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Robust and automatic measurement of grinding-induced subsurface damage in optical glass K9 based on digital image processing

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Optical glass K9 is a critical kind of optical materials, however experiments have indicated that the mechanical grinding of K9 easily led to subsurface damage (SSD). Although substantial SSD measurement methods have been suggested, the problems including the prior knowledge of SSD and slow measurement speed still impede the reported method applications. To this end, this paper has presented an image-process-based method that can identify and measure the grinding-induced SSD in K9 specimens. By performing grinding trials, the method has been found to be able to accurately (with biggest relative error of 3.13% in comparison with the manually measured results) and quickly (with the measurement speed of 1.68 s per image) measure SSD depths. Without any parameter presetting, the method enables automatic SSD measurements, allowing the users without SSD knowledge to be able to use the method. Moreover, the method has shown the good robustness to the input image size, illumination, tilted specimen placement, and material flaws. The method is therefore anticipated to be meaningful for the industrial manufacturing, design and application of optical glass.
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Original
Research
Article
Robust
and
automatic
measurement
of
grinding-induced
subsurface
damage
in
optical
glass
K9
based
on
digital
image
processing
Yong
Jie
Zhao,
Yun
Hui
Yan,
Ke
Chen
Song,
Hao
Nan
Li *
School
of
Mechanical
Engineering
and
Automation,
Northeastern
University,
Shenyang
110819,
China
1.
Introduction
Optical
glass
K9
offers
good
optical
transparency,
high
hardness,
and
superior
wear
resistance,
and
therefore
is
considered
as
one
of
the
most
widely
employed
materials
in
the
optics
industry
[1].
However,
many
experimental
observations
[1,2]
have
indicated
the
mechanical
grinding
process
of
K9
easily
led
to
subsurface
damage
(SSD).
The
grinding-induced
SSD
can
be
characterized
by
the
cracks
nucleating
at
the
machined
surface
and
vertically
spreading
tens
of
micrometers
to
the
specimen
bottom
[3],
and
has
been
found
[4,5]
harmful
to
both
mechanical
properties
and
optical
performances
of
K9
products.
To
this
end,
many
methods
have
been
suggested
to
evaluate
the
grinding-induced
SSD
in
brittle
materials,
and
most
proposed
methods
can
be
generally
categorized
into
(i)
indirect
and
(ii)
direct
methods.
Indirect
methods
usually
evaluate
SSD
depths
based
on
certain
physics,
chemistry
or
mechanics
principles,
so
that
any
additional
operations
to
expose
subsurface
cracks
can
be
avoided.
Lundt
et
al.
[6]
have
quantied
the
subsurface
cracks
by
utilizing
the
scanning
infrared
depolarisation
effect,
where
the
SSD
depths
were
quantied
by
analyzing
the
missing
wavelengths
of
the
polarized
laser
beam
that
can
penetrate
the
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
4
May
2017
Accepted
25
July
2017
Available
online
Keywords:
Measurement
Optical
glass
Image
processing
Subsurface
damage
Grinding
a
b
s
t
r
a
c
t
Optical
glass
K9
is
a
critical
kind
of
optical
materials,
however
experiments
have
indicated
that
the
mechanical
grinding
of
K9
easily
led
to
subsurface
damage
(SSD).
Although
substantial
SSD
measurement
methods
have
been
suggested,
the
problems
including
the
prior
knowledge
of
SSD
and
slow
measurement
speed
still
impede
the
reported
method
applications.
To
this
end,
this
paper
has
presented
an
image-process-based
method
that
can
identify
and
measure
the
grinding-induced
SSD
in
K9
specimens.
By
performing
grinding
trials,
the
method
has
been
found
to
be
able
to
accurately
(with
biggest
relative
error
of
3.13%
in
comparison
with
the
manually
measured
results)
and
quickly
(with
the
measurement
speed
of
1.68
s
per
image)
measure
SSD
depths.
Without
any
parameter
presetting,
the
method
enables
automatic
SSD
measurements,
allowing
the
users
without
SSD
knowledge
to
be
able
to
use
the
method.
Moreover,
the
method
has
shown
the
good
robustness
to
the
input
image
size,
illumination,
tilted
specimen
placement,
and
material
aws.
The
method
is
therefore
anticipated
to
be
meaningful
for
the
industrial
manufacturing,
design
and
application
of
optical
glass.
©
2017
Politechnika
Wrocławska.
Published
by
Elsevier
Sp.
z
o.o.
All
rights
reserved.
*
Corresponding
author.
E-mail
address:
lhnlwfb@163.com
(H.N.
Li).
Available
online
at
www.sciencedirect.com
ScienceDirect
journal
homepage:
http://www.elsevier.com/locate/acme
http://dx.doi.org/10.1016/j.acme.2017.07.009
1644-9665/©
2017
Politechnika
Wrocławska.
Published
by
Elsevier
Sp.
z
o.o.
All
rights
reserved.
K9
substrate.
However,
the
precise
control
of
the
laser
beam
poweris also in demandotherwisethe laserwouldprobably burn
the
K9
sample.
Aida
et
al.
[7]
have
evaluated
the
grinding-
induced
SSD
depths
in
the
GaN
substrate
based
on
the
cathodoluminescence
effect.
However,
the
additional
experi-
ments
[8]
haveproved that the electrons
impactingon the optical
glass
would
probably
degrade
the
functional
performances
(e.g.
optical
transmissivity)
of
K9.
A
series
of
interesting
studies
by
Li
et
al.
[9],
Lv
et
al.
[4]
and
Yao
et
al.
[1]
established
the
explicit
mathematical
relationships
between
the
ground
surface
rough-
ness
R
z
and
the
SSD
depths
so
that
SSD
values
can
be
obtained
based
on
measured
R
z
.
However,
substantial
assumptions
have
been
made
in
these
above
studies.
Although
indirect
methods
would
not
introduce
any
additional
SSD,
expensive
equipment,
high
requirement
of
professional
knowledge,
and
complex
calculationsduringthe SSD measurementare still neededforthe
indirect
SSD
evaluation.
Moreover,
the
material
aw
may
also
largely
inuence
the
measurement
accuracy
[10,11].
In
comparison,
direct
SSD
evaluation
methods
have
been
believed
more
reliable,
because
the
subsurface
cracks
would
be
somehow
exposed
in
the
direct
methods
so
that
the
crack
depths
are
visible
and
measureable.
Tonshoff
et
al.
[12]
and
Esmaeilzare
et
al.
[13]
have
proposed
the
angle
polishing
method
(APM),
where
the
ground
K9
surface
was
lapped
and
polished
under
an
angle
of
about
308
and
then
the
exposed
subsurface
cracks
were
measured.
The
results
have
proved
the
method
feasibility,
but
the
polishing
operation
may
introduce
additional
SSD.
Pei
et
al.
[14]
have
proposed
the
section
polishing
method
(SPM),
where
before
grinding
the
K9
sample
was
rstly
cleaved
into
two
parts,
then
the
interested
cross-
sections
were
carefully
polished
to
remove
any
cracks,
and
nally
glued
together,
so
that
SSD
can
be
measured
after
the
grinding
process
by
melting
the
glue
and
observing
the
subsurface
cracks
in
the
interested
cross-sections.
However,
during
the
grinding
process,
the
material
behaviors
of
the
glued
sample
may
differ
from
the
original
sample
as
the
second
phase
material
(i.e.
glue)
was
introduced.
A
more
reliable
direct
method
has
been
presented
by
Li
et
al.
[911],
in
which
a
slot
(1
mm
width
and
5
mm
uncut
margin)
was
rstly
produced
from
the
bottom
of
the
specimen,
and
then
a
soft
rubber
hammer
impacted
the
specimen
so
that
the
specimen
can
be
cleaved
along
the
energetically
preferential
crystalline
plane
and
therefore
the
newly-introduced
SSD
can
be
minimized.
Although
direct
SSD
evaluation
methods
have
been
believed
more
reliable
than
indirect
methods,
the
SSD
measurement
in
direct
methods
still
requires
human
involvement
after
the
SSD
micrographs
(see
typical
example
given
in
Fig.
1)
are
captured.
Even
trickier
problems
may
include:
(i)
the
ground
surface
in
most
cases
is
tilted
therefore
the
SSD
depth
in
Fig.
1
should
be
‘‘SSD’’,
rather
than
‘‘L
1
’’
according
to
the
SSD
denition
[15].
However,
most
microscopes
can
not
precisely
identify
and
measure
this;
(ii)
the
prior
professional
knowledge
of
SSD
is
required
during
the
manual
measurements,
and
(iii)
the
manual
measurement
of
SSD
depths
may
be
feasible
only
when
small
quantities
of
measurements
are
required.
Based
on
above,
the
critical
need
for
the
automatic
SSD
measurements
would
become
increasingly
pronounced
when
considering
the
demanding
requirements
from
the
modern
industrial
manufacturing.
To
ll
this
gap,
this
paper
presents
an
image-process-technique-based
method
that
can
robustly
and
automatically
identify
and
measure
the
grinding-induced
SSD
in
optical
glass
K9.
The
method
is
believed
to
be
able
to
considerably
stretch
the
limitations
of
most
of
the
direct
methods
reported
in
the
literature
(e.g.
Ref.
[914]),
and
promote
the
realization
of
the
automatic
SSD
measurements
in
large
quantities.
Therefore
the
method
is
anticipated
to
be
meaning-
ful
and
helpful
for
not
only
the
industrial
manufacturing,
but
also
the
design
and
application
of
optical
glass.
2.
Method
description
2.1.
Method
owchart
The
proposed
method
mainly
includes
three
modular
algo-
rithms
(MAs)
(see
Fig.
2):
MA
(i)
the
recognition
and
reconstruc-
tion
of
the
tilted
ground
specimen
surface,
MA
(ii)
the
recognition
of
the
subsurface
cracks,
MA
(iii)
the
calculation
of
the
SSD
depths
by
using
the
unit
of
pixels,
and
MA
(iv)
the
recognition
of
the
scale
bar
and
the
SSD
length
unit
conversion
from
pixels
to
length
units.
2.2.
Recognition
and
reconstruction
of
the
ground
specimen
surface
The
basic
principle
of
the
ground
surface
recognition
is
based
on
an
important
feature
of
SSD
micrographs:
a
dark
region
without
any
visual
details
is
located
at
the
top
of
the
ground
specimen
surface
because
the
specimen
thickness
changes
the
optical
pathway
around
the
ground
surface
(see
Fig.
3a).
Therefore,
no
matter
the
surface
is
tilted
or
not,
the
bottom
prole
of
the
dark
region
can
be
approximately
regarded
as
the
ground
specimen
surface,
which
can
be
further
employed
as
the
landmark
for
the
SSD
measurement.
The
detailed
recognition
procedures
are
as
follows:
(i)
Considering
the
aim
of
the
proposed
method
is
to
automatically
measure
SSD
depths
in
large
quantities,
the
measurement
speed
should
be
as
fast
as
possible.
Therefore
the
captured
SSD
micrographs
(see
Fig.
1)
are
rstly
converted
into
the
gray
images
(see
Fig.
3b).
Fig.
1
Captured
cross
section
micrograph
with
subsurface
damage.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
321
Fig.
3
(a)
The
basic
principle
of
the
recognition
of
the
ground
specimen
surface
based
on
the
dark
region,
(b)
the
converted
gray
SSD
micrograph,
(c)
the
edge
detection
result
by
using
the
Canny
edge
detector,
(d)
the
extraction
of
the
bottom
profile
of
the
dark
region,
(e)
the
morphological
erosion,
(f)
the
morphological
reconstruction,
(g)
the
linear
fitting,
and
(h)
the
final
detection
result
of
the
ground
specimen
surface.
Fig.
2
Proposed
method
flowchart.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0322
(ii)
Because
from
the
cross-section
view
the
ground
surface
should
be,
in
theory,
a
prole
with
the
micro-scale
details
(e.g.
the
roughness
and
waviness),
the
classic
multi-scale
Canny
edge
detection
algorithm
[16]
is
therefore
employed
to
the
captured
SSD
micrographs
so
that
the
ground
surface
prole
(see
'A'
in
Fig.
3c)
can
be
successfully
detected.
(iii)
The
next
step
to
identify
the
ground
surface
is
to
extract
the
upper
part
of
the
detected
edges
in
Fig.
3(c)
by
keeping
the
uppermost
pixel
of
the
detected
edges
in
each
pixel
column
of
the
micrograph
and
removing
all
the
other
detected
edge
pixels
(Fig.
3d).
(iv)
Some
false
ground
surface
pixels
(see
'B'
in
Fig.
3d)
may
be
kept
due
to
the
discontinuity
of
the
ground
surface
in
certain
pixel
columns.
To
x
this,
the
morphological
erosion-reconstruction
algorithm
is
employed.
Morpho-
logical
erosion
can
be
considered
as
an
operation
that
can
effectively
recognize
certain
specic
features
and
then
present
the
features
by
using
the
merged
structure.
Suppose
I
is
the
binary
data
of
Fig.
3(d),
the
morphological
erosion
operation
can
be
mathematically
expressed
as
[17]
O
¼
IQB1¼
faB1Þa
Ig
(1)
where
the
structure
element
B
1
is
set
as
[1,1,1,1,1,1,1,1]
to
recognize
straight
lines.
Morphological
reconstruction
can
expand
the
erosion
result
by
iteratively
presenting
certain
features,
i.e.
[17]
Hkþ1¼
ðHkB2Þ
\
I
(2)
where
H
k
denotes
the
reconstructed
result
after
the
kth
iteration
(k
=
1,
2,
3.
.
.),
the
structuring
element
B
2
is
set
as
1
1
1
1
1
1
1
1
1
2
43
5to
expand
certain
features,
and
the
operator
refers
to
the
dilation
operation,
i.e.
[17]
HkB2¼
fa~
B2Þa\
Hk
Hkg:
(3)
The
SSD
micrographs
processed
by
the
morphological
erosion
and
reconstruction
algorithms
are
separately
presented
in
Fig.
3(e)
and
(f),
where
the
false
detected
ground
surface
pixels
are
effectively
removed.
(v)
The
ground
surface
is
approximately
considered
as
the
linear
tting
result
of
the
extracted
uppermost
pixels
of
the
ground
surface
prole
given
in
Fig.
3(f).
The
basic
tting
function
form
is
set
as
y
=
ax
+
b,
therefore
the
tilted
angle
b
of
the
specimen
can
be
expressed
as
b
=
arctan(a).
2.3.
Recognition
of
the
subsurface
cracks
After
the
ground
surface
is
recognized,
the
deepest
SSD
depth
should
also
be
determined
by
the
following
steps:
(i)
The
revised
saliency
estimation
method
is
performed
to
the
converted
gray
images.
The
revised
method
is
similar
to
the
classic
one
proposed
in
Ref.
[18],
but
the
difference
is
all
the
operations
are
performed
to
the
gray
value
of
each
pixel,
rather
than
to
the
3D
color
data
in
the
CIELAB
color
space.
When
the
image
coordinate
origin
is
dened
as
the
left-top
corner
of
the
image
(see
the
coordinate
in
Fig.
4),
then
the
revised
method
can
be
mathematically
expressed
as:
Sðx;
yÞ
¼
kPxþx0
xx0Pyþy0
yy0Gðx;
yÞ
APðx;
yÞk
(4)
where
G(x,y)
is
the
gray
value
of
the
pixel
locating
at
the
coordinate
(x,y),
S(x,y)
is
the
saliency
value
of
this
pixel,
P(x,y)
is
the
pixel
gray
value
ltered
by
the
Gaussian
lter,
A
is
the
total
number
of
the
pixels
within
the
neighboring
Fig.
4
The
results
by
performing
the
(a)
revised
saliency
estimation,
(b)
threshold
segmentation,
(c)
morphological
erosion,
and
(d)
morphological
reconstruction.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
323
rectangular
region
with
[x
x
0
,
x
+
x
0
]
along
the
x
direction
and
[y
y
0
,
y
+
y
0
]
along
the
y
direction.
The
output
result
by
using
the
revised
saliency
estimation
method
is
presented
in
Fig.
4(a).
(ii)
Then
the
threshold
segmentation
is
adopted
to
segment
the
subsurface
cracks.
Here
the
self-adapted
Otsu
thresh-
old
based
on
Ref.
[17],
rather
than
the
xed
(or
constant)
threshold,
is
calculated
and
used
for
each
different
image.
The
basic
idea
of
the
determination
of
the
Otsu
threshold
T
is
[17]:
when
the
gray
image
can
be
segmented
into
two
groups
(i.e.
the
interested
target
and
the
background),
the
Otsu
threshold
T
would
result
in
the
maximal
difference
of
the
sum
of
the
gray
values
of
each
group,
i.e.
Let
n
i
denote
the
number
of
the
pixels
having
the
gray
value
i
and
L
refers
to
the
maximal
gray
level
of
the
image
(with
M
pixel
length
and
N
pixel
width),
the
probability
of
pixel
having
the
gray
value
i
would
be
pi¼ni
MN:
(5)
Hence,
the
probabilities
of
the
two
groups
(i.e.
the
interested
target
and
the
background)
v
1,2
are
respectively
v1¼X
T
0
pi
v2¼X
L
Tþ1
pi¼
1v1
:
(6)
Therefore,
the
average
gray
value
for
the
two
groups
are
respectively
g1¼PT
0ipi
v1
g2¼PL
Tþ1ipi
v2
:
(7)
Thus,
the
total
gray
value
of
all
the
pixels
in
the
image
is
gT¼X
L
0
ipi(8)
i.e.,
the
difference
of
the
sum
of
the
gray
values
of
the
two
groups
(denoted
as
s2
B)
is
s2
B¼
v1g1gT
2þ
v2g2gT
2
:
(9)
Hence,
the
Otsu
threshold
T
is
the
gray
value
which
allows
Eq.
(9)
to
reach
the
maximum
value.
Fig.
4(b)
presents
the
result
by
performing
the
Otsu
threshold
segmentation.
(iii)
Noise
pixels
(see
'C'
in
Fig.
4b)
are
also
remained
in
the
image
after
performing
the
threshold
segmentation,
therefore
the
similar
morphological
erosion-reconstruction
(see
Section
2.2)
is
conducted
once
again
(see
results
in
Fig.
4d).
(iv)
The
deepest
subsurface
crack
depth
then
can
be
obtained
by
searching
each
pixel
within
the
detected
subsurface
cracks
in
Fig.
4(d)
until
the
pixel
having
the
maximum
y
coordinate
is
found
(see
the
pixel
(x,
y
max
)
in
Fig.
4d).
2.4.
Calculation
of
the
SSD
depths
When
both
the
ground
surface
and
the
deepest
subsurface
crack
are
recognized,
the
SSD
value
can
be
obtained
based
on
the
geometrical
relationship
as
shown
in
Fig.
5.
The
SSD
depth
can
be
obtained
based
on
the
point-to-line
distance
[19],
i.e.
SSDpixel ¼
distance
axy
þ
b
¼
0;
x;
ymax
¼jaxymax þ
bj
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a2þ
1ð
Þ2
q:
(10)
2.5.
SSD
Length
conversion
based
on
the
automatic
recognition
of
the
scale
bar
Note
that
the
SSD
calculated
by
Eq.
(10)
is
expressed
by
the
unit
of
pixels,
therefore
the
realistic
SSD
depths
can
only
be
achieved
by
the
length
conversion
based
on
the
scale
bar
given
in
the
image.
However,
in
most
measurement
cases,
the
scale
bar
is
automatically
placed,
and
more
importantly,
scaled
and
changed
depending
on
the
used
magnication
of
the
micro-
scope.
This
section
therefore
aims
to
automatically
recognize
the
scale
bar
so
as
to
nally
express
SSD
depths
by
length
unit.
The
scale
bar
automatically
generated
by
the
microscope
Olympus
BX51M
is
employed
as
an
example
in
this
study.
As
seen
in
Fig.
6(a),
the
automatic
recognition
of
the
scale
bar
generally
includes
three
steps:
recognition
of
the
(i)
scale
bar
region
and
scale
bar
length
(unit:
pixels),
(ii)
recognition
of
digit
and
unit
character,
and
(iii)
conversion
of
the
SSD
depth
from
the
pixels
to
the
length
unit.
For
the
step
(i),
because
the
color
variation
near
the
boundary
of
the
white
scale
bar
region
tends
to
be
sharp,
the
scale
bar
region
is
detected
by
using
the
sobel
edge
detector
[20]
(see
the
result
in
Fig.
6b).
To
remove
noise
pixels
(see
'A'
in
Fig.
6b),
digits
and
unit
characters,
the
morphological
erosion-reconstruction
is
performed
by
using
the
structure
element
[1,1,1,1,1,1,1,1]
(detailed
in
Section
2.2)
so
that
only
the
straight
lines
including
the
region
boundary
and
the
scale
bar
can
be
recognized
and
kept
(see
the
result
in
Fig.
6c).
The
scale
bar
region
then
can
be
found
by
(i)
summing
up
the
gray
values
of
all
the
pixels
within
a
certain
row
and
column,
and
(ii)
searching
the
rst
and
last
peak
values
of
the
summed
gray
values
separately
among
all
the
rows
and
columns
in
the
image
(see
Fig.
6c).
Similarly,
the
scale
bar
length
N
c
(unit:
pixels)
can
be
determined
by
the
column
number
difference
between
Fig.
5
SSD
depth
calculation
(with
the
unit
of
pixels).
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0324
the
second
and
the
third
peaks
in
summed
gray
values
among
all
the
columns
in
the
image
(see
Fig.
6c).
For
the
step
(ii),
the
digits
and
the
unit
characters
are
extracted
by
removing
the
scale
bar
from
the
scale
bar
region
in
the
original
image
(see
Fig.
6d).
The
digit
and
character
recognition
is
implemented
by
using
the
template
matching
technique
[21]
with
the
templates
including
the
digits
from
0
to
9
and
the
characters
'd',
'c',
'm'
and
'm'
so
that
all
the
possible
units
automatically
generated
by
the
microscope
can
be
captured.
For
the
step
(iii),
assuming
the
recognized
digit
and
the
unit
is
l
c
,
the
realistic
SSD
depth
SSD
can
be
expressed
as:
SSD
¼
SSDpixellc
Nc
:
(11)
3.
Experimental
validation
of
the
method
To
validate
the
proposed
method,
grinding
trials
of
optical
glass
K9
have
been
performed
in
this
section.
The
commercial
optical
glass
K9
bricks
(Zenni
Optics
Co.)
with
25
mm
(length)
*
25
mm
(width)
*
5
mm
(height)
have
been
used.
Before
the
trials,
the
specimens
have
been
carefully
polished
so
that
any
scratches
from
previous
processing
was
removed.
As
seen
in
Fig.
7,
all
the
grinding
trials
have
been
performed
on
the
grinding
machine
tool
(M7150,
Shenyang
Machine
Tools
Co.)
by
using
the
diamond
grinding
wheel
(D120N100V751/8,
JR
Diamond
Tools
Co.).
Before
the
trials,
the
wheel
has
been
dressed
by
another
diamond
wheel
(D80S100V61/6,
JR
Diamond
Tools
Co.)
with
the
dressing
ratio
of
-0.6
and
dressing
depth
of
15
mm
(10
times).
During
the
trials,
the
K9
specimen
has
been
xed
on
the
jig,
and
a
wide
range
of
grinding
parameters
(see
Table
1)
have
been
used
so
that
different
depths
of
SSD
can
be
Fig.
6
(a)
illustration
of
the
scale
bar
region,
bar
length,
digits
and
unit
character,
(b)
results
by
using
the
sobel
edge
detector
[20],
(c)
recognition
of
the
scale
bar
region
and
bar
length,
and
(d)
digits
and
unit
characters
are
extracted
by
removing
the
scale
bar
from
the
scale
bar
region.
Fig.
7
The
experimental
setup
of
the
grinding
trials.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
325
Table
1
The
used
grinding
parameters.
Grinding
parameters
Values
Depth
of
cut,
a
p
(mm)
0.1,
0.2,
0.5,
0.8,
1.0,
1.2,
1.5,
2.0,
2.5,
2.7,
3.0,
3.5,
3.9,
4.0,
5.5,
6.0,
7.1,
8.0,
9.0,
10.0,
11.0,
12.0,
13.0,
14.0,
15.0,
20.0
Grinding
wheel
speed,
vs(m/s)
11,
12.4,
13.8,
15.3,
16.5,
17.9,
19.2,
20.6
Workpiece
feed
rate,
vw(mm/min)
2,
10,
20,
30,
40,
50,
60,
70,
80,
90,
100
SPECIFIC
material
removal
rate,
Q
(mm
3
/mm
min)
0.00021.5
Fig.
8
The
comparison
of
the
manually
measured
SSD
values
and
the
values
obtained
by
the
proposed
method
when
different
grinding
parameters
have
been
used.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0326
obtained.
The
SSD
measurement
method
has
been
completely
the
same
as
the
one
suggested
in
Refs.
[911].
4.
Validation
and
discussion
By
comparing
the
manually
measured
SSD
values
and
the
values
obtained
by
the
proposed
method,
the
method
evaluation
is
performed
from
the
following
three
aspects:
the
measurement
(i)
accuracy,
(ii)
speed
and
automaticity,
and
(iii)
robustness.
4.1.
Measurement
accuracy
4.1.1.
For
the
micrographs
captured
in
grinding
trials
Fig.
8
presents
the
validation
result
of
the
method
accuracy.
It
can
nd
that,
although
a
wide
range
of
grinding
parameters
have
been
used
and
the
SSD
depths
cover
from
4.95
to
24.17
mm,
a
good
agreement
between
the
manually
measured
SSD
values
and
the
values
obtained
by
the
proposed
method
is
presented.
The
biggest
relative
error
is
only
3.13%,
while
for
the
other
three
sets
of
comparisons
the
relative
errors
are
all
smaller
than
2%.
Considering
the
SSD
depths
in
the
industrial
grinding
process
are
commonly
within
the
range
from
5
to
15
mm
[9,10],
the
proposed
method
is
anticipated
to
be
able
to
measure
SSD
depths
with
high
accuracy.
4.1.2.
For
the
micrographs
reported
in
previous
studies
Fig.
9
presents
the
comparison
between
the
SSD
values
reported
in
Ref.
[13]
and
the
ones
detected
by
the
proposed
method.
It
shows
that,
the
subsurface
cracks
given
in
Ref.
[13]
can
be
accurately
recognized,
although
the
SSD
values
varied
from
24.27
mm
to
34.71
mm.
Among
the
comparisons
of
all
the
three
SSD
micrographs
provided
in
Ref.
[13],
the
biggest
relative
error
is
only
4.71%
while
the
smallest
one
even
reaches
2.10%,
proving
the
proposed
method
accuracy
to
a
large
extent.
4.2.
Measurement
speed
and
automaticity
By
measuring
the
SSD
depths
in
the
12
micrographs
given
in
Fig.
10,
the
total
SSD
measurement
time
is
found
to
be
20.12
s
(the
employed
computer
is
InterCore
i7-6500U
2.5
GHz),
meaning
the
method
measurement
speed
is
1.68
s
per
image.
It
would
be
almost
impossible
for
the
manual
measurement
to
be
faster
than
this
speed,
even
for
the
highly
skilled
operators,
indicating
the
advance
of
the
automatic
SSD
measurement.
It
is
also
noteworthy
that,
as
long
as
the
original
images
are
inputted
into
the
proposed
algorithm,
the
method
can
automatically
measure
SSD
depths
without
the
requirement
of
any
parameter
presetting.
This
high
automaticity
allows
the
users,
even
without
any
prior
professional
knowledge
about
SSD,
to
be
able
to
use
the
proposed
method.
4.3.
Method
robustness
As
mentioned
above,
the
realistic
SSD
images
may
be
various
in
terms
of
the
image
size,
the
surrounding
illumination,
the
tilted
angle
of
the
ground
surface,
and
the
material
aw
interference.
Therefore
the
proposed
method
should
be
robust
enough.
4.3.1.
Robustness
to
the
image
size
Fig.
11
shows
that
the
method
robustness
to
the
image
sizes.
It
can
nd
that,
although
for
the
shrinked
images
some
details
Fig.
9
The
comparison
between
the
SSD
values
reported
in
Ref.
[13]
and
the
ones
detected
by
the
proposed
method.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
327
are
missing
during
the
detection,
the
deepest
crack
depth
as
well
as
the
tilted
ground
surface
is
still
accurately
recognized.
Among
all
the
twelve
sets
of
comparisons
between
the
manually
measured
SSD
depths
and
the
automatically-
detected
ones
(see
Fig.
11a5d5),
only
two
relative
errors
are
more
than
8.88%,
indicating
the
good
robustness
of
the
proposed
method
to
the
image
resolution/size.
However,
it
should
also
note
that,
the
relative
errors
increase
when
the
image
sizes
are
reduced.
This
may
because
the
scale
bars
in
the
low-resolution
images
have
few
pixels,
and
therefore
the
failure
detection
of
even
one
pixel
would
lead
to
considerable
error.
Therefore
the
future
work
may
contain
the
investigation
of
more
accurate
measurement
strategies
for
the
low-resolution
micrographs,
although
more
and
more
advanced
microscopes
that
can
output
high-quality
micrographs
are
produced.
4.3.2.
Robustness
to
the
surrounding
illumination
It
can
also
observe
from
Fig.
11(g1,
g2,
h1,
h2,
i1,
i2,
j1,
j2,
k1,
k2)
that,
although
different
surrounding
illumination
including
the
blue,
green,
yellow,
and
white
light
are
used,
the
proposed
method
is
still
capable
of
accurately
recognizing
and
measur-
ing
the
SSD
depths.
This
high
robustness
to
the
surrounding
Fig.
10
The
original
SSD
micrographs
and
the
images
processed
by
the
proposed
method
that
are
used
to
evaluate
the
measurement
speed.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0328
illumination
may
be
because
the
rst
step
of
the
proposed
method
is
to
convert
the
input
image
into
the
gray
format
(see
Section
2.2)
therefore
the
surrounding
illumination
effect
can
be
largely
weakened.
4.3.3.
Robustness
to
the
tilted
angle
of
the
ground
surface
It
is
also
important
to
note
from
Fig.
11(b1,
b2,
h1,
h2,
l1,
l2)
that,
the
proposed
method
can
also
accurately
recognize
the
ground
specimen
surfaces
when
the
surfaces
are
tilted
during
the
microscope
observation.
Therefore,
SSD
depths
can
be
accurately
dened
by
calculating
the
point-to-line
distance.
For
the
manual
measurement,
on
the
contrary,
the
accurate
measurement
of
the
distance
from
the
deepest
subsurface
crack
to
the
tilted
ground
surface
may
be
a
tricky
and
time-
consuming
task.
4.3.4.
Robustness
to
the
material
aw
interference
Figs.
8,
10,
11
indicate
that,
although
the
material
aws
are
found
in
the
specimen
subsurface
in
the
captured
image,
the
subsurface
crack
recognition
of
the
proposed
method
would
not
be
affected,
showing
the
method
robustness
to
the
material
aw
interference.
This
robustness
to
the
aws
is
probably
resulted
from
the
employed
morphological
erosion-
reconstruction
operation
during
the
subsurface
crack
recogni-
tion
(see
Section
2.3),
by
which
only
the
lines
(or
continuous
points)
rather
than
the
discrete
points
can
be
recognized
and
kept.
5.
Conclusions
This
paper
has
presented
an
image-process-technique-based
method
that
can
identify
and
measure
the
grinding-induced
SSD
in
optical
glass
K9.
The
main
ndings
may
include:
The
method
can
accurately
measure
SSD
depths
where
the
biggest
relative
error
was
only
3.13%;
The
method
measurement
speed
was
approximately
1.68
s
per
image,
which
would
be
much
faster
than
the
manual
measurement,
even
for
the
highly
skilled
operators;
The
method
can
automatically
measure
SSD
depths
without
the
requirement
of
any
parameter
presetting,
allowing
the
users,
even
without
any
prior
professional
knowledge
about
SSD,
to
be
able
to
use
the
proposed
method;
The
method
showed
the
good
robustness
to
the
(i)
input
image
resolution/size,
(ii)
surrounding
illumination,
(iii)
the
tilted
angle
of
the
ground
surface,
and
(iv)
material
aw
interference.
Based
on
above,
the
proposed
method
is
believed
to
be
able
to
considerably
promote
the
realization
of
the
automatic
SSD
measurements
in
large
quantities,
and
therefore
is
anticipated
to
be
meaningful
and
helpful
for
not
only
the
industrial
manufacturing,
but
also
the
design
and
application
of
optical
glass.
Fig.
11
Method
robustness
to
different
sized
images.
a
r
c
h
i
v
e
s
o
f
c
i
v
i
l
a
n
d
m
e
c
h
a
n
i
c
a
l
e
n
g
i
n
e
e
r
i
n
g
1
8
(
2
0
1
8
)
3
2
0
3
3
0
329
Funding
National
Nature
Science
Foundation
of
China.
Acknowledgements
This
work
is
supported
by
the
National
Key
Research
and
Development
Program
of
China
(2017YFB0304200),
the
Nation-
al
Natural
Science
Foundation
of
China
(51374063)
and
the
Fundamental
Research
Funds
for
the
Central
Universities
(N141008001,
N150308001).
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e
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e
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0330
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