ISO 8721:2010

INTERNATIONAL ISO
STANDARD 8721
Second edition
2010-09-01
Road vehicles — Measurement
techniques in impact tests — Optical
instrumentation
Véhicules routiers — Techniques de mesure lors des essais de
chocs — Instrumentation optique

Reference number
©
ISO 2010
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ii © ISO 2010 – All rights reserved

Contents Page
Foreword .iv
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Symbols.5
5 Performance.7
5.1 General requirements .7
5.2 Reference distance.7
5.3 Time base system.8
5.4 Performance of the optical data channel.8
5.5 Accuracy of the optical data channel.10
5.6 Types of procedure .11
5.7 Conformity statement .13
5.8 Derived quantities .13
5.9 User-defined variables.13
6 Documentation .13
Annex A (normative) Index determination methods .14
Annex B (informative) Measurements methods.42
Annex C (informative) Clarification of parameters .43
Annex D (informative) Dependences between the indices and the variables .46
Bibliography.47

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 8721 was prepared by Technical Committee ISO/TC 22, Road vehicles, Subcommittee SC 12, Passive
safety crash protection systems.
This second edition cancels and replaces the first edition (ISO 8721:1987), which has been technically revised.

iv © ISO 2010 – All rights reserved

INTERNATIONAL STANDARD ISO 8721:2010(E)

Road vehicles — Measurement techniques in impact tests —
Optical instrumentation
1 Scope
This International Standard defines performance criteria for an optical data channel used in impact tests on
road vehicles, when numerical time and space data are taken from images to analyse impact test results.
The objective of this International Standard is to facilitate comparison between results obtained by different
laboratories by specifying minimum quality criteria.
Annexes A, B, C and D present a method of measuring several indices like quality parameters of
subprocesses of the optical data channel, using a calibration target, reference distances and analysis systems.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 6487, Road vehicles — Measurement techniques in impact tests — Instrumentation
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
analysis system
system to measure and collect the coordinates of target points in image space as a function of time
NOTE The calculation results of the analysis system are 3D coordinates in object space, whereas in the case of 2D
analysis, the depth of the target points is known and considered.
3.2
cell size
distance of neighbouring pixels on the sensor of an image recording device
NOTE If there are different distance values in the two main directions of the image, the cell size is the maximum of
these values.
3.3
control point
point that was determined with a higher accuracy and is further accepted as an error-free point
3.4
frame rate
f
r
frequency of renewal of information for a given point, expressed in renewals per second, or in images per
second if all points of the image are renewed simultaneously
3.5
image recording device
system composed of a camera/lens unit together with a recording system
3.6
location accuracy
a
loc
desired accuracy of the object or target being measured
3.7
optical data channel
system composed of one or more image recording devices and a system for analysing the images, including
any analysis procedure and data correction that validate and modify the content of the data
3.8
reference distance
known distance between a validation target pair
3.9
synchronism device
device to identify the synchronism effect in two or more corresponding image recording devices
3.10
time base system
device allowing determination of the time interval elapses between any two recorded events for each image
recording device
3.11
time origin identification device
device to identify the instant chosen as the time origin, usually the contact between the test objects
3.12
validation target pair
pair of targets placed in the field of view so that the distance separating them remains constant
NOTE Both of them are visible during the impact test.
3.13
accuracy value
a
value that represents the relative overall accuracy of any point measurement within the optical data channel
when the performance value is satisfied
3.14
accuracy value limit
r
avl
user-defined limit for the accuracy value that represents the relative overall accuracy of any point
measurement within the optical data channel when the performance value is satisfied
2 © ISO 2010 – All rights reserved

3.15
camera position calculation index
i
cpc
index that gives the possibility to evaluate whether the accuracy of the optical data channel determined from
one time step is representative for the entire sequence
3.16
camera set-up index
i
cs
index that makes it possible to evaluate whether the set-up of the camera with respect to the movement plane
permits a reliable analysis
NOTE Only for 2D film analysis.
3.17
control point distribution index
i
cpd
index that makes it possible to evaluate whether the distribution of the control points in the image permits a
reliable orientation of the used images
3.18
distortion index
i
d
index that makes it possible to evaluate whether the interior orientation parameters of the used camera are
still valid
3.19
focal length index
i
fl
index that makes it possible to evaluate whether the focal length of the used image recording device is still
valid
3.20
index value
value that is determined by the index calculation equation
NOTE 1 See Annex A.
NOTE 2 The index value is the result of the index determination and is a floating point number.
3.21
index condition
condition of the check of the index
NOTE The index condition can be true (value 1) or false (value 0). The condition true means that the index check is
fulfilled and the condition false means that the index check is not fulfilled.
3.22
intersection index
i
i
index that makes it possible to evaluate the intersection geometry of the rays from the image recording
devices to the object points
NOTE Only for 3D film analysis.
3.23
length measurement error
value that represents the absolute overall accuracy of any point measurement within the optical data channel
when the performance value is satisfied
3.24
motion blur index
i
mb
index that allows one to evaluate whether the exposure time used in the test is small enough with respect to
the appropriate object movement, in order to ensure a reliable point identification and point measurement in
the images
3.25
performance value
value that guarantees suitable general conditions for the estimation of the accuracy of the optical data channel
NOTE It is derived from all indices which describe the performance of the optical data channel.
3.26
plane scale index
i
ps
index that makes it possible to evaluate whether there is the possibility to calculate the scale in each
movement plane
NOTE Only for 2D film analysis.
3.27
point motion index
i
pm
index that makes it possible to estimate whether the selected frame rate is high enough, in order to
correspond to the test requirements
3.28
scale index
i
s
index that gives the possibility to evaluate whether there are enough independent reference distances to
control the system scale
3.29
synchronism index
i
sy
index that makes it possible to estimate whether the data produced in the test can be regarded as
synchronous
NOTE Only for 3D film analysis.
3.30
target detection index
i
td
index that makes it possible to evaluate whether the measuring accuracy of the image coordinates is small
enough, in order to correspond to the test requirements
3.31
target size index
i
ts
index that makes it possible to evaluate whether the signalized points, used in the test, are large enough, in
order to ensure a reliable point identification and point measurement in the images
3.32
time base index
i
tb
index that makes it possible to evaluate whether the time accuracy of the used time base system corresponds
to the test requirements
4 © ISO 2010 – All rights reserved

3.33
time origin identification index
i
toi
index that makes it possible to evaluate whether the time accuracy of the used time origin identification device
corresponds to the test requirements
4 Symbols
Symbol Definition
A control point formed area
cf
A image area
i
a accuracy value of the optical data channel
a allowed location accuracy in depth
alaid
a current location accuracy (distortion)
clad
a current location accuracy (focal length)

claf
a current location accuracy (intersection)
clai
a current location accuracy in depth
claid
a current location accuracy (target)
clat
a current location accuracy (time base)

clatb
a current location accuracy (time origin identification)
clatoi
a distortion accuracy
d
a focal length accuracy
fl
a frame rate accuracy
fr
a location accuracy
loc
a accuracy value of the reference distance, r
refdist,r
a target detection accuracy
td
d object distance
e exposure time
f focal length
f frame rate
r
i camera position calculation index
cpc
i control point distribution index
cpd
i camera set-up index
cs
i distortion index
d
i focal length index
fl
i intersection index
i
i motion blur index
mb
i point motion index
pm
i plane scale index
ps
Symbol Definition
i scale index
s
i synchronism index
sy
i time base index
tb
i target detection index
td
i time origin identification index
toi
i target size index
ts
∆L length measurement error of the optical data channel
∆l length measurement error of reference distance, r

r
l asynchronism effect in viewing direction
aed
l asynchronism effect perpendicular to the viewing direction
aep
l allowed point motion between two sequenced images in object space

apm
l calibrated length of reference distance, r

c,r
l camera base
cb
l current motion blur value
cmbv
l current point motion between two sequenced images in object space
cpm
l cell size
cs
l current target diameter
ctd
l distance camera base to object
dco
l fix point distance
fpd
l image height
ih
l image width
iw
l (t) measured length of reference distance, r, as a function of time
m,r
l maximum displacement in image space
mdi
l maximum displacement in object space
mdo
l required target diameter
rtd
l theoretical target diameter
ttd
p 3D performance value of the optical data channel
p control point area
cpa
p control point distribution
cpd
p distance to plane of motion i
dtp,i
p number of planes of motion
np
p reference distance
rd,r
p reference distance in direction i
rd,i
p reference distance in plane of motion i

rdp,i
p scale information in all planes of motion
siap
p scale information in plane of motion i
sip,i
6 © ISO 2010 – All rights reserved

Symbol Definition
p synchronism index in viewing direction
syd
p synchronism index perpendicular to the viewing direction
syp
p target in image section i
t,i
p type of camera set-up
tpc
p type of position determination
tpd
Q performance value of the optical data channel
q 2D performance value of the image recording device i

i
r allowed accuracy relation
aar
r accuracy value limit
avl
r current accuracy relation
car
t beginning of the analysed time interval

b
t user-defined time within the analysed time interval

c
t current asynchronism
ca
t difference between t -image and -signal
dtz 0
t end of the analysed time interval

e
t time interval
int
t time drift
td
t total time drift
ttd
v velocity
5 Performance
5.1 General requirements
The performance of the optical data channel shall be evaluated initially to establish performance levels. This
evaluation shall be repeated whenever the system is modified to an extent which could cause a change in
accuracy. This shall be done with an offline procedure.
It is also possible to measure the performance of the optical data channel during an impact test. This is called
the online procedure.
The performance of the optical data channel shall be estimated using 2D performance values, or 3D
performance values, or both. These values consist of different performance indices depending on the test
constellation. To verify the estimated performance values, an accuracy value shall be determined using two or
more reference distances.
If a film analysis is carried out using the image sequences of onboard cameras, the used equipment (camera
and lens) shall correspond to the expected shock.
5.2 Reference distance
The reference distances shall be determined ten times more precisely than the desired location accuracy. The
determination of the reference distances should be done before the test.
The reference distances shall be located on approximately perpendicular (90 ± 10)° lines (see A.3.2). For 3D
analysis, all three directions in space shall be covered.
5.3 Time base system
The time base shall be determined ten times more precisely than the desired time accuracy.
5.4 Performance of the optical data channel
5.4.1 General
The performance of the optical data channel consists of different indices (see Table 1). The determination
depends on the application (2D or 3D).
5.4.2 Performance indices
Each index value shall be at least 0,5. If this minimum requirement is not fulfilled for every index, then the
impact test does not conform to this International Standard. The index condition of a certain index is 0 if the
requirements for this index (see Annex A) are not fulfilled; otherwise the index condition is 1.
Table 1 — Performance indices
Number per optical
Index 2D 3D Comment
data channel
a a
Focal length index one per image recording device in a suitable image
a a
Distortion index one per image recording device in a suitable image
a a
Target detection index one per image recording device worst target used in the analysis
a a
Target size index one per image recording device worst target used in the analysis
a a
Motion blur index one per image recording device at maximum object speed
a a
Point motion index one per image recording device at maximum object speed
a a
Control point distribution index one per image recording device in a suitable image
a a
Time base index one per image recording device —
a a
Time origin identification index one per image recording device —
a b
Camera set-up index one per image recording device —
a b
Plane scale index one per image recording device —
b a
Intersection index one best pair of image recording devices
b a
Synchronism index one worst pair of image recording devices
a
Index value is used for the performance value.
b
Index value is not used for the performance value.
5.4.3 2D performance value
The performance value for every image recording device is estimated by all 2D related index conditions
(see Table 1). The 2D performance value, q , is the ratio of the achieved sum to the possible sum of index
i
conditions with respect to the test requirements, and is calculated as shown in Equation (1):
n
x
∑ ji
j=1
q = (1)
i
n
8 © ISO 2010 – All rights reserved

where
i is the image recording device number;
j is the 2D performance index number;
x is the index condition of the 2D performance index, j, of the image recording device, i;
ji
n is the number of 2D performance indices (2D film analysis: n = 11; 3D film analysis: n = 9).
5.4.4 3D performance value
The 3D performance value of the optical data channel, p, is calculated as shown in Equation (2):
m
p = y (2)
∑ k
k =1
where
k is the 3D performance index number;
y is the index condition of the 3D performance index, k, of the optical data channel;
k
m is the number of 3D performance indices (m = 2).
5.4.5 Performance value of the optical data channel
For 2D analysis, the performance value of the optical data channel, Q, is identical to the 2D performance
value, q , as shown in Equation (3):
Qq= (3)
For 3D analysis with only one image recording device, the intersection index and the synchronism index are
not defined. In this case, the performance value of the optical data channel, Q, is equal to the 2D performance
value, q .
For 3D analysis, the performance value of the optical data channel, Q, is the ratio of the achieved sum to the
possible sum of all index conditions, calculated according to Equation (4):
uu
⎛⎞ ⎛ ⎞
n
⎜⎟ ⎜ ⎟
nq×+p×u × q+p
()
∑∑ii
⎜⎟ ⎜ ⎟
u
ii==11
⎝⎠ ⎝ ⎠
Q== (4)
()nu×+(m×u) n+m
where
i is the image recording device number;
q is the 2D performance value of the image recording device, i;
i
u is the number of image recording devices;
n is the number of 2D performance indices (2D film analysis: n = 11; 3D film analysis: n = 9);
m is the number of 3D performance indices (m = 2);
p is the 3D performance value of the optical data channel.
5.5 Accuracy of the optical data channel
5.5.1 Accuracy indices
The accuracy indices are shown in Table 2.
Table 2 — Accuracy indices
Index Number per optical data channel Comment
Camera position calculation index one per image recording device —
Scale index one indispensable index
5.5.2 Length measurement error and accuracy value of a reference distance
The length measurement error and accuracy value of a reference distance are defined as follows:
⎯ the length measurement error, ∆l , of the reference distance, r, is the maximum difference between the
r
measured length, l (t), and the calibrated length, l , within the analysed time interval;
m,r c,r
⎯ the accuracy value, a , of the reference distance, r, is the maximum relative difference between the
refdist,r
measured length, l (t), and the calibrated length, l , within the analysed time interval.
m,r c,r
All used image recording devices shall be used for the calculation of the reference distances.
If the index condition of the camera position calculation index, i , of all used image recording devices is
cpc
fulfilled, the length measurement error, ∆l , can be determined at a single time step within the analysed time
r
interval. If the index condition of only one image recording device is not fulfilled, the length measurement error,
∆l , shall be calculated for every time step within the analysed time interval. The accuracy value, a , of
r refdist,r
the reference distance, r, is the ratio between the length measurement error, ∆l , and the calibrated length, l .
r c,r
If every i W 1, then the length measurement error, ∆l , is calculated according to Equation (5):
cpc,i r
∆=ll ()t −l (5)
rrm, c c,r
where
i is the index value of the camera position calculation index of the image recording device, i;

cpc,i
i is the image recording device number;
r is the reference distance number;
l (t) is the measured length of reference distance, r, as a function of time;
m,r
l is the calibrated length of reference distance, r.
c,r
If any i < 1, then the length measurement error, ∆l , is calculated according to Equation (6):
cpc,i r
t
e
∆=llmax (t)−l (6)
rrm, c,r
t
b
10 © ISO 2010 – All rights reserved

where
t is the beginning of the analysed time interval;
b
t is the end of the analysed time interval;
e
t is a user-defined time within the analysed time interval.
c
The accuracy value, a , is calculated according to Equation (7):
refdist,r
∆l
r
a = (7)
refdist,r
l
c,r
5.5.3 Length measurement error and accuracy value of the optical data channel
⎯ The length measurement error of the optical data channel, ∆L, is the maximum of the length
measurement errors, ∆l , of all reference distances, r.
r
⎯ The accuracy value of the optical data channel, a, is the maximum of the accuracy values, a , of all
refdist,r
reference distances, r
.
∆=L max∆l (8)
()
r
aa= max (9)
()
refdist,r
5.6 Types of procedure
5.6.1 General
Conformity with this International Standard can be verified by different types of procedure, depending on the
desired complexity. The different types of procedure are shown in Table 3.
Table 3 — Types of procedure
Before the real impact test During the real impact test
Type of
procedure
Performance value Accuracy value Performance value Accuracy value
∆L u a
loc
Q W 0,7
Online — —
a u r
avl
Synchronism index
∆L u a ∆L u a
loc loc
Q W 0,8 i W 1
Offline
sy
a u r a u r
avl avl
(only 3D analysis)
Key
Q performance value of the optical data channel
∆L length measurement error of the optical data channel
a accuracy value of the optical data channel
r user-defined accuracy value limit of the optical data channel
avl
a user-defined location accuracy of the optical data channel
loc
5.6.2 Type of procedure — Online
5.6.2.1 The online procedure is of the highest complexity. All work shall be done for every impact test.
The performance and the accuracy of the optical data channel can be checked during the test.
This procedure can be used, if the equipment of the optical data channel will often be changed essentially
between the impact tests, or if no prior information about the optical data channel is available.
The user has the possibility to evaluate every component of the optical data channel for every impact test.
5.6.2.2 Tasks during the impact test are specified below.
⎯ All described performance and accuracy indices shall be calculated during the real impact test.
⎯ All described performance index values shall be at least 0,5.
⎯ The performance value of the optical data channel, Q, shall be greater than 0,7.
⎯ The length measurement error of the optical data channel, ∆L, shall be lower than the location accuracy,
a .
loc
⎯ The accuracy value of the optical data channel, a, shall be lower than the accuracy value limit, r .
avl
5.6.3 Type of Procedure — Offline
5.6.3.1 The offline procedure is of middle complexity. The main part of the calculation shall be done once
in the preliminary test. The performance of the optical data channel can only be checked in this test. During
the impact test, only the accuracy can be calculated. For a 3D analysis, the synchronism shall be checked.
This procedure can be used if the equipment of the optical data channel will not be changed, or if only minor
changes will be done.
The user has the possibility to evaluate every component of the optical data channel once in the preliminary
test. For every impact test, the user only has the possibility to evaluate the overall result of the optical data
channel.
5.6.3.2 Tasks in the preliminary test are specified below.
⎯ The lighting and the frame rates of the image recording devices in the preliminary test shall be similar to
an impact test. The using of a VDI/VDE 1634 Part 1 artefact is recommended (see Reference [2]). The
size of the artefact should correspond to the size of the measuring area of the impact test.
⎯ All described performance index values shall be at least 0,5.
⎯ The performance value of the optical data channel, Q, shall be greater than 0,8.
⎯ The length measurement error of the optical data channel, ∆L, shall be lower than the location accuracy,
a .
loc
⎯ The accuracy value of the optical data channel, a, shall be lower than the accuracy value limit, r .
avl
5.6.3.3 Tasks during the impact test are specified below.
⎯ For 3D analysis, the synchronism index shall be fulfilled, i W1.
sy
⎯ The length measurement error of the optical data channel, ∆L, shall be lower than the location accuracy,
a .
loc
⎯ The accuracy value of the optical data channel, a, shall be lower than the accuracy value limit, r .
avl
12 © ISO 2010 – All rights reserved

5.7 Conformity statement
The accuracy value represents the overall accuracy of any point measurement within the optical data channel
when suitable general conditions are valid. This is guaranteed by the performance value.
An optical data channel conforms to this International Standard if the index value of the scale index is 1 and
the accuracy value and the performance value fit the requirements of the used procedure.
5.8 Derived quantities
For derived computed quantities, the requests for the digital signal processing of a data channel shall be
considered in accordance with ISO 6487.
5.9 User-defined variables
The user is able to influence the results of the testing procedure by the specification of user-defined variables.
The conformity or non-conformity of this International Standard depends on these user-defined variables.
They shall be listed in the inspection record. With these variables, the user specifies his desired measurement
accuracy.
User-defined variables are given in Table 4.
Table 4 — User-defined variables
Variable Symbol Definition Unit
desired accuracy of the object or target being measured (target
location accuracy a detection index, focal length index, distortion index, motion blur length unit
loc
index, length measurement error)
allowed point motion between two sequenced images in object
allowed point motion l length unit
apm
space (point motion index)
allowed accuracy relation between the accuracy perpendicular to
allowed accuracy relation r the camera base in the direction to the object and the accuracy in —
aar
the other two directions (intersection index)
desired accuracy relation of the reference distances being
accuracy value limit r —
avl
measured (accuracy value)
6 Documentation
For the interpretation of the accuracy and performance values, it is necessary to specify the used type of
procedure (online/offline), the type of analysis (2D/3D), the number of image recording devices and the time
interval used for the evaluation. All user-specific input values and all index values shall be recorded.
If the frame rate is not constant over the time interval, the time vector shall be recorded.
For the documentation of the performance of an optical data channel, an inspection record is recommended
(see Clause A.4).
Annex A
(normative)
Index determination methods
A.1 2D performance indices
A.1.1 Focal length index, i
fl
The focal length index determines the influence of an incorrect focal length on the location accuracy. The
accuracy of the determined focal length is calculated by algorithms determining the camera internal
parameters.
For a 2D film analysis using a perpendicular set-up of the camera with respect to the movement plane
(see A.1.8), and if reference distances are available in each motion plane (see A.1.9), the index value of the
focal length index is 1. Otherwise, the index value shall be calculated by Equations (A.1) and (A.2), using the
parameters in Table A.1.
Table A.1 — Parameters to determine focal length index
Parameter Symbol Definition Unit
focal length f focal length of the used image recording device length unit
Input parameters
object distance d distance between object and image recording device length unit
focal length accuracy a accuracy of the determined focal length length unit
fl
User-defined desired accuracy of the object or target being
location accuracy a length unit
loc
variables measured
current location
Derived values a current accuracy of the object or target being measured length unit
claf
accuracy
The functional connection is as shown in Equation (A.1):
d
aa=× (A.1)
claf fl
f
The requirement for the parameter focal length index, i , is as shown in Equation (A.2):
fl
a
loc
i = W 1 (A.2)
fl
a
claf
EXAMPLE If f = 16 mm, d = 5 000 mm, a = 10 mm and a = 0,02 mm, then
loc fl
a = (5 000 mm/16 mm) × 0,02 mm = 6,25 mm
claf
i = 10 mm/6,25 mm = 1,6
fl
i W 1  9
fl
14 © ISO 2010 – All rights reserved

A.1.2 Distortion index, i
d
The distortion index determines the influence of incorrect distortion parameters of the interior orientation on
the location accuracy. The distortion accuracy is the remaining maximum residual of the process of
determining the internal camera parameters. The distortion index value shall be calculated by Equations (A.3)
and (A.4), using the parameters in Table A.2.
Table A.2 — Parameters to determine distortion index
Parameter Symbol Definition Unit
focal length f focal length of the used image recording device length unit
object distance d distance between object and image recording device length unit
accuracy of the determined distortion parameters
Input parameters
distortion accuracy a pixel
d
(maximum residuals)
length
cell size l cell size of the digital image
cs
unit/pixel
User-defined desired accuracy of the object or target being
location accuracy a length unit
loc
variables measured
current location
Derived values a current accuracy of the object or target being measured length unit
clad
accuracy (distortion)
The functional connection is as shown in Equation (A.3):
d
aa=× ×l (A.3)
clad d cs
f
The requirement for the parameter distortion index, i , is as shown in Equation (A.4):
d
a
loc
i = W 1 (A.4)
d
a
clad
EXAMPLE If f = 16 mm, d = 5 000 mm, a = 10 mm, a = 1 pixel and l = 0,016 mm/pixel, then
loc d cs
a = (5 000 mm/16 mm) × 1 pixel × 0,016 mm/pixel = 5 mm
clad
i = 10 mm/5 mm = 2,0
d
i W 1  9
d
A.1.3 Target detection index, i
td
The target detection index determines the influence of the target detection accuracy on the location accuracy.
The worst target used in the analysis shall be used for the determination of the target detection index. The
target detection index value shall be calculated by Equations (A.5) and (A.6), using the parameters in
Table A.3.
Table A.3 — Parameters to determine target detection index
Parameter Symbol Definition Unit
focal length f focal length of the used image recording device length unit
object distance d distance between object and image recording device length unit
target detection target detection accuracy (e.g. determined by measurement
Input parameters
a pixel
td
accuracy on similar target type and target size of known location)
length
cell size l cell size of the digital image
cs
unit/pixel
User-defined location
a desired accuracy of the object or target being measured length unit
loc
variables accuracy
current location
Derived values a current accuracy of the object or target being measured length unit
clat
accuracy (target)
The functional connection is as shown in Equation (A.5):
d
aa=× ×l (A.5)
clat td cs
f
The requirement for the parameter target detection index, i , is as shown in Equation (A.6):
td
a
loc
i = W 1 (A.6)
td
a
clat
EXAMPLE If f = 16 mm, d = 8 000 mm, a = 10 mm, a = 0,1 pixel and l = 0,016 mm/pixel, then
loc td cs
a = (8 000 mm/16 mm) × 0,1 pixel × 0,016 mm/pixel = 0,8 mm
clad
i = 10 mm/0,8 mm = 12,5
td
i W 1  9
td
A.1.4 Target size index, i
ts
The target size index compares the current and the required diameter of the targets in object space. The worst
target used in the analysis shall be used for the determination of the target size index. The target size index
value shall be calculated by Equations (A.7) and (A.8), using the parameters in Table A.4.
Table A.4 — Parameters to determine target size index
Parameter Symbol Definition Unit
focal length f focal length of the used image recording device length unit
object distance d distance between object and image recording device length unit
required target required target diameter in image space (required by
l pixel
rtd
diameter the analysis system developer)
Input parameters
length
cell size l cell size of the digital image
cs
unit/pixel
current target
l real target diameter in object space length unit
ctd
diameter
theoretical target
Derived values l theoretical target diameter in object space length unit
ttd
diameter
16 © ISO 2010 – All rights reserved

The functional connection is as shown in Equation (A.7):
d
ll=× ×l (A.7)
ttd rtd cs
f
The requirement for the parameter target size index, i , is as shown in Equation (A.8):
ts
l
ctd
i = W 1 (A.8)
ts
l
ttd
EXAMPLE If f = 25 mm, d = 5 000 mm, l = 10 pixel and l = 0,016 mm/pixel and l = 35 mm, then
rtd cs ctd
l = (5 000 mm/25 mm) × 10 pixel × 0,016 mm/pixel = 32 mm
ttd
i = 35 mm/32 mm = 1,09
ts
i W 1  9
ts
A.1.5 Motion blur index, i
mb
The motion blur index determines the influence of the motion blur on the location accuracy. The motion blur
index value shall be calculated by Equations (A.9) and (A.10), using the parameters in Table A.5.
Table A.5 — Parameters to determine motion blur index
Parameter Symbol Definition Unit
length
maximum speed of the object perpendicular to the
object speed v unit/time
optical axis
Input parameters
unit
exposure time e exposure time of the used image recording device time unit
User-defined
location accuracy a desired accuracy of the object or target being measured length unit
loc
variables
current motion blur
Derived values l current motion blur value at the object length unit
cmbv
value
The functional connection is as shown in Equation (A.9):
lv=×0,5 ×e (A.9)
cmbv
The requirement for the parameter motion blur index, i , is as shown in Equation (A.10):
mb
a
loc
i = W 1 (A.10)
mb
l
cmbv
EXAMPLE If v = 18 m/s, e = 0,4 ms and a = 5 mm, then
loc
l = 0,5 × 18 mm/ms × 0,4 ms = 3,6 mm
cmbv
i = 5,0 mm/3,6 mm = 1,39
mb
i W 1  9
mb
A.1.6 Point motion index, i
pm
The point motion index determines the current point motion between two images of a sequence with respect
to the test requirements. The point motion index value shall be calculated by Equations (A.11) and (A.12),
using the parameters in Table A.6.
Table A.6 — Parameters to determine point motion index
Parameter Symbol Definition Unit
length
maximum speed of the object perpendicular to the
object speed v unit/time
optical axis
Input parameters
unit
frame rate f frame rate of the image recording device during the test 1/time unit
r
User-defined allowed point motion between two sequenced images in
allowed point motion l length unit
apm
variables object space
current point motion between two sequenced images in
Derived values current point motion l length unit
cpm
object space
The functional connection is as shown in Equation (A.11):
lv=× (A.11)
cpm
f
r
The requirement for the parameter point motion index, i , is as shown in Equation (A.12):
pm
l
apm
i = W 1 (A.12)
pm
l
cpm
EXAMPLE If v = 14 m/s, f = 1 000 Hz and l = 15 mm, then
r apm
l = 14 mm/ms × 1 ms = 14 mm
cpm
i = 15 mm/14 mm = 1,07
pm
i W 1  9
pm
A.1.7 Control point distribution index, i
cpd
The control point distribution index determines the number of control points in the different image sections
(see Figure A.1) and the percentage coverage of the control point area over the image.

Figure A.1 — Sections of the image (specifications in accordance with Clause A.12 and Figure A.2)
18 © ISO 2010 – All rights reserved

For a 2D film analysis using a perpendicular set-up of the camera with respect to the movement plane
(see A.1.8), the index value of the control point distribution index is 1. Otherwise, the index value shall be
calculated by Equations (A.13) and (A.14), using the parameters in Table A.7.
Table A.7 — Parameters to determine control point distribution index
Parameter Symbol Definition Unit
target in image
p presence of targets in the special image sections —
t,i
section i
image width l width of the digital image pixel
iw
Input parameters
image height l height of the digital image pixel
ih
control point formed area which is formed by the control points (e.g. a
A pixel × pixel
cf
area triangle, if three points are used)
control point
p parameter for the distribution of the control points —
cpd
distribution
Derived values
control point area p parameter for the area of the control points —
cpa
image area A area of the digital image pixel × pixel
i
The functional connection is as shown in Equation (A.13):
p = 1 if at least one target exists in image section i
t,i
p = 0 if no target exists in image section i
t,i
p =+p ppp+ +
cpd t,1 t,2 t,3 t,4
A=×ll
iiw ih
A
cf
if > 10% , then p = 1
cpa
A
i
A
cf
if u 10 % , then p = 0 (A.13)
cpa
A
i
The requirement for the parameter control point distribution index, i , is as shown in Equation (A.14):
cpd
pp×
cpd cpa
i = W 1 (A.14)
cpd
EXAMPLE During the exposure, five control points are visible in the image: one is in section 2 (p = 1), one in
t,2
section 3 (p = 1), two are in section 4 (p = 1) and one is in the centre of the image in section 0 (no effect).
t,3 t,4
If l = 768 pixel, l = 512 pixel and A = 122 290,3 pixel , then
iw ih cf
p = 0 + 1 + 1 + 1 = 3
cpd
A = 768 pixel × 512 pixel = 393 216 pixel
i
A
122 290pix
cf
= = 0,311 = 31,1 % > 10 % : p = 1
cpa
A
393 216 pix
i
i = (3 × 1)/3 = 1
cpd
i W 1  9
cpd
A.1.8 Camera set-up index, i (only for 2D film analysis)
cs
The camera set-up index describes the requirements to the orientation of the camera with respect to the plane
of motion, which can be perpendicular or non-perpendicular.
Using the perpendicular set-up, the camera shall be oriented precisely perpendicular to the plane of motion.
A non-perpendicular set-up of the motion plane with respect to the optical axis of the camera is only allowed if
all measured objects only move in the considered plane of motion. Using the non-perpendicular set-up the
camera position and orientation shall be calculated with respect to the plane of motion and a perspective
correction of the measurements shall be carried out. Furthermore, the control point distribution index and the
focal length index shall be ca
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