or adaptive binarization, so that the cell area of various
brightness can be found from the microscope image. Such intensity-based
techniques are easy to use, but it is difficult to expect good performance for
complex background or splitting of adjacent cells with two or more overlapping.
Recently, a method of using the distance map based on the Otsu method as an
initial value for Watershed has been proposed to improve the segmentation
accuracy 22.

Energy-minimization based image segmentation
techniques can produce better results than the intensity based techniques in
the above-mentioned difficult environmental conditions. ACM (Active Contour
Model) 67 is a representative energy-minimization technique using
area-based partitioning 8 and edge-based partitioning 9, and shows good
performance in noise image. However, ACM-based techniques require initial points
so that it is impossible to perform a full-automatic segmentation and the initial
point affects the accuracy. Moreover, because of high computational complexity
caused by the iterative convergence process, it is not suitable for the purpose
of finding multiple cells at the same time.

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Gradient flow tracking (GFT) 2324, graph
cut10-14, and level set25-27 are energy minimization based techniques that
are more suitable than ACM-based techniques for multiple cell segmentation. GFT
identifies the cells by clustering the slope vector using the characteristic
that the slope vector around the cell becomes very congested, but in the noisy
environment, the slope at the cell boundary is very small and the direction is
unreliable. GC-based algorithms 10-1428-32 are widely used because they are
guaranteed to find a global optimal solution for pixel boundaries between
distinct regions. However, these methods may produce the boundaries of the
uneven step-like shape or different from the boundary that perceived by human,
so that a more advanced segmentation method are required.

feature definition and classifier design have been suggested in various machine
learning-based cell segmentation techniques 15-19. Bayesian inference and
Kalman filter 17 showed good performance in cell segmentation and tracking. Dynamic
shape modeling (DSM) extended the state vector of a classical Kalman filter to
compute the morphological changes. The slope of the sigmoid function at the
cell boundary is used as a probability model for shape inference by modeling
the uncertainty of the shape. The cell detection technique 18 using the
classifier trained from the seed provided as the ground truth is possible to
classify by binary support vector machine (SVM) in various datasets including
histopathological images of breast cancer, fluorescence images of HEK (human
embryonic kidney) cells, and phase-contrast images of HeLa cells. Seeds should
be provided for each cell for learning, and a 92-dimensional histogram of the
brightness, shape and the brightness difference of the boundary is used as a
characteristic. Supervised learning-based cell segmentation 15 can identify
cells from histopathologic images using color and texture features extracted by
local Fourier transforms. MDC (most discriminant color) space using intra-class
and inter-class covariance matrices of local Fourier transforms for cell and
non-cell regions is better than RGB, and accuracy was improved by cell
separation through concave dot detection. However, this way of simply cutting
the border of adjacent cells straight is different from the actual boundary of
the cell. ilastik 16 classify the features of color, edge, and texture around
each pixel with a random forest classifier to detect the objects or regions. These
learning-based image segmentation techniques generally have good segmentation
ability, but can not perform segmentation at a very precise level.

The study of
dividing the connected cell region of interest (ROI) by assuming the ROI as a
2D Gaussian mixture model (GMM) and using the expectation-maximization method produces
results close to the perceived boundaries of humans2021. However, since there are a plurality of parameters, it is necessary
to set the image data set depending on the image data set. Furthermore, the
segmentation quality is not good for a cell region in which a difference in
contrast between the foreground and background regions is small.