IEEE Systems, Man and Cybernetics Magazine - April 2018 - 28

◆ step 2: take each corner coordinate as the center of the

(a)

(b)

(c)

(d)

Figure 5. a sample of CCS corner detection: a (a)

gray image, (b) binary image, (c) contour, and (d)
the corners.

Figure 6. the refinement of a concave point in its

neighborhood.

(a)

(b)

Figure 7. the result of concave point positioning: (a)

a mask image and (b) the concave points location.

The Accurate Detection of Concave Points
The corners exist not only in the region overlapping the
two particles but also in the convex point of the particles,
which lie all along their contours. From the method based
on the area ratio of a circular mask, convex points and
some concave points with small concavity are filtered out,
and the concave points for segmentation are then
reserved. The relevant steps are as follows:
◆ step 1: obtain the index and coordinates of each corner, and set the radius of the circular mask according
to particle size in actual situations
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IEEE SyStEmS, man, & CybErnEtICS magazInE A pr il 2 0 1 8

circular mask, and cut out the region through an AND
operation between the mask and the particle image
◆ step 3: calculate the number of white pixels as the
area, which corresponds with the particle region; if
there are many white regions, the largest area should
be selected
◆ step 4: compute the area ratio of the white area in the
circular mask
◆ step 5: select the points with the largest area ratios as
the candidate separating points according to the estimated number of particles
◆ step 6: refine each candidate point in its neighboring region.
For each candidate point obtained from step 5, the points
along the boundary are selected in its [m # m] neighboring
pixel region; these points are used to calculate the area
ratios, and the maximum ratio is selected as the final concave point. This underlying principle is shown in Figure 6.
Suppose the green rectangular point to be the concave point
from step 5; the red-dotted square is in the neighborhood of
the concave point, and the blue circular points represent the
other points on the contour of particles. Taking each of
these points as the center of the circle to calculate the area
ratio according to steps 2-5, the final concave point with
the maximum area ratio is selected. As shown in Figure 6,
the final concave point chosen is the red point rather than
the green point.
A sample of the positioning of concave points is shown
in Figure 7, where (a) shows the area ratio of the mask
image, the red circle is the mask, and the white area in the
red circle represents the particle area. Figure 7(b) shows
the final result, and the four concave points are marked
with a plus (+) sign.
Concave Point Pairing
Concave point pairing is intended to determine the concave point pair for the segmentation of two particles,
which is the premise for performing an accurate line segmentation. Since the two particles adhere to one another, a
concavity phenomenon appears in the contact parts,
which imbues the pattern of the adhered particle with the
characteristic of a concave graph [26]. Gray projection is,
therefore, used for matching, i.e., cutting the region into a
specific size consisting of two concave points as the candidate point pair; the gray projection then proceeds in vertical and horizontal directions, respectively. Finally, the two
concave points are assessed to determine whether they
belong to a pair according to specific rules.
When gray projection is implemented onto the image
extended from the connection between concave points
(according to prior knowledge of a concave point pair),
the projection curve along with the connection line indicates that the middle value is smaller than the end point
values; whereas, the vertical projection curve indicates
that the middle value is larger than the end point values.

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - April 2018