PCB Image Defects Detection by Artificial Neural Networks and

Resistance Analysis

ROMAN MELNYK, VITALII VOROBII

Software Department,

Lviv Polytechnic National University,

12 Stepan Bandera St., Lviv, 79013,

UKRAINE

Abstract: - The approach contains the sequence of algorithms and formulas for image processing. They are

single-layer neural networks, thinning, clustering, mathematical image comparison, and measurements of the

trace length and width. All these procedures solve the task of selection and separation of the main objects in the

printed circuit board: contacts, traces, and defects. The calculated features connect the conductance resistance

of traces with the characteristics of defects. Imposing a tolerance on the distributed or concentrated changes of

resistance it is possible to mark the defective and suspicious printed circuit boards.

Key Words: - Printed circuit board, chain, trace, defects, clustering, flood-filling, artificial neural networks,

skeleton, edge, thinning, cumulative histogram, resistance, width of trace, overlay, tolerance.

Received: August 25, 2023. Revised: February 19, 2024. Accepted: March 16, 2024. Published: May 23, 2024.

1 Introduction

There are many special devices based on lasers,

ultrasound, and X-ray radiation which are used to

detect defects in printed circuit boards. Their

purpose is to measure the thickness, the amount of

solder, the quality of the layers of the components,

as well as the shape of the drawing. The collected

data are input for image recognition algorithms in

the context of post-production defect detection, [1],

[2], [3], [4]. Such devices and algorithms are

implemented in powerful complex control systems

to prevent damage to manufactured printed circuit

boards and surfaces, [5], [6].

Many works consider the visual presentation of

printed circuit boards. They contain traditional

image processing algorithms including subtraction

algorithms, wavelet, and a table of connection traces

based on contacts from the etalon image, [7], [8], [9].

In the last time, for inspection of inaccuracies in

PCB production, neural networks were used, and the

approaches were described in articles, [10], [11],

[12], [13], [14], [15]. Three surveys contain many

references to publications describing approaches and

methods for the detection and classification of

defects in printed circuit boards, [16], [17]. [18].

Short, open circuits and depression changes in

computer vision and artificial intelligence inspection

systems are subjects in the publications, [19], [20],

[21], [22]. The subtraction operations between PCB

images used in many works are sensible to a

deviation of the sizes of traces and contacts from the

etalon. They give extra or lacking pixels that do not

affect the correct operation of the electrical scheme.

Defects in traces and contacts of such types as shift

and extra metal are not analyzed.

All mentioned approaches differ between

themselves by complexity, input data, and

characteristics of their implementation.

In this work, the following approaches to solving

the given problem are applied: mathematical

comparison formulas, a filling algorithm for

dividing and selecting circuits, artificial neural

networks for the classification of printed circuit

board images, and formulas for calculating the

resistance characteristics of traces and contacts.

The advantages of the proposed method are the

preliminary division by artificial neural networks of

images of printed circuit boards into two classes,

followed by the detection of three classes of defects

in the defective class: connections, excess, and lack

of metal on traces and contacts. The influence of

these defects on the conduction resistance is

calculated. Areas with detected defects are marked

on traces and contacts. This creates the possibility of

additional analysis of the circuits for repairability or

failure.

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2 Separation of Chains in PCB Image

2.1 Determination of chain coordinates

Each printed circuit board has a geometry such that

all pins assigned to one circuit are connected, and

two or more pins assigned to different circuits are

not connected. As a result, they are characterized by

a planar topology of wires or traces. Automatic

access to each chain is possible only if the

coordinates of the pixels in the traces are known and

with their help, one chain can be selected and

separated from the entire set of black traces on the

board. This can be done by changing the color of the

selected chain.

The Hilditch thinning algorithm, [8], works with

binary (black and white) images and is reliable and

easy to program. It is modified to find the pixel

coordinates of specific points, which are taken as the

output pixels for the fill algorithms, which select

and separate circuits in PCB images by painting

them with specified colors.

Figure 1 shows a skeleton image created for a

template PCB. It has two types of specific points:

switches (circled in blue) and terminations (circled

in red). Specific points on the image next to the

coordinates are not identified, that is, they are not

assigned the identification number of the chain that

contains them.

Fig. 1: Skeleton with endings and switches

The specific points are united in the set P. All

elements in the set denote only the coordinates of

their location. Taking elements from the set as

starting points the flood-fill algorithm fills chains

with different colors. The filling algorithm is

applied as many times as there are chains in the

scheme.

For illustration, the skeleton is overlaid with the

template PCB image. The two chains are filled with

green and blue and are shown in Figure 2.

Fig. 2: Overlay of PCB image with skeleton, and

filled chains (green and blue)

Each color gives the identification number for

the chain and its specific points. This allows to split

the set P into subsets of specific points connected

with the concrete chain:

P(p1, p2,…,pN)=P(P1,P2,…,Pn),

where p1, p2,…,pN are coordinates of all specific

points, P1, P2,…, Pn are sets of points assigned to

the chains with the sequence numbers 1, 2, …,n.

In the extended version they are as follows:

P1={(x11,y11, c11), (x12,y12, c12), (x1n(1),y1n(1) ,

c1n(1), )}→1,

P2={(x21,y21, c21), (x22,y22, c 22),., (x2n(1),y2n(1) ,

c2n(1) )}→2,

…,

Pn={(xn1,yn1, c n1), (xn2,yn2, c n2),., (xnn(1),ynn(1),

cnn(1) )}→n,

where ci1 is a variable of color, and the number of all

points is N=n(1) +n(2)+…+n(n).

The determined array is the input data for all the

following processing algorithms working with

chains of the circuit.

2.2 The Flood-Filling Algorithm

The flood fill algorithm is sometimes called initial

fill. The seed is the starting pixel and then other

seeds are planted in the area to change the color of

the pixels. The algorithm replaces the internal color

Io of the object with the fill color In. When there are

no more pixels of the original interior color, the

algorithm terminates. This algorithm is based on a

four-join or eight-join method for pixel filling. It

searches for all adjacent pixels that are part of the

interior.

The standard flood-filling algorithm requires for

its work a uniform color surface when all pixels are

of equal intensity. To improve the properties of the

algorithm to apply to PCB images its principal

formula is modified. For the available intensity

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value Io and the target intensity value In the

algorithm fulfills the modified formulas:

a) tolerance only on lower intensities

If I(xi, yi) = Io -( Io *Tol), then I(xi,yi) = In ,

b) tolerance only on higher intensities

If I(xi, yi) = Io +( Io *Tol), then I(xi,yi) = In ,

c) tolerance on lower and higher intensities

If I(xi, yi) = Io ±( Io *Tol), then I(xi,yi) = In ,

where Tol is a relative tolerance to regulate rules on

what surrounding pixel intensities must be changed

(filled).

An example of the image to be filled and its

distributed cumulative histograms from the OX and

OY axes is shown in Figure 3. Arrows indicate the

intensity values for red and blue. The intensity value

of black is 0.

Fig. 3: Image “Three srips” (a) and its DCH images

from OX and OY axes with an indication of the

color intensity (b)

Two examples of filling of areas with equal and

lower intensities in the image “Three strips” are

shown in Figure 4. Starting from black with a big

tolerance the algorithm fills red and black rectangles

in orange. For a bigger tolerance starting from blue,

the algorithm fills three rectangles in orange. So, the

tolerance allows to marking of different components

with the same color.

a b

Fig. 4: Two flood-filled images: red pixel as starting

point (a) and blue pixel as starting point (b)

An example of the result of the filling algorithm

when selecting circuits with different colors on a

printed circuit board is shown above in Figure 2.

3 Separation of Defects

Defects are of various sizes and shapes. By their

appearance, it is difficult to determine what effect

they have on the functionality of the scheme. A very

small strip can disrupt the transition of a signal, and

a large round excess of connecting metal makes

small changes in the operation of the circuit. This

especially applies to short circuits and their breaks.

The shape, size, and location of defects are random

and may vary from one printed circuit board to

another. Some examples of the most important

defects as short and open are shown in Figure 5.

a b

Fig. 5: Two short (a) and two open (b) defects

A more difficult problem is to determine the

type of track and contact defects. What amount of

excess or insufficient metal is not just a defect, but

an inaccuracy that affects the operation of the circuit

and may or may not be corrected? Some examples

of metal inaccuracies, such as metal excess and

metal shortage, are encircled and shown in Figure 6.

Examples of thinner (the width W is less than

standard) and wider lines (the width W is greater

than standard) are also shown in Figure 6.

a b c d

Fig. 6: Extra metal (a), shortage of metal (b), thinner

(c) and wider (d) circuits

The first two defects in Figure 6 affect the

passage of current and, in principle, are subject to

repair. The third and fourth defects also change the

value of the electric current, but they are difficult to

eliminate.

When the PCB image is presented in a binary

form possible defects are detected by the XOR

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operations. They work with pixels by following

formulas:

0 ^1 1, 1^ 0 1, 0 ^ 0 0, 1^1 0,   

where 0 denotes white and 1 denotes black or vice

versa.

These operations show surpluses and

shortages of metal on the traces and contacts of

the manufactured printed circuit board about the

reference image. All defects belong to one class

according to the way of their detection.

Subtraction operations with the binary image

allow the separation of positive and negative defects:

, , ,

Such operations are repeated twice: to a pair of

the input images and swapped images. Positive and

negative results form two classes of defects

according to the way of their detection.

The third type of the subtraction operation is

planned to realize the following tasks: to keep tracks

and pins on the board, to separate defects into two

classes by the intensity value, to separate

constructive elements and defects by the intensity

value, to keep defects visible on their places near

constructive elements.

The operations to realize these tasks are as

follows:

0-1=red, 1-0=blue, 0-0=0, 1-1=1,

where 0 denotes white and 1 denotes black or vice

versa. Red and blue are of the constant intensity

values.

An example of the last subtraction operation is

shown in Figure 7.

Fig. 7: The comparison difference between the two

PCB images

The resulting image contains red and blue pixels

reflecting associated and isolated areas that mark

different types of defects.

4 Artificial Neural Networks for

Defect Recognition

4.1 Defects Recognition by Cumulative

Histograms

Reducing the inspection time in the production

process of many printed circuit boards is possible

thanks to the use of artificial neural networks

(ANNs). They carry out a preliminary division of

schemes into two classes: without defects and with

defects. Later, the suspected circuit defects are

processed by the developed software.

So, both the reference and the test images are

prepared for the artificial neural networks to train

and identify defective PCBs. But instead of images

from two classes, the following approach uses the

different images or their extracted features.

This approach is based on a single-layer neural

network in Figure 8 with a reverse spread learning

algorithm.

Fig. 8: Architecture of a single-layer ANN.

The single-layer ANN consists of m entries

(vector X) connected to neural elements by a weight

ratio. Neural elements, in their turn, consist of NET–

elements and an activation function. The output

neurons (vector OUT) represent the classification

result for the input image. An important role in

training and recognizing plays an activation function

in which values are at the output neurons. The most

common type of activation function used in neural

networks is the exponential sigmoid, shown in

Figure 9.

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Fig. 9: Exponential sigmoid curve and the formula

The value range of this function is (0; 1),

obviously, during the recognition process, the closer

the value of the output neuron is to 1, the more

likely the input image belongs to a certain class.

The cumulative histogram was the first

experimental feature for learning and recognition. It

contains information about how many pixels belong

to a certain brightness range (from 0 to 255).

The neural network was implemented in the

Python programming language, in addition to the

PyTorch and NumPy libraries, and was trained

using the DeepPCB dataset [23], which contains

1500 pairs of images, each consisting of a defect-

free template image and an aligned test image with

annotations , including the location of the six most

common types of PCB defects: open, short, mouse

bite, spurs, pinholes, and false copper.

The accuracy of the neural network is calculated

using this formula:

where TP are instances belonging to the positive

class that are accurately predicted as positive, FP

are instances belonging to the negative class that are

incorrectly predicted as positive, TN are instances

belonging to the negative class that is accurately

predicted as negative, FN are instances belonging to

the positive class that is incorrectly predicted as

negative.

The cross-entropy loss function was employed as

the loss metric during the training of the neural

network:

where n is the size of the dataset, yi is a true label

for the instance i, yi is the predicted probability of

the instance i belonging to the positive class.

When yi= 0 a loss for the instance i will be lower

when yi approaches 0. When yi= 1 loss for the

instance i will be lower when yi approaches 1, [15].

In the first experiment, cumulative histograms

for the reference, sample, and image of the

difference were calculated. They are shown in

Figure 10 for one pair of tested images. Analysis of

the charts demonstrates that two pairs of charts can

be used as input in the artificial neural network.

These pairs are cumulative histograms of the

original template and sample images or cumulative

histograms of the image differences. In the second

case the difference between the two correct images

does not contain pixels of defects and the

cumulative histogram has only zero values. The

second case was taken for the experiment because it

allows to increase in the distance between the zero-

value chart and the chart of the difference.

a b

Fig. 10: Cumulative histograms of two PCBs (a) and

of the difference image (b)

For the experiment, the two classes were

selected, which ANN should recognize and

distinguish from one another – images with defects

(fragments of PCBs), and without defects (two

examples are shown in Figure 11).

a b

Fig. 11: Two fragments of PCB images: with defects

(a), and without defects (b)

In the first experiment, 90 percent of the dataset

was used for training the neural network, and 10

percent for testing it. The neural network was

trained over 200 epochs, and the training process

required a total duration of approximately 3 hours.

As a result, the accuracy of the test dataset was

approximately 75 percent. The change in the

accuracy of the training process is shown in Figure

12.

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Fig. 12: Neural network accuracy evolution over

epochs for training and testing data

As a result, fragments are divided into two

classes. Two examples from them are shown in

Figure 13, defective and valid circuits with a

probability of their recognition.

a b

Fig. 13: Correct classification result of the printed

circuit board with defects (a) and without defects (b)

The second experiment involves the use of the

average mathematical value of the brightness of

pixels. Each corresponds to a separate grid cell.

This grid covers and divides the image into small

parts. This feature encapsulates a variety of

information, including the brightness in certain areas

and the corresponding coordinates associated with

that brightness.

The grid covers not the sample but the different

image containing positive and negative pixels.

Figure 14 illustrates the input image for the

calculation of the mathematical means and later for

processing by ANN. For illustration, a grid has a

dimension of 10×10. In practice 20×20.The input

chart for the ANN is shown in Figure 15.

Fig. 14: Grid 10×10 on the difference image (its

sizes are on the OX, and OY axes)

Fig. 15: Mathematical means in cells (opposite signs

mark the two colors)

For the second experiment, 90% of the dataset

was used for training of the neural network, 10% for

testing of it. The cell size was set to 32 pixels in two

coordinates. With a configuration of (640 / 32) *

(640 / 32) = 400 input nodes, the neural network

was trained over 200 epochs, which took

approximately 4 hours. As a result, the accuracy of

the test dataset was approximately 90 percent and

fragments were divided into two classes. Two

examples from them are shown in Figure 16.

a b

Fig. 16: Correct classification result of the printed

circuit board without defects (a) and with defects (b)

In summary, the more pixels the difference

image contains, the higher the probability observed

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in both experiments when classifying defective

samples.

5 Separation of Defects

After the subtraction-comparison operation, two sets

of defects are distinguished. The first is

characterized by metal deficiency and the second by

excess metal. They are denoted as positive (red p)

and negative (blue n) defects if the reference image

is reduced and the sample image is subtracted:

P= Pe + Ps or P= Pp + Pn.

All shortage metal defects are neighboring to

the constructive elements: tracks and pins. Among

extra metals, defects are neighboring to the

constructive elements and some are isolated:

P= Pes +Pei + Ps ,

where Pei is a set of isolated defects, and Pes is a set

of extra metal defects having contact with tracks or

pins.

All defects from the previous PCB image are

segmented and shown in Figure 17. By colors they

are grouped into two classes encircled by red and

blue.

Fig. 17: Two classes of defects: encircled with blue

is an extra metal, and with red is a shortage of metal

Colors are auxiliaries for defects, which

otherwise are grouped into two classes: those

isolated from the circuit and those associated with

traces or contacts. In turn, the second class is

divided into two subclasses: connection defects and

defects in the size and shape of structural elements.

Isolated defects are separated from the image

difference by an additional procedure. The

procedure applies the flood-filling algorithm to n

starting points representing each chain of the circuit.

The target color is white. Due to the tolerance value

black traces, red extra-metal defects, and shortage of

metal become white which is invisible for other

processing algorithms. An example of one filled

component is shown in Figure 18. For visual

demonstration, yellow is used in the figure instead

of white.

a b

Fig. 18: Two chains with defects before (a) and after

filling (b)

When all components are filled in white, defects

from Pes , Ps are invisible, and other defects from Pei

are marked in green to distinguish them from all

others previously discovered.

No one can tell if it is a short circuit, an open

circuit, or some other type of defect. In automatic

mode, all defects are grouped into only three classes

by color. As a rule, in the production process, all

defects are of different types, shapes, and sizes.

Neural networks trained on one type of defect will

necessarily miss other types.

All defects are visual, but there is no access to

their pixels. In such a presentation, they cannot be

taken as starting points or separated for analysis.

They cannot be transferred from one image to

another.

In this case, the hierarchical clustering

algorithm with a step 1×1 (one pixel) over a black

image is applied to form all connected areas of

defects. Two classes of defects Des and Ds associated

with traces and contacts are separated and then

clustered. This is illustrated in Figure 19(a) by

examples with clustered defects in two classes. In

Figure 19(b) defects are marked and selected with

different colors.

a b

Fig: 19: Increased clustered defects (a) and marked

with full colors (b)

All clustered defects are described as objects

with the coordinates of the pixels that form these

defects:

Pp (i)={(x1i,y1i),…,(xki,yki)}, k= | Pp(i) |,

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i=1,2,…,|Pp |

Identifiers are assigned to these objects. Class

numbers and the sequence positions in the class

serve as keys for access to them. They are planned

to be transferred to the canvas of the reference PCB

image. In this stage, defects are not identified by the

circuit number to which they belong.

6 Determination of Type and

Intensity of Defects

6.1 The Metal Deficiency Class

In automatic mode to identify these defects by the

trace sequence number there is no other way except

to fill the chain with a color different from the

existing one. The reference image of the printed

circuit board is a working model for the procedure

to determine open and short defects. It serves also

for the investigation of the influence of trace and

contact inaccuracies on the stability of the circuit.

Firstly, blue, and then red defects from

corresponding classes one by one are transferred to

the reference image. An example of one transferred

defect is shown in Figure 20.

Fig. 20: The reference PCB covered by an object

(defect)

Initial points are formed earlier according to the

thinning algorithm. They form the so-called chain

status monitor. It is shown in Figure 21 only for the

two k-th and (k+1)-th chains.

Fig. 21: Two status monitors of two chains: the

(k+1)-th chain is filled

It's like a traffic light: green - no fill result, red -

all identification points of the chain have changed

color. Since the monitors are linked to tracking

numbers, the transmitted defect receives its

identification number when all points of the chain

have changed color.

The received identifier makes it possible to

select a clean reference chain and a manufactured

chain with a defect by adding to the reference a

transferred defect. These two circuits are the basis

for analyzing the effect of the defect on the

operation of the circuit.

Such a procedure is implemented for each

object belonging to the metal deficiency class Ps and

the additional metal class Pe. Elements from the first

class insert defects such as circuit breaks and

reduction of the conductive surface, and from the

second-class short circuits and an increase in the

conductive surface.

The input data are the starting points of the k-th

chain, coordinates of the pixels forming the s-th

defect, and a traffic green light with all green

components.

When the object defect is transferred the filling

algorithm is applied to its pixels marking it with

white. This operation returns the state of the circuit

to what it was in the produced circuit with one

defect. Figure 22 shows one chain in which the red

defect was marked in white.

Fig. 22: One chain for testing

Now, taking on the element from the set Pk as

the starting point the flood-fill algorithm fills this

chain with red. After filling, the traffic light is

yellow because its components are red and green

(Figure 23(a)). The k-th chain receives two

components of contacts and traces marked with

black and red (Figure 23(b)).

a

b

Fig. 23: The chain status monitor (a) of the partially

filled chain (b)

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As a result, after one iteration, a type of defect

and its coordinates are determined.

6.2 The Extra Metal Class

When an additional metal object representing a short

defect is transferred to the image, a similar process

takes place. This involves barrier-free filling from

the pixel of the extra metal object to ascertain the

number of connected chains, whether it's one or a

few. Filling the blue object with black, and then

together with the rest of the associated chain with

red, selects the circuit. Figure 24(a) demonstrates

how the short defect causes the two chains to be

filled with red. Status monitors of these chains

signal this occurrence. An example is shown in

Figure 24(b) indicating the number of the filled

chains (or numbers of some filled chains).

a

b

Fig. 24: Two chains with short circuit (a) and their

filled status monitors (b)

After termination of the procedure, all tested

objects are classified as three types of defects: open,

short circuit, and other associated with traces but not

affecting the connectivity of contacts.

6.3 Trace Resistance Defects

If the next object is not a connection defect, it

displays an increase or decrease in conduction

resistance due to a decrease or increase in metal

surface area. It is difficult to find an accurate

estimate of the value that indicates a hundred

percent failure because the defect can be

concentrated in one place or distributed over traces

and contacts. Therefore, the defect is measured as

distributed, which is calculated by the surface

square and the surrounding perimeter. Also, the

defect can be measured as concentrated when

calculated only in areas of its placement.

A distributed change in the resistance of the

entire track is indicated by a change in the width of

the entire track DW. A local concentrated change in

resistance in a certain section of the track is

indicated by a local change in the width Wd of the

track in this section.

For example, Figure 25 shows two fragments of

traces without and with defects of a lack of metal.

The width of the track and its length are marked.

Defects with a lack of metal, which causes a change

in resistance, are circled. Sections with a decreased

width are marked.

Fig. 25: Two chains: reference (a), with defects (b)

The trace conductance resistance Rs is

proportional to the length L of the trace and

inversely proportional to its width W:

Rs ≈(L/ W)

Traces in the reference and manufactured PCBs

have almost the same length but due to defects can

differ by a width in some places. This difference

can be measured approximately. For that squares S1,

S2 of two chains are calculated. Borders of two

chains are found by the edge detection algorithm [24]

and their two lengths are measured. A border’s

length is twice as large as a trace’s length. For two

traces in Figure 26(a) and Figure 26(c), measured

values for the reference circuit are S1=865, L1=204,

and for the circuit with defects S2= 780, L2=236, i.e.,

in the second case, the area is smaller, and the

length is longer.

a b

c d

Fig. 26: Chains and their edges with and without

defects: small chains (a, c), large chains (b, d)

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A trace’s length is twice as short as a border’s

length:

L1(t)=L1/2, L2(t)=L2/2.

The approximated average widths of the two

traces are as follows:

W1=S1/L1(t), W2=S2/ L2(t).

These widths are average and approximate.

They are not equal exactly to real widths. They are

required only for the estimation of losses in the

resistance.

In the case of the small trace in Figure 26(a)

W1=8.4, W2=6.6. For the whole length the integrated

distributed width difference DW=W2-W1=-1.8 is

essential due to the small sizes of the traces (only

two close contacts). For large sizes, it is much

smaller.

The concentrated difference caused by a change

in squares and lengths in chains with defects is

calculated by the following formulas:

Sd= S2 -S1, Ld= L2 -L1 , Wd= Sd/ Ld.

For the example in Figure 26(c) a change in the

width caused by a defect approximately is equal:

Sd=-85, Ld=32, and Wd=-2.7.

The minus sign in Wd indicates that the defect is

due to a lack of metal. The obtained value is

compared to the average width W1 of the reference

chain (8.4) to determine whether a new width or a

new resistance will affect the work of the

manufactured circuit. In the considered case the new

width is as follows:

W1n=W1+Wd=8.4-2.7= 5.7.

So, the width difference in a place of defects is

2.7 which exceeds 30 percent of the reference

value. The conduction resistance of the trace

increases in accordance.

One more example with the larger chain is

shown in Figure 26(b) and Figure 26(d). For this

sample, the calculated features are of the following

values: S1=5529, S2=5421, L1=1348, L2=1410,

L1(t)=674, L2(t)=705,

W1=8.20, W2=7.68,

Sd=-108, Ld=62, and Wd=-1.74

The integrated difference W2-W1=-0.52 is small

compared with the reference width W1=8.20 (6

percent). However, the concentrated average

difference Wd=-1.74 is about 22 percent of the

reference value. Defects in some places can increase

the resistance by a larger percentage. In this case,

the scheme's failure is a matter of time.

All measured values are in pixels and easily

converted to real values. The difference in width is

negative in the case of a lack of metal and positive

in the case of an excess of metal in traces and

contacts.

The last case is demonstrated in Figure 27.

a b

Fig. 27: Fragments and their edges without defects

(a), and with defects (b)

For separated fragments S1=775, L1=120 (240/2),

and for the circuit with defects S2= 870, L2=124

(247/2), i.e., in the second case, the area is greater,

and the length is longer. After the calculation of

intermediate values, the widths of the chains and the

difference are as follows:

W1=6.46, W2=7.04, DW= W2- W1=0.58.

The difference between the lengths

Ld= L2 – L1= 7

does not correspond to the real size of a defect

because a part of the defect length belongs also to

the reference trace and is subtracted.

So, in the case of an extra metal, a defect must

be presented in its determined color: red or blue. An

example is shown in Figure 28(a). Then, the

determined edge contains three components: the

main native black, red for the external border of the

defect, and green for the common border between

the trace and defect.

a b

Fig. 28: A fragment with defect (a) and its edge (b)

Now the difference between trace areas is Sd=95

which is a square of the defect, and the length of the

red edge is Ld=43. Under these conditions, the

concentrated width of the trace in one place is

Wd=95/43=2. Additional metal causes the final

difference Wd=2 which is more than 30 percent of

the reference width. The conduction resistance is

reduced by one-third in this place. On the contrary,

the distributed losses of resistance show less than 10

percent.

In conclusion, two criteria of the failure caused

by defects in traces are possible: tolerance on the

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DOI: 10.37394/23201.2024.23.7

Roman Melnyk, Vitalii Vorobii

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distributed width of the trace DW and tolerance on

the concentrated width of the trace Wd.

6.4 Division of Traces into Fragments

The conduction resistance can be accepted as a

criterion function for detecting defects and checking

the functionality of the circuit by analyzing its

printed circuit board. In this case, the shift of tracks

and small changes in their size are not considered

automatically. For example, Figure 29 shows two

fragments: one is the reference image and the

second is the difference between it and the shifted-

by-pixels fragment. Are there defects in the traces?

It is difficult to answer. The summary number of red

or blue pixels is large enough.

a b

Fig. 29: Fragments of PCB image (a) and its

difference with shifted one (b)

When considering the traces as reference, with a

lack of metal and with an excess of metal in Figure

30 their approximate widths are of the following

values W1=3.46, W2=3.26, W3=4.35.

Fig. 30: Chains without and with defects

Unfortunately, in this approach, only one

parameter characterizes the chain in the reference

and sample PCB image. Changes in the local

conductance resistance could be distributed along

the resistance of other parts belonging to the long

trace. Then the defect is compensated by the correct

values of the parameter. So, in the previous

approach, only places with defects were analyzed.

It is possible to exclude the preliminary

detection of the location of defects if the concept of

distributed conductive resistance of the track is used.

Namely the values of the width of the track in its

various sections. Instead of one parameter W, the

trace should be characterized by the vector W= (W1,

W2,…,Wn), where n is the number of sections of a

trace.

In general, trace division is a complex and

separate problem, [25], since the traces have a

horizontal, vertical, and hybrid arrangement. They

are of different sizes and irregular shapes. Traces are

uniform in color. The number of parts is planned

according to the area of the entire trace and the size

of the separated part. Therefore, each trace is

considered for division into parts separately.

The main idea used for the division of a trace is

flood-filling them with different colors. At the

beginning the mask image with n parts – for

example, rectangles is generated. Each rectangle is

filled in its random color. An example with 6 parts

is shown in Figure 31(a).

a b

Fig. 31: Rectangles with 6 random colors (a) and

overlay with a black chain (b) by its sizes

Then an image with the black trace is overlayed

with rectangles by the following formula applied to

every channel of the pixel:

󰇛󰇜󰇛󰇜󰇛  󰇜󰇛󰇜󰇛󰇜

where Ir, Ic, Ib are the pixel intensity of the resulting,

rectangles, and chain images, α is the coefficient of

transparency. The resulting image with four

rectangles is shown in Figure 32(a).

Now, four fragments are characterized by four

various colors. They are easy to select by applying

the flood-filling algorithm to fragments and

backgrounds. They are shown in Figure 32(b).

Fragments of the trace are ready for the principal

processing: edge detection and measurements of the

area and length of the perimeter.

a b

Fig. 32: Overlay of the chain and rectangles (a) and

its filled sections (b)

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DOI: 10.37394/23201.2024.23.7

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Volume 23, 2024

In the case of the trace with defects from Figure

30 rectangles and the trace are overlayed, flood-

filled, and separated too (Figure 33).

a b

Fig. 33: Overlay of the chain with defects and

rectangles (a) and its filled sections (b)

After processing the two traces in the reference

and sample images they are characterized by two

vectors of fragmentary conductance resistance (in

this case, the trace width):

Wr = (Wr1, Wr2, …,Wrn) , Ws= (Ws1, Ws2, …,Wsn),

where n is the number of fragments, the same for

similar traces and different for other traces.

The two conduction resistance vectors are

calculated and have the following components:

Wr = (8.20, 7.42, 9.16, 9.41),

Wr = (7.20, 7.53, 8.96, 7.12).

The vectors show that the two metal deficiency

defects increase resistance on the green and red

sections of the trace. Losses are 12 and 24 percent in

accordance.

The two types of defects affect resistance

diametrically oppositely: a lack of metal increases,

and an excess of metal decreases the resistance in

the trace. Therefore, criterion functions are formed

separately for each case:

M=sqrt { 1/N-*∑ (Wrk (i) - Wsk-(i))2},

P=sqrt{ 1/N+*∑ (Wrk(i) - Wsk+(i))2},

where M is a standard deviation for defects Wsk-(i)

reducing the resistance, and P is a standard

deviation for defects Wsk+(i) increasing the

resistance, N-, N+ are the numbers of correspondent

defects in all traces determined after they were

processed, i is the sequence number of the trace, k is

the sequence number of the section in the trace.

As a result, all inaccuracies in the components

of the printed circuit board are measured and

prepared to decide the readiness of the circuit for

operation or not.

To visualize the location and type of defects, the

difference in the resistance parameters is checked in

comparison with the tolerance value set by the user:

tol+ for additional resistance, and tol- for reduced

resistance:

Wrk (i) - Wsk-(i)> tol-,

Wrk(i) - Wsk+(i)> tol+.

If one of the equations is satisfied, the section

Wsk-(i) is filled in blue, or the section Wsk+(i) is filled

in red. the tolerance can be chosen such a value that

the scheme should not only be marked but also

rejected.

7 Conclusion

The work is devoted to the investigation of the ANN

application to learn and recognize defective PCB

images by their features, particularly: the cumulative

histograms of defect pixels, and the grid cell

intensity mean. Testing of the implemented

algorithms has revealed, that trained single-layer

ANN can successfully classify the PCB images,

where the aspect is placed on the range of defect

colors and their location.

The approach includes such algorithms and

methods as mathematical formulas of comparison,

the filling algorithm for selecting, separating, and

dividing chains, formulas for calculating the

resistance characteristics of circuit components, and

K-means clustering for the selection of objects in

the PCB image.

The proposed approach contains operations for

the selection of three classes of defects: negative,

positive, and connection. Marked with different

colors, these defects are used to train the single-

layer neural network for further automatic division

of the PCB image into two classes: having defects

and without defects. It reduces the time consuming

of the developed software which is planned to

indicate the location and determine the intensity of

defects. In conclusion, such software will reduce

hardware and make the PCB diagnostic process

cheaper.

The goal of future work is to modify the

subtraction operation using an approach that is

independent of the bias and dimensions of the tracks

and pins. To do this, it is necessary to investigate

new features of printed circuit boards, such as the

description of connection defects, excess and lack of

metal, resistance properties, and the absence of

contact areas. The development of the automation of

circuit division into parts, the creation of specific

neural networks for printed circuit board images,

and their application to recognize defective circuits

is envisaged.

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DOI: 10.37394/23201.2024.23.7

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E-ISSN: 2224-266X

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Volume 23, 2024

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors contributed in the ratio of 70 (Melnyk)

to 30 (Vorobii) in the present research, at all stages

from the formulation of the problem to the final

findings and solution.

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.

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

https://creativecommons.org/licenses/by/4.0/deed.en

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