Defects Detection in PCB Images by Clustering, Rotation and
Distributed Cumulative Histogram
1ROMAN MELNYK, 2ROMAN KVIT
1Software Department
Lviv Polytechnic National University
12 Stepan Bandera St., Lviv, 79013
UKRAINE
2Department of Mathematics
Lviv Polytechnic National University
12 Stepan Bandera St., Lviv, 79013
UKRAINE
Abstract: The K-means clustering of pixels intensity to segment the PCB image to a binary form, hierarchical
clustering and separation of elements on the PCB image, flood-filling of chains for their comparison with the
reference ones, three methods of determination of the turn angle for alignment of the board, subtraction
formulas, algorithms to rotate the image to its normal position, algorithms to build the image of the distributed
cumulative histogram are considered in this paper.
Key Words: printed circuit boards, chains, defects, clustering, flood-filling, pixel histogram, distributed
cumulative histogram, image rotation, alignment.
Received: January 2, 2023. Revised: August 11, 2023. Accepted: September 19, 2023. Published: October 8, 2023.
1 Introduction
Many publications are devoted to problems of
defect detection in the printed circuit boards. In the
last time, new works describe an application of
artificial networks for inspection of inaccuracies of
PCB production. Among them, neural networks are
used in articles [1-3]. Many publications contain
subtraction algorithms. Examples are in works [4-6].
As a rule, defects are classified to facilitate their
correction. The earlier article [7] uses a table of
connectivity wires based on contacts from the
reference image. Inaccuracies of contacts and traces
such as shift, extra metal, and others are not
considered.
The surveys [8-10] contain many publications
describing approaches and methods of the detection
of defects in printed circuit boards as well as their
classification. The main ideas of the following
works [11-13] are image subtraction, defects
extraction, thinning, and increasing the visibility of
elements on the board. Different techniques to
elaborate a plane are applied. The subtraction
operations between PCB images are very sensible to
a deviation of the sizes of contacts and traces from
the reference ones and give extra or lacking pixels
that do not influence the correct work of the circuit.
Short, open circuits and depression changes are
discussed and researched in the works [14,15] for
machine vision and learning inspection systems. All
mentioned approaches differ between themselves by
complexity, application objects, and efforts for their
implementation. Some use the SURF method to
determine the image features [16,17] for matching
and alignment. In common, most of the mentioned
approaches are very time-consuming to realize. In
this paper, some simple approaches are presented.
They are the following: K-means clustering of the
pixel intensity to segment the PCB image to a
binary form, hierarchical clustering and separation
of elements in the PCB image, flood-filling of
chains for their comparison with the reference ones,
three methods of determination of the turning angle
for alignment of the board, subtraction formulas,
algorithms to rotate the image to its normal position,
algorithms to build the image of the distributed
cumulative histogram, measurement of the chain
position and its defects.
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2 Clustering of PCB images
Two clustering algorithms have been developed
for the analysis of the printed circuit board image.
The former algorithm is assigned for preprocessing
and preparation of the printed circuit board image
for basic image processing and defect detection. The
second algorithm is applied to find and separate
analyzed objects such as contacts, circuits, and
electronic devices. Two algorithms considered are
K-means clustering and agglomerative hierarchical
clustering.
A. K-means clustering algorithm
The K-means clustering algorithm divides all
pixels of the PCB image into K segments of pixels
and assigns equal intensity for them.
Iterations of the algorithm repeat to distribute
pixels into clusters to minimize all distances
between the centroids and their pixels. The module
criterion function is as follows:
() _
01
||
mk
K
ki ki k
ki
S w I I
where wik= 1 if a pixel with intensity
ir
I
enters into
the cluster k, otherwise, wik= 0;
k
I
is the intensity of
the
k
-th centroid.
The process of assignment of pixels to different
clusters is shown in Fig. 1. The input data are pixels
of different intensity. The first iteration is a random
assignment of
K
centroids and searching for
closest pixels to them. The mean intensity of
centroids is recalculated. Then the iterative process
continues until replacement of pixels is not fixed.
Fig. 1. Iterations of pixels’ assignment
in the
K
-means algorithm
The process is less time-consuming when the
clustering algorithm works with rectangles created
after covering the image with a grid. The input
image is covered with a grid of
33
rectangles in
Fig. 2a. In this case, in Fig. 2b, the edges of the
clustered image are blurred. After the end of the
algorithm steps all pixels in clusters are redrawn
with the mean intensity value or other.
a b
Fig. 2. An image covered by a grid (a) and its
clustered segments (b)
The clustering algorithm includes the following
steps:
S0. For all points of the input set
j
xX
.
S1. Assignment of
K
clusters centroids
0( 1, ..., )
i
x i K
having an interval of the image
intensity
S
0( / ( 1)) , 1, ...,
i
x s K i i K
,
S2. Searching for leaf pairs by the similarity
function
0
( , )
ij
xx
count
0
( , )
ij
F x x
.
S3. Calculating and searching for pairs with the
smallest distance value
00
( , ) min ( , ), 1, ..., ,
i j i j
F x x F x x i K j I
,
and adding the member
j
x
to a cluster with the
centroid
0
i
x
.
S4. Recalculating the cluster’s centroids
0( 1, ..., )
i
x i K
.
S5. The end of the procedure (for all
j
xX
).
Steps S0-S4 are run until the centroids do not
change their positions.
If a clustering algorithm is applied to the input
image to obtain two segments (
2K
) the
advantages of the approach are as follows:
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1. No one pixel is deleted;
2. Pixels are grouped naturally near their centroids;
3. Segment colors are uniform and their values do
not affect the subsequent fill.
The input image, for example, is shown in Fig.
3a. The DCH image (the algorithm is described
below) in Fig. 3b distinctly illustrates how pixels are
distributed in the input grey image.
a
b
Fig. 3. The PCB image (a) and its DCH image (b)
Fig. 4a shows two groups of pixels in the
clustered image. The first one contains contacts with
traces, and the second group contains background.
a
b
Fig. 4. The PCB image with two clusters (a) and
its DCH image (b)
The DCH image in Fig. 4b distinctly illustrates
how pixels are distributed in the clustered image. It
confirms that only one intensity of objects in every
segment of a 2-clustered image is available.
For better illustration, the image histogram is
calculated as follows:
}),(|),{()( ivuIvucardih
,
0,1, ..., 255i
,
and the cumulative histogram is calculated:
i
j
jhi)H
1
)((
,
where
),( vuI
is the pixel intensity,
()hi
is the
intensity frequency,
()Hi
is the accumulating
frequency for the given intensity.
These four histograms for the input and clustered
images are shown in Fig. 5.
a
b
Fig. 5. Histograms of the input (red) and clustered
(blue) images: ordinary (a), cumulative (b)
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Two red histograms characterize the input grey
image; two blue histograms are properties of the
clustered image. They illustrate that all objects on
the circuit board after clustering are uniform in color
and ready for further processing.
B. Hierarchical clustering of the binary image
The hierarchical clustering algorithm is a more
complex procedure because it solves the
decomposition problem. All connected areas are
formed and described by the hierarchical algorithm.
An example to illustrate a transformation process
to build one area from its components is shown in
Fig. 6. The number of rectangles corresponds to the
number of nodes in the hierarchical tree.
a b c
Fig. 6. Formation of rectangles: input 1-11 (a),
four new 12-15 (b), five new 12-16 (c)
In Fig. 6a eleven elementary rectangles are input
data for the algorithm. After the first step of the
algorithm in Fig. 6b new rectangles are formed and
shown:
(3,4 12)
,
(5,6 13)
,
(7,8 14)
,
(10,11) 15
. After the second step in Fig. 6c only
one new rectangle is formed
(13,14 16)
. The
reason is that no more rectangles are to join with
others.
For this small example, the hierarchical tree is
shown in Fig. 7.
Fig. 7. Hierarchical process of formation of
rectangles
Such a process is organized by applying the
criterion and constraint functions to rectangles-
candidates planned to be united. For them, the
functions are calculated, and the best pair is ready to
join:
,,),min(
*IjkFF ki
where
I
is a set of possible pairs of initial
rectangles and their combinations. As the criterion,
the length of the common border for two rectangles
is accepted and calculated. The criterion is
calculated only for two input rectangles forming a
new one of a rectangular form.
The sequence of steps in the hierarchical
algorithm is as follows.
1. Space dividing. Imposing a grid with a step from
a set of values
1 1, 2 1, ...,3 3
on an input image
to form the set of micro-rectangles (
MR
).
2. For each
MR
their neighbors are searched around
the rectangle.
3. If the new planned rectangle
R
is of rectangular
form and satisfies the brightness constraint it is
added to the list
L
of the candidates for merging.
4. If some pairs of
MR
have common elements they
are removed from the list
L
. In the
( , )ab
,
( , )bc
,
( , )ad
,
( , )df
two pairs
( , )ad
,
( , )bc
are removed.
5. New rectangles are formed, and previous steps
are repeated with them.
These five steps of the clustering algorithm for a
grid with a step
11
(one pixel) over a black image
are fulfilled. There are no extra or lacking pixels in
the resulting image. This is illustrated in Fig. 8 by
two examples with the input and clustered images.
Fig. 8b contains rectangles with different colors.
a b
Fig. 8. Input (a) and clustered (b) images
The hierarchical clustering algorithm has
nonlinear complexity
2
()ON
. Thus, for large
images, a process is time-consuming if additional
operations are not realized.
The first step to improve time characteristics is
covering of the image by a grid with a step of
22
.
In this case, initial rectangles are fully and partially
filled by black pixels as this is shown in Fig. 9.
Fig. 9. Different types of input rectangles for
clustering
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In a process of clustering new rectangles are
built. Some of them have empty positions as this is
shown by examples in Fig. 10. Positions are empty
because the input image and initial rectangles have
no black pixels with these coordinates.
To control the process of rectangle formation the
criterion function is formulated. Let the number of
black pixels in an area be
o
S
, and in the area of the
clustered rectangle
oc
S
. If clustering is accurate a
condition
oc o
SS
is satisfied.
To control the relation between
oc
S
and
o
S
a
brightness of clusters as a control parameter is
accepted in the merging algorithm. The parameter
indicates percentage relations between black and
white pixels entering rectangles, for example,
1/ 6
,
3/8
,
3/ 9
,
4/10
as this is shown in Fig. 10.
Fig. 10. Different filling of intermediate rectangles
An example of clustering for a grid with a step of
a
22
cell is shown in Fig. 11a. In Fig. 11b a
difference between the clustered image and error
pixels is shown. Error pixels are marked with red.
a b
Fig. 11. Clustered image with a
22
cell (a) and its
difference between error pixels (b)
New rectangles in the image are of larger sizes
than in the previous
11
pattern. They contain extra
pixels because final rectangles are filled with black
without checking positions of rectangles what they
contain. Then positions of error pixels are checked,
marked, and isolated.
When clustering by rectangles
12
,
21
,
22
and higher steps the original clustering image
oc
I
is
easily obtained by subtraction of the clustered and
error images:
(2 2) (2 2)
oc c e
I I I
,
where
(2 2)
c
I
is the clustered image,
(2 2)
e
I
is
the image with error pixels. The subtraction
operation is special because in the first input image
it fills
0
in positions where the second input image
has a value of
1
and does not change an input pixel
when the second pixel has a value of
0
:
0 0 0
,
1 1 0
,
0 1 1
,
0 0 1
.
The computing complexity of such subtraction is
()ON
.
In conclusion, no additional operations are
required when a grid with a step
11
is applied.
N
additional simple operations are required for a grid
with a step of a 2 × 2 cell. In the second case, the
number of input rectangles is essentially smaller.
For example, complexity
2
()ON
is changed by
2
(( / 4) )O N N
for
22
step and
2
(( / 9) )O N N
for
33
step. For large images, it is a significant
gain in time.
C. Hierarchical clustering of the binary image.
Clustering to connected areas
Preliminary previous clustering does not give the
result because all connected areas are not considered
as a single whole but as systems of filled rectangles.
Thus, the second stage of the algorithm is developed
to unite rectangles into connected areas.
Intermediate objects are clusters.
The clustering procedure to unite rectangles in
clusters of undefined shape and connected areas is
based on the criterion function for two clusters. Two
rectangles-clusters are merged if they have one or
more common edges (Fig. 12).
Fig. 12. Two cases of different common borders
To account for some pixel loss rectangles-
clusters can participate in merging under conditions
that they are located at a distance
s
(Fig. 13). The
distance criterion includes a “diagonal” or “main”
distance which is useful sometimes for ring
structures.
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Fig. 13. Non-zero distances between clusters
The process terminates when the merging of
rectangles does not occur.
3. Clustering for separation of chains
The results of the clustering algorithm are useful
for the separation and comparison of connected
circuits in the reference and manufactured PCB
images. For example, two PCB images are
clustered. The first one is the reference and the
second is the manufactured one with short and open
defects. The first is marked with different colors and
shown in Fig. 14a. Four histograms for them are
calculated and shown in Fig. 14b, c.
a
b
c
Fig. 14. PCB image (a), cumulative histograms of
correct and defective PCBs (b), their histograms (c)
Due to similarity the defective PCB image is
missed. Blue corresponds to the correct PCB and
red is for the defective one in the two graphs of
histograms. When one blue peak is absent in the
new graph of a histogram it means that one chain as
an independent object disappeared and by a short
defect is joined to another chain. When one extra
red peak appeared in the new graph it means that
one independent fragment arose due to an open
defect in some chain. The cumulative histogram also
illustrates these two facts.
In conclusion, after obtaining such data the
answer to the question about possible open or short
defects is ready. Even if the numbers of components
are the same in the correct and defective PCBs.
Obtained data also are suitable for the
determination of coordinates, types, and other
inaccuracies in the controlled PCB. Every chain has
with own color (intensity). Thus, for every chain a
histogram of pixels in the
OX
or
OY
axis is
applied. For the given interval of intensity
(int)I
the
numbers of pixels in columns or in rows are
calculated as follows
( ) {( , ) ( , ) (int)},
( ) {( , ) ( , ) (int)},
( 0,1, ..., ; 0,1, ..., ).
h c card x y I x y I
h r card x y I x y I
c w r H
It is not required to select and separate one chain
from the resulting image because all of them have
their own intensity marked in histograms in
Fig. 14b, c. For illustration, only two chains are
drawn with black and shown in Fig. 15 with a short
defect (two chains are connected) and without it.
a b
Fig. 15. Short defect in two chains (a) and correct
chain (b)
Two graphs of histograms in columns and rows
are shown in Fig. 16. Differences are distinct.
Additional functions determine the coordinates of
defects. Black graphs are of defective chain, red is
of the reference chain. They mark the coordinates
of different positions. Pink marks a difference in the
number of black pixels for every coordinate.
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a
b
Fig. 16. Histogram from
OX
(a) and
histogram from
OY
(b) of two chains
The second approach is designed for the
determination of coordinates and visual inspection
of defects. It uses images of separated chains and
their distributed cumulative histograms.
Two images are compared according to the
following comparison formulas:
( , ) ( , ) | ( , ) ( , )|
r d e d
I x y I x y I x y I x y Tol
,
)(),00|,),(),((|),( redyxIyxIRGByxI der
TolyxIyxI de |),(),(|
,
and a sign is +,
)(),0|,),(),(|,0(),( blueyxIyxIRGByxI der
( , ) ( , ) ,
de
I x y I x y Tol
and a sign is -,
where
),( yxIr
is the pixel intensity of the resulting
image,
),( yxIe
is the pixel intensity of the first
image,
),( yxId
is the pixel intensity of the second
image,
Tol
is the tolerance value for controlling the
difference between the pixel intensity of the
reference and controlled samples.
The comparison formula is applied to two chains
shown in Fig. 17. Differences between them and
their DCH images are shown in Fig. 18.
a b
Fig. 17. Open defect (a) and correct chain (b)
a b
Fig. 18. Difference: between two chains (a)
and their DCH images (b)
In Fig. 18a red marks inaccuracies of traces and
the open defect. In Fig. 18b a red wide stripe
corresponds to coordinates of the open defect in the
OX
axis. Other red strips mark inaccuracies.
In conclusion, there are many other approaches
to determining the coordinates of defects by
comparison of two separated chains from the
reference and controlled images.
4. Rotating image and distributed cumulative
histogram
A. Determination of angle by sizes of images
Sometimes a controlled PCB image is not
correctly aligned with the reference PCB image for
reasons of positions of the installation equipment or
the camera angle.
In Fig. 19 two examples of the rotated PCB
image and its clustered pattern are shown.
a b
Fig. 19. Turned images: input (a), clustered (b)
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Due to different angles, traces change their
positions and sizes. Directly comparison with traces
from the reference PCB image will give
unpredictable results. In this case, two variants are
possible: to rotate the reference image or the
controlled image. Only the angle is required to be
determined and software to realize rotation.
The unaligned PCB image as a rectangle is
shown in Fig. 20a. An extra place connected with
camera requirements and incorrect placement of the
PCB image is marked with red. In Fig. 20b two
triangles for the angle determination are shown.
a b
Fig. 20. Marked area on the incorrect placement of
the PCB image (a) and heights of triangles (b)
The angle
is determined from the equation for
two rectangles and a height h of the input image:
12 cos sinh h h a b
,
where values of
,,h a b
are known.
The equation is transformed into the quadratic
equation with one unknown:
2 2 2 2 2
( ) 2 ( ) 0a b x hbx h a
.
For the simple example, if
1, 1, 2a b h
, in
the result
cos 2 / 2x
and
45o
.
The determined angle is the input data for
software to rotate and align the input image.
B. Determination of angle by centers of the image
and pixels
The second approach is also simple and requires
some mathematical calculations.
Two points are determined for the reference and
inclined images. They are a center of the image and
a center of black pixels. The first has coordinates
( / 2, / 2)
i
c W H
. The second center has the
coordinates corresponding to the level of 0.5 in the
cumulative histogram of black pixels, i.e.,
( (0.5 ), (0.5 ))
p
c x ch y ch
. It is calculated for both
images from the
OX
and
OY
axes. These
coordinates mark a border dividing black pixels into
equal parts. The lines dividing the image into parts
are shown in Fig. 21a. One coordinate in the
OY
axis for the unaligned image is shown in Fig. 21b.
a b
Fig. 21. Divided PCB image with turning angle (a),
and division of its cumulative graph (b)
The found coordinates for two images give two
vectors:
[(0, / 2), (0, / 2)],
[0, (0.5 )),(0, 0.5 ],
u
r
A W H
B x ch y ch
where
(0.5 )x ch
,
(0.5 )y ch
are the coordinates
corresponding to the level of
0.5
in two cumulative
histograms for the
OX
and
OY
axes of the input
PCB image.
Examples of vectors are shown in Fig. 22 only
for illustration not reflecting the considered PCB
image. In practice, they are built separately because
the sizes of the non-aligned and reference images
are a little different (the first one is larger).
Fig. 22. Vectors to centers of black pixels
For two vectors two angles to vertical vector
C
are trivially calculated by the following formulas:
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cos [( ) / (| | | |],
cos [( ) / (| | | |] .
Io oc
a
Io oc
b
a a c
b b c
To align the controlled image a difference in
found angles is required:
aa
.
In the above-considered example with the turned
PCB image relative values of direction vectors are
𝑎 = [(0.8), (0.13)], 𝑏 = [(0.8),(0.17)].
The angle of the turning is
63 58 5
.
This angle is the input data for the algorithm of
rotation and building the distributed cumulative
histograms.
C. Rotation of images
It is useful to construct DCH from different
viewpoints to measure image properties. Depending
on the viewing angle, the distributed histograms of
the same image show a different distribution of
pixels and their intensity.
The image intensity values are transformed into
greyscale. The simple formula is used to average the
pixel component values
R G B
' ' ' , 1,..., , 1,...,
3
ij ij ij
ij ij ij
R G B
R G B i B i A
,
where
,,
ij ij ij
R G B
are values of new image pixels, B
and A are sizes of the input image.
The final rotated image is of larger dimension
due to an extra area surrounding it. Thus, to present
them a new canvas is required. It is determined by
the formulas:
22
,d A B
arcsin ( / ), | | / 2,
arcsin ( / ), | | / 2
Ad
Bd
mod( / 2), | | / 2,
, | | / 2
The sizes of the new image are from the
following formulas:
sin(| | ) ,
2
Ad
sin( | |) ,Bd
where
,AB
are the width and height of the new
canvas,
is the angle between the base and
diagonal of the input image,
is the turning angle,
d
is the diagonal.
Then every pixel of the input matrices image by
the affine transformations is transferred to the new
canvas:
1 0 1 0
cos sin
11
22
sin cos
11
0 1 0 1
22
AA
x
BB
y
.
An example of the turned PCB image is shown
in Fig. 23 where an extra area is marked with red.
Fig. 23. Turned PCB image and extra area in canvas
In the rotated image all intensity, color
properties, and center of the image are the same as
in the input image. Geometrical properties measured
horizontally and vertically are changed.
D. Building of image of distributed cumulative
histogram
For all pixels’ intensity values in rows and
columns of the image matrix are stored
(transparent positions are not accepted):
[256] {0}, 1,
i
m i B
,
[256] {0}, 1,
j
m j A
,
1, 0
[ ] , 1, , 1,
0, 0
ij
i ij ij
m R i B j A
,
1, 0
[ ] , 1, , 1,
0, 0
ij
j ij ij
m R i B j A
,
where
[256]
i
m
,
[256]
j
m
are histograms data in the
rows and in the columns,
ij
R
is the color component,
ij
is the transparency value.
For two or more rows (columns) of the image
matrix the procedure is complicated because
average values are taken into account:
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()
() ()
1, 0
[ ] , 1, , 1, , 1,
0, 0
i E k j
i i E k j i E k j
AB
m R i k E j A
AE
()
() ()
1, 0
[ ] , 1, , 1, , 1,
0, 0
i j E k j
j i j E k i j E k j
AA
m R i B k E j
AE
.
Then the cumulative histograms are calculated for
all rows (columns):
1
, 1, , 0,255
k
ik ij
j
M m i B k
,
1
, 1, , 0,255
k
kj ij
i
M m j A k
,
where
,
ij
mm
represent the values of the intensity
histograms,
,
ij
MM
are the values of cumulative
histograms called distributed cumulative
histograms.
The following step is to draw an image of the
distributed cumulative histogram (DCH). The
value of each pixel of this image corresponds to a
value of the cumulative histogram. The new
image will have a
BN
pixel size (for rows)
with the pixel values are calculated by the
following formulas:
1
255 , 1, , 1,
max
ij ij ij ij
i
jN
R G B M i B j N
M
.
For columns, the new image is of
NA
size and
the pixel values are calculated by the similar
formulas:
1
255 , 1, , 1, ,
max
ij ij ij ij
j
iN
R G B M i N j A
M
where
,,
ij ij ij
R G B
are the pixel components in the
DCH image,
i
M
is the cumulative histogram of
i
-
row,
ij
M
is the value of
j
-element of the
histogram,
N
is the number of elements in the
cumulative histogram.
The 0 or 255 values of the DCH image pixels are
replaced by transparent pixels (
0
)
0, {0,255} , 1, , 1, ,
255, {0,255}
ij
ij ij
Ri B j A
R
where
,AB
are the DCH image sizes.
To illustrate the rotation results, the PCB image
turned by some angle is taken for experiments. The
angle is determined, and the image is rotated
backward for this angle. During the rotation, the
second extra area has arisen and is shown in Fig.
24a with blue.
a b
Fig. 24. Input image rotated back (a) and its DCH
image from
OY
(b)
The new blue area appears when the new canvas
is constructed. The sizes of the real PCB image are
the same as those for the input image. After cutting
(cropping) or flood-filling of blue and red areas
images are processed by defects detection
algorithms. The resulting PCB image after rotating
backward and its DCH image are shown in Fig. 24.
E. Alignment by DCH images
DCH images are useful for adjusting the position
of an unaligned image. In Fig. 25 two images with
marked parts are shown. These marked parts are
cropped and their DCH images are built. Areas for
cropping are chosen as
35
rows of pixels in the
middle of the image. A direction of cropping is
chosen to intersect a larger number of elements. As
a rule, along the larger side.
a b
Fig. 25. Central parts in input image (a) and turned
image (b)
The DCH images are calculated and built from
the
OX
axis for cropped parts. Comparison by
mathematical subtraction of these images gives up
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2023.22.11
Roman Melnyk, Roman Kvit
E-ISSN: 2224-266X
95
Volume 22, 2023
the result image with many red and blue areas
meaning no coinciding areas in the input images.
Two differences in DCH images built for the 5-
degree angle and 1-degree angle of the turned PCB
strips are shown in Fig. 26.
a b
Fig. 26. Differences in DCH images:
5
-degree
angle (a) and
1
-degree angle (b)
When the angle equals
0
-degree the difference
fully coincides with the input pattern. It is shown in
Fig. 27a. The cumulative histogram is applied to
measure this difference. There are three histograms
in Fig. 27b: red for the difference of
00
, green for
01
, and blue for
05
angles.
a
b
Fig. 27. Difference between DCH images of aligned
and reference strips (a) and cumulative histograms
from the
OY
axis (b) of DCH images
The green graph is close to the required one.
Only blue and red pixels in the image form steps
indicating the main contribution to the difference.
The blue graph is far away indicating absolutely no
coincidence with the required result. Histograms
give the number of blue and red pixels. Thus, this
characteristic is accepted to adjust alignment to the
required position.
5. Conclusion
The approach is based on the K-mean and
hierarchical clustering algorithms. The first one is
applied to segment PCB images into a binary form.
The second algorithm is used to separate all
contacts, traces, and chains. Separated elements of
two printed circuit boards are compared.
Connectivity and intensity defects are detected and
measured. They are visually presented by the
mathematical comparison and in images of
distributed cumulative histograms. Three
approaches for the alignment of the PCB image
based on the determination of angles are considered.
The image rotation algorithm to the reference view
is developed. Images of distributed cumulative
histograms help to adjust angles of alignment and
mark possible defects and inaccuracies.
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Roman Melnyk, Roman Kvit
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96
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The authors contributed in the ratio of 70 (Melnyk)
to 30 (Kvit) in the present research, at all stages
from the formulation of the problem to the final
findings and solution.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2023.22.11
Roman Melnyk, Roman Kvit
E-ISSN: 2224-266X
97
Volume 22, 2023
