ISO 17850:2015

INTERNATIONAL ISO
STANDARD 17850
First edition
2015-07-01
Photography — Digital cameras
— Geometric distortion (GD)
measurements
Photographie — Caméras numériques — Mesurages de distorsion
géométrique (DG)
Reference number
©
ISO 2015
© ISO 2015, Published in Switzerland
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ii © ISO 2015 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Measurement methods . 2
4.1 General . 2
4.2 Local geometric distortion . 3
4.3 Line geometric distortion . 3
5 Requirements . 4
5.1 Apparatus and hardware . 4
5.2 Lighting . 4
5.3 Dot chart . 5
5.3.1 Design and characteristics. 5
5.3.2 Requirement for the chart planarity . 6
5.4 Grid chart . 7
5.4.1 Design and characteristics. 7
5.5 Image/camera settings . 8
5.5.1 General. 8
5.5.2 Basic settings and influencing factors . 8
5.5.3 Specific test procedures . 8
5.5.4 Positioning of the camera . 8
5.5.5 Exposure, white balance, and focus . 9
6 Determination of geometric distortion .10
6.1 Local geometric distortion .10
6.1.1 Numerical definition . .10
6.1.2 Outline of the practical algorithm .10
6.2 Line geometric distortion .11
6.2.1 Horizontal line distortion .11
6.2.2 Vertical line distortion .12
6.2.3 Total line distortion .12
7 Presentation of results .13
7.1 General .13
7.2 Local geometric distortion .13
7.3 Line geometric distortion .14
Annex A (informative) Illustrative example and validation .15
Annex B (informative) Extracting the dots from the target .17
Annex C (informative) Dot centre validation .25
Annex D (informative) Grid sort .30
Annex E (informative) Example of subjective evaluation .40
Bibliography .48
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
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electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 42, Photography.
iv © ISO 2015 – All rights reserved

Introduction
A digital still camera (DSC) typically employs a taking lens that is a rotationally symmetric optical
system. Generally, the function of rotationally symmetric optical systems is to form an image that is
geometrically similar to the object except some particular systems, such as fish-eye lenses and eyepieces,
where this condition is deliberately not maintained. This function is accomplished ideally according to
the geometry of perspective projection. Departures from the ideal image geometry are called distortion.
The distortion is a position-dependent quantity which generally has a vectorial character. In a given
image plane (which may also lie at infinity), this vector, representing the difference between theoretical
and real image position, has a radial and a tangential component. In optical systems, the tangential
component is basically conditioned by imperfect rotational symmetry. The systems manufactured in
accordance with the present state of the art have a negligible tangential distortion.
Geometric distortion (GD) of DSCs is mainly caused by the variation of magnification in the image field of
the camera lens. The most well-known effect of distortion is that straight lines appear curved. Generally
speaking, the proportions between objects are not preserved in a distorted image, which can be very
unpleasant for some natural scenes, architecture, or portraits. Distortion is fully described by a 2D map,
giving the displacement from a point in an ideal undistorted image to the point in the actual distorted
image. The image centre is usually assumed to be undistorted; the magnification factor at this position
actually defines the focal distance.
Different types of distortion are usually characterized by how the magnification radially varies within
the image field. Barrel and pincushion are the most usual types of distortion for which magnification
is respectively monotonously decreasing and monotonously increasing when moving along from the
centre to the border of the image field. Other types which cannot be categorized into above two types
are usually called wave distortion.
a) Barrel (or negative) distortion
b) Pincushion (or positive) distortion
NOTE The magnification is decreasing for barrel distortion and increasing for pincushion.
Figure 1 — Two main types of distortions
ISO 9039 defines methods to measure a lens that is separated from a camera. On the other hand, this
International Standard was developed and defines methods to measure the total image distortion of a
camera including a lens and signal processing.
This International Standard is based on both Reference [3] prepared by the Camera Phone Image Quality
(CPIQ) group within the International Imaging Industry Association (I3A) and Reference [4] prepared
by Camera and Imaging Products Association (CIPA).
vi © ISO 2015 – All rights reserved

INTERNATIONAL STANDARD ISO 17850:2015(E)
Photography — Digital cameras — Geometric distortion
(GD) measurements
1 Scope
This International Standard specifies a protocol to measure geometric distortion of a digital camera. It
is applicable to the measurement of digital cameras including camera phones.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 14524, Photography — Electronic still-picture cameras — Methods for measuring opto-electronic
conversion functions (OECFs).
IEC 61146-1, Video cameras (PAL/SECAM/NTSC) — Methods of measurement — Part 1: Non-broadcast
single-sensor cameras
EBU Tech3249, Measurement and analysis of the performance of film and television camera lenses
3 Terms and definitions
3.1
geometric distortion
GD
displacement from the ideal shape of a subject (lying on a plane parallel to the image plane) in
the recorded image
Note 1 to entry: Geometric distortion basically derives from variation of lateral magnification in the image field of
a camera lens and results in straight lines being rendered as curves. There are other factors to induce geometric
distortion, for example, rotational asymmetricity of a camera lens or position shift processing in a camera imaging
process.
3.2
image height
3.2.1
image height
distance between an image point and the centre of the image area or its relative expression
which is the value normalized by one half of the diagonal of the image area
Note 1 to entry: This is an extension of the definition in ISO 9039 which is a measurement for optical systems.
3.2.2
actual image height
image height of an actual recorded image point in the recorded image area
Note 1 to entry: “Actual recorded image point” corresponds to “observed image point” in ISO 9039.
Note 2 to entry: “Image height” in ISO 9039 basically means “actual image height” but the usage is sometimes
confusing.
Note 3 to entry: The adjective “actual” is used in similar meaning, “actual point” and “actual position”, for example.
3.2.3
ideal image height
image height of a theoretical corresponding point in the recorded image area, assuming a
geometrically undistorted image formation
Note 1 to entry: This is an extension of the definition in ISO 9039 which is a measurement for optical systems.
Note 2 to entry: The adjective “ideal” is used in similar meaning, “ideal point” and “ideal position”, for example.
3.3
image quality
impression of the overall merit or excellence of an image, as perceived by an observer neither associated
with the act of photography nor closely involved with the subject matter depicted
Note 1 to entry: The purpose of defining image quality in terms of third-party (uninvolved) observers is to
eliminate sources of variability that arise from more idiosyncratic aspects of image perception and pertain to
attributes outside the control of imaging system designers.
3.4
noise
unwanted variations in the response of an imaging system
3.5
resolution
measure of the ability of a digital image capture system or a component of a digital image capture system
to distinguish picture detail
3.6
TV distortion
line distortion measured by conventional method of TV field defined in IEC 61146-1 (24 Geometric
distortions) or EBU Tech3249 (2.11. Picture height distortion)
4 Measurement methods
4.1 General
As defined in 3.1, geometric distortion basically derives from the variation of magnification in the image
field. If this phenomenon occurs in an image, it means that a regular structure in an object does not
appear to be regular in the image taken with the camera. There are two ways defined in this International
Standard to quantify the amount of geometric distortion in an image. Both have their pros and cons.
2 © ISO 2015 – All rights reserved

Figure 2 — Regular grid (solid lines) in the scene is distorted and the red diamonds mark the
position of the intersections in the image produced by the camera
4.2 Local geometric distortion
Geometric distortion can be measured on a white chart containing black dots at the position of a regular
grid or on a grid chart formed by straight lines. The local geometric distortion method analyses the grid
formed by the test chart in the centre of the image and calculates the ideal positions of the structure
based on the measured distances. After that, it analyses the rest of the image and locates all actual
positions of the grid. The distance between the ideal position and the actual position is the geometric
distortion at that location in the image.
The distance between the two positions can be plotted as a function over the distance to the image
centre. This curve indicates the variation of image magnification versus the actual image height, which
is an expression of the geometric distortion called local geometric distortion. In order to limit the result
to a single value that might get reported with the cameras specifications, the maximum (peak to peak)
value shall be reported.
The manufacturing tolerances, such as lens tilt or off-centring, can result in a non-rotationally symmetric
GD behaviour. If the system is not rotationally symmetric, it can lead to increased distortion levels in the
image corners. In this case, the measured geometric distortion is correct for the camera under test but
might not represent a standard camera of the tested model.
4.3 Line geometric distortion
The principle of line geometric distortion is to measure the bending of a straight horizontal or vertical
line at defined distances from the image centre and to report the maximum of the measured bending.
This bending is preferably measured on a chart with a regular line grid.
Line geometric distortion is the direct measured result of this method and it is easy to understand
intuitively for consumers. However, it can also be interpreted from the measured result using the local
geometric distortion method.
NOTE The line geometric distortion has a long history and it has been used in the video technology for
decades. The reason is that it was easy to determine this value with standard measurement equipment used in the
analogue video world. The fundamental concept of this method was first standardized by the IEC in IEC 61146–1
in 1994.
5 Requirements
5.1 Apparatus and hardware
The following hardware is necessary to control and report the test conditions:
— dot target or a grid chart;
— two light sources;
— device to measure the chart height captured in the image;
— mirror (for camera alignment with the target).
5.2 Lighting
Lighting uniformity is recommended to ease the processing of the target but does not influence the
phenomenon of distortion. The light sources should be adjusted such that illumination is uniform on the
target at ±10 %. Light sources should be baffled to prevent the direct illumination of the camera. The
light sources should be located so as to minimize the occurrence of specular reflections off the surface
of the target when viewed by the camera under test.
The illumination should be set so that the auto-exposure of the camera gives a suitable result. More
precisely, the image should not be clipped in either bright or dark parts of the target. The camera should
be positioned so that it casts no shadow on the chart.
4 © ISO 2015 – All rights reserved

~45° ~45°
Key
1 test target
2 illumination
3 camera
Figure 3 — Lighting system
5.3 Dot chart
5.3.1 Design and characteristics
The test chart contains black circular dots placed on a perfectly regular square grid on a uniform white
background.
The dot centres may be connected by straight black lines with a thickness of approximately 1/10 of the
dot diameter as shown in Figure 4 b). That way, it does not affect the dot detection but helps to better
align the camera to the chart for example, by eliminating rotation between the chart and camera’s image
sensor axes. The straight black lines are especially useful if the mirror method described in 5.5.4 is not
possible or available.
The chart can be either a reflective test chart, which is front illuminated, or a transparency test chart,
which is rear illuminated. The chart contrast level should at least be 40:1 and not be higher than 10 000:1.
The size and the number of dots should depend on the resolution of the camera and the shooting distance.
The chart shall be shot compliant with the condition specified in 5.5.3.
a) Simple dot chart b) Dot chart with connecting lines
Figure 4 — Dot chart
5.3.2 Requirement for the chart planarity
Non-planarity can be caused by bending of a chart.
Requirement for the chart planarity is as follows.
Surface deviation which is a height or depth from the reference plane [indicated as bending “a” in
Figure 5 a)] shall be less than 1,5 % of the width of the chart.
The required accuracy for a specific measurement sets the requirement for the chart planarity as follows.
For small bending, c is equal to half the width of the chart to which all numbers are normalized. If
bending a occurs in a chart, the effective chart width seen by the camera is b. The difference between c
and b causes the deviation in % measured due to the bending of the chart and calculated by (1-b/c) × 100.
The standard requirement for local geometric distortion measurement should be a maximum error of
0,045 % due to deviation in planarity of the chart. This equals a maximum deviation in planarity of 3 %.
And 3 % of half the width equals to 1,5 % of the full width of the chart.
6 © ISO 2015 – All rights reserved

Deviation a/c b/c = Deviation of
-1
in % cos (sin a/c) measured
distortion in %
0,5 0,005 0,999 987 0,001 3
1 0,01 0,999 950 0,005 0
2 0,02 0,999 800 0,020 0
3 0,03 0,999 550 0,045 0
4 0,04 0,999 200 0,080 0
5 0,05 0,998 749 0,125 1
6 0,06 0,998 198 0,180 2
8 0,08 0,996 795 0,320 5
9 0,09 0,995 942 0,405 8
10 0,1 0,994 987 0,501 3
a) Explanation of the parameters b) Table of numerical relation
Figure 5 — Explanation for the chart planarity and its effect on measured value
5.4 Grid chart
5.4.1 Design and characteristics
Figure 6 — Line grid pattern chart
The line grid pattern chart shown in Figure 6 is an example of a test chart for line distortion. The
horizontal and vertical lines of the grid shall be located between reference lines at no less than 1,0, 0,9,
0,8, 0,7, and 0,6 times the distance between the pairs of reference lines with the tolerance of ±2 %. The
pairs of reference lines are the sides of the outermost rectangle.
The chart shall be shot compliant with the condition specified in 5.5.3.
All other aspects regarding size and contrast shall be as described for the dot chart in 5.3.
5.5 Image/camera settings
5.5.1 General
Set the camera at minimal gain to minimize noise (if possible). All special colour modes or tone mode
should be deactivated. Quality factors, if available, should be set to their maximum.
5.5.2 Basic settings and influencing factors
The magnification is an important factor in measuring the distortion. The standard shooting distance
should be 30 times the focal length equivalent to 35 mm film camera. This means that a chart height of
720 mm fills the complete image. If the chart height differs more than 30 % from this requirement, the
chart height captured in the image shall be reported together with the results.
The camera shall be accurately focused on the chart.
Since distortion depends on the wavelength, it also depends on the illuminant and the spectral responses
of the sensor. Only the distortion on the green channel shall be reported.
5.5.3 Specific test procedures
5.5.3.1 Local geometric distortion
The chart shall be shot so that
— chart shall fill the field of view,
— number of dots should be no less than 15 dots in height and the related number of dots depending
on the image aspect ratio (for 4:3, 20×15 dots; for 3:2, 23×15) to form a regular grid,
— diameter of each dot should be no less than 10 pixels, and
— in case of reporting the single value as ISO local geometric distortion (see 7.2), and when using the
method of measuring actual dots, the corner 4 dots in the output image shall be positioned so that
the centre of each dot is on a vertex of the frame of the output image with the tolerance of 0 %, −2 %
(i.e. the centre of each dot is positioned from 98 % to 100 % at the actual image height).
5.5.3.2 Line geometric distortion
The chart shall be shot so that each reference line pair inscribes the frame of the output image with the
tolerance of 0 %, −2 % (i.e. the contact points of the reference line pair and the frame are positioned from
98 % to 100 % at the picture height or at the picture width).
5.5.4 Positioning of the camera
The chart shall be orthogonal to the optical axis. The alignment can be performed by using a mirror set
up on the target plane (i.e. parallel to the target plane), as shown in Figure 7.
Pan, tilt, and laterally displace the camera position to the left, right, up, and down until the centre point
of the taking lens in the viewfinder image is positioned at the image centre.
8 © ISO 2015 – All rights reserved

Figure 7 — Alignment of the camera with the target plane using a mirror
If the mirror is not available or the positioning method is not applicable, a manual alignment using
the straight lines in the chart shall be performed so that the intersection of the central horizontal and
vertical lines of the chart is in the centre of the image. For each horizontal/vertical line, the lines shall be
oriented “parallel” to the horizontal/vertical image borders meaning that the line shall be at the same
image height for the same distances from the vertical/horizontal centre of the image.
5.5.5 Exposure, white balance, and focus
The exposure shall be set by automatic exposure or set to an exposure level such that the uniform white
background becomes 110 to 160 (8-bit digital).
For a colour camera, the white balance shall be in a variable white balance mode or an automatic white
balance mode. The camera white balance should be adjusted, if possible, to provide proper white balance
for the illumination light source as specified in ISO 14524.
The focusing shall be adjusted in focus by a proper way, for example, a manual-focusing mode or an auto-
focusing mode.
6 Determination of geometric distortion
6.1 Local geometric distortion
6.1.1 Numerical definition
The local geometric distortion D (in %) is defined as given in Formula (1):
local
Dh=−'h'h'%×100 (1)
()
local 00
where
h’ is the distance to the actual dot position from the centre of the image (i.e. actual image height);
h’ is the distance to the ideal dot position from the centre of the image (i.e. ideal image height).
H’
H
H’
a) Undistorted grid b) Barrel distortion
c) Pincushion distortion
(negative) (positive)
Figure 8 — Common types of geometric distortion
The image is assumed to have no distortion at the centre. Therefore, h’ can be estimated from the
position of a few dots at the centre of the image. Each detected dot provides a value of local geometric
distortion, D . If the distortion is rotationally perfectly symmetrical, D is then plotted as a single-
local local
valued function of the distance to the image centre.
6.1.2 Outline of the practical algorithm
The following are the processing steps of the algorithm.
— Extract the dots.
— Determine precisely the position of the centre of the dots.
— Compare the position of the dots with the ideal position.
— Calculate the average grid spacing vector, based on the grid locations adjacent to the central pixel.
The use of a vector to represent the grid spacing is necessary to provide robustness against rotation
in the grid (a practical issue) (see Figure 9).
— The centre of the image is considered as the (0,0) grid location and all ideal grid positions are
calculated on a grid whose positions are integer values (it is not necessary but natural for usual
case).
10 © ISO 2015 – All rights reserved

— The geometric distortion for a grid position is the difference between the radial distance of the
actual grid position (h’) and radial distance to the ideal grid position (h’ ), divided by the ideal grid
position (h’ ).
If h’ < h’ , then distortion is negative. If h’ > h’ , then distortion is positive
0 0
— The above geometric distortion value is calculated for each valid grid position. This provides a 2D
data set for the lens distortion.
— The geometric distortion is plotted as a function of actual radial distance from the centre of the
image (i.e. actual image height: h’) for each grid point.
An algorithm for the detection of dots is provided in Annex B. An algorithm for sorting the grid from the
dots positions is provided in Annex D.
NOTE The distortion reference spacing is used to generate an “averaged” vector.
Figure 9 — Distortion reference spacing
6.2 Line geometric distortion
6.2.1 Horizontal line distortion
Let the maximum value of the height of the output image of the line grid pattern of each picture height
be Ai and the minimum value be Bi, and the number of pixels of the short side of the frame of the output
image be V, then horizontal line distortion is numerically defined as follows (see Figure 10).
When the vertical line Ai is located closer to the vertical line through the image centre than Bi, use
Formula (2):
DhiB=−iAiV2 ×100% (2)
()
Otherwise, use Formula (3):
DhiA=−iBiV2 ×100% (3)
()
where
i is a suffix representing each picture height;
Ai, Bi, and V shall be represented by the number of pixels of the output image.
NOTE The height means the vertical distance of the regarded line pair of the line grid pattern.
6.2.2 Vertical line distortion
Let the maximum value of the width of the output image of the line grid pattern of each picture width
be αi and the minimum value be βi, and the number of pixels of the short side of the frame of the output
image be V, then vertical line distortion is numerically defined as follows (see Figure 11).
When the horizontal line αi is located closer to the horizontal line through the image centre than βi, use
Formula (4):
Dvii=−βαiV2 ×100% (4)
()
Otherwise, use Formula (5):
Dvii=−αβiV2 ×100% (5)
()
Where
i is a suffix representing each picture width;
αi, βi, and V shall be represented by the number of pixels of the output image.
NOTE The width means the horizontal distance of the regarded line pair of the line grid pattern.
6.2.3 Total line distortion
— Line geometric distortion D i in each size is defined as Formula (6):
line



DhiDhi ×+DhiDhi %in case: DhiD> vi
() ()


Di= (6)

line

2 2

DviDvi ×+Dhi DDhi% in case: Dhi ≤ Dvi
() ()


— The expression for D i can be rewritten as Formula (7), where the sign shall either be Dhi or Dvi,
line
whichever has the larger absolute value:
Di =+DhiDvi % (7)
line
— Total line geometric distortion, D , is defined as the maximum D i value for i in absolute value.
line line
12 © ISO 2015 – All rights reserved

a) Pincushion type b) Barrel type
c) Wave type
Figure 10 — Schematic drawings for measuring the horizontal line distortion
a) Pincushion type b) Barrel type
c) Wave type
Figure 11 — Schematic drawings for measuring the vertical line distortion
7 Presentation of results
7.1 General
Two metrics of geometric distortion are defined in this International Standard and it is required to note
which distortion is reported, “local geometric distortion” or “line geometric distortion”.
7.2 Local geometric distortion
The presentation of local geometric distortion should be in the form of curves or tables of “D versus
local
the actual image height (h’)”.
If the actual image height is not indicated in relative expression, the absolute value of the maximum
image height in the same unit (e.g. in millimetres or in pixels) shall be reported beside.
NOTE This value understandably corresponds to 100 % in relative expression then equals to one half of the
diagonal of the image area.
Two examples of distortion profiles are shown in Figure 12, for both barrel and pincushion distortion.
A single value may be reported as ISO local geometric distortion when it is the largest absolute value of
an average of the distortion value at the same actual image height in the image field. If the largest local
geometric distortion appears to be at the maximum actual image height, the average distortion value
shall be determined by one of the following.
— Using an appropriate polynomial fitting of the distortion over actual image height and the value
appearing at the maximum actual image height shall be reported, if the profile of distortion (i.e. the
shape of the curve) is known and the accuracy of the fitting is expected less than or equal to 2 %.
— Measuring the dots at the maximum actual image height (i.e. the corner dots) positioned in
accordance with 5.5.3, the actual measured values shall be used.
a) Example of barrel b) Example of pincushion
Figure 12 — Examples of the presentation of local geometric distortion in the form of curves
7.3 Line geometric distortion
The presentation of line geometric distortion shall be a D value.
line
EXAMPLE Examples are listed below.
— ISO line geometric distortion +2,5 %
— Geometric distortion -2,0 % (ISO line geometric distortion).
14 © ISO 2015 – All rights reserved

Annex A
(informative)
Illustrative example and validation
There are generated simulated dot chart images with known levels of geometric distortion applied.
— 22 images in total
— Negative and positive geometric distortions in the 0 % - 16 % range
— 10 % negative and 10 % positive wave geometric distortion
— Image size 1 600 × 1 200 (image height = 1 000 pixels)
Simulated Geometric Distortion Measured Geometric Distortion
Figure A.1 — Reference images: simulated vs. measured geometric distortion values (X-Axis in
per mille of image diagonal and Y-Axis in %)
For all graphs, the x-axis is actual image height in per mille, i.e. the position in the image field (1 000 is
100 % of the diagonal), and the y-axis represents the amount of distortion in %.
There is good correlation between the level and shape of the simulated distortion and the measured
geometric distortion in the region of the image height that the measured points exist. However, the
maximum image height for measured values depends on the position of the farthest dot from the centre.
Care needs to be taken about the effects on actual measurements.
16 © ISO 2015 – All rights reserved

Annex B
(informative)
Extracting the dots from the target
B.1 Overview
This International Standard only uses the green channel to determine the geometric distortion. Because
there is difference of the dot positions for the three colour channels, which is evaluated as lateral
chromatic displacement.
NOTE This Annex describes about not only single channel but three colour channels. Readers are able to use
any partial information of this Annex as necessary.
The dot-finding method consists of two distinct phases.
The first phase uses the Green channel information to determine the region of interest for each dot.
Separating the dot finding into two steps allows each dot to be pre-processed individually prior to
determining the centre of mass. The following Clause describes the main ingredients of the algorithms
and then gives the related MATLAB code lines. The complete code is available from the following URL:
www.iso.org/17850
The following are several issues that a robust centre-finding method should manage:
— lens distortion (up to 15 %);
— lens shading (radial roll off in image intensity) (up to 40 %);
— ±10 % lighting illumination non-uniformity;
— different intensities of the red, green, and blue channels;
— noise.
Red Green Blue
Figure B.1 — What a dot really looks like
The simplest approach to finding the dots is to binarize the image using an appropriately chosen
threshold value. The presence of lens shading and colour channel imbalance complicates matters.
As Figure B.1 shows, the dots will have a variable depth and a variable tilt depending on where on the
lens shading profile the dot is. The presence of diffraction-based infrared filters in mobile phone camera
modules results in the uncorrected red channel data having faster colour shading roll off than the other
colour channels.
Management of the variable dot tilt and depths leads to an approach that individually pre-processes
each dot on each colour plane to correct the tilts and normalize the depths.
B.2 Finding dot regions of interest
B.2.1 Binarization threshold
As the green channel is typically the channel with the lowest noise and the highest resolution, it is used
to find the region of interest (ROI) of each dot. To find the region of interest for each dot, the image is
binarized.
The effects of lens shading mean that the threshold for binarization cannot be based on the whole image.
The solution to this is to calculate the threshold for an 8 × 8 grid of region of interests, each 1/8 of the
image in size.
The threshold used for the binarization is then the minimum of the thresholds for all of the regions of
interest.
This implementation uses Otsu’s method (MATLAB graythresh function) to calculate the thresholds.
Figure B.2 — Region of interest for each dot
B.2.2 Finding ROIs
The above threshold is used to binarize the green colour plane.
bw = im2bw(double(input)/double(max_code), threshold);

The max code is used to normalize the input data to ensure that both 8-bit and 10-bit are correctly
handled by MATLAB’s binarization function.
Invert to make black dots white for the subsequent processing.
bw = ~bw;
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Use MATLAB’s image processing functions to fill in any small gaps.
se = strel(‘disk’,2);
bw = imclose(bw,se);
Then fill any holes, so that region props can be used to estimate the area enclosed by each of the
boundaries.
bw = imfill(bw,’holes’);
The next step is to find the area, centroid, and bounding box for each object (dot) in the binarized green
plane data.
[B,L] = bwboundaries(bw,’noholes’);
stats = regionprops(L,’Area’,’Centroid’,’BoundingBox’);

The three sets of checks below use the above information to filter out any unwanted objects.
The first check is on the roundness of the object. The ratio of the bounding box area to the area of the
shape is used as a measure of roundness. For a circle, the value should ideally be 4/3,14 = 1,27. The range
of acceptance is 1,05 to 2,00. This wide range is necessary as geometric distortion will convert the dots
in the chart into ellipses.
dot_check(area_ratio < 1.05) = 0;
dot_check(area_ratio > 2.00) = 0;

Typically, there should be about 300 dots of similar diameter in the image; thus, the median diameter of
all the objects will represent the desired dot size. The assumption is that the 300 dots will be the most
common objects in the binarized image.
For the median calculation, only use dot sizes greater than the specified minimum allowed dot size
(default: 5 pixels).
dotSizeList = dot_size(dot_check > 0);
dotSizeList = sort(dotSizeList(dotSizeList > MinDotSize));

Find the median index of the list of dot sizes, clipping if necessary.
dot_count = length(dotSizeList);
median_index = uint16(dot_count / 2);
if median_index < 1, median_index = 1; end

Find the median dot size value.
if dot_count > 0
MedianDotDiameter = dotSizeList(median_index);
else
MedianDotDiameter = MinDotSize;
end
if MedianDotDiameter < MinDotSize
Config.MedianDotDiameter = MinDotSize;
end
Build the dot size check limits on the median dot size value.
MinDotDiameter = MedianDotDiameter / 2;
if MinDotDiameter < MinDotSize
MinDotDiameter = MinDotSize
end
MaxDotDiameter = MedianDotDiameter * 2;
The diameter check looks to see if the diameter of an object is within −50 % and +100 % of the median.
dot_check(dot_size < MinDotDiameter) = 0;
dot_check(dot_size > MaxDotDiameter) = 0;

For each object, a region of interest that is 1,9 times the width and 1,9 times the height of the object is
generated.
The final check is to reject any region of interest that touches the edge of the image.
dot_check(roi_x_ll < = 1) = 0;
dot_check(roi_y_ll < = 1) = 0;
dot_check(roi_x_ur > = image_width) = 0;
dot_check(roi_y_ur > = image_height) = 0;

Only objects that pass all of the above checks are considered to be valid dots.
B.2.3 Dot region of interest processing
The shape/profile of the dot is dependent on the following factors:
— noise;
— lens shading;
— channel sharpness;
— spatial resolution;
— matrix values.
For each ROI on each colour plane, the ROI data are processed as follows.
B.2.4 Dot pre-processing
The first step is to generate two masks, one for the background and a second for the dot. These masks
are used
...