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International Journal of Computer Applications (0975 - 8887)
Volume 180 - No.9, January 2018
Measurement of Unique Pupillary Distance using
Modified Circle Algorithm
A. F. M. Saifuddin Saif
Assistant Professor, Department of Computer Science
American International University-Bangladesh
Dhaka, Bangladesh
Md. Shahadat Hossain
M Scholar, Department of Computer Science
American International University-Bangladesh
Dhaka, Bangladesh
Khandaker Tabin Hasan
Associate Professor, Department of Computer Science
American International University-Bangladesh
Dhaka, Bangladesh
Mashiour Rahman
Associate Professor, Department of Computer Science
American International University-Bangladesh
Dhaka, Bangladesh
ABSTRACT
This research investigated several equations and calculated the
pupillary distance using pupils center coordinate. The prior re-
search has provided two conceptual frameworks which may give
a unique distance to all human. As Pupillary distance provides a
core and unique information as like bio-metric for every human.
The researcher did not explore the equation or pattern yet. This re-
search proposed a framework called as Pixellary Pupil Distance and
analyze the result. This research use pixel to calculate the pupillary
distance where subtracts left pupil pixel with the right pupil and
sum up with its distance pixel. Finally, the research sum all the
pixel subtraction and its distance what this research called pupil-
lary distance. This research builds and describes a custom dataset
for test purpose because the pupil is the core element of eyes and
this research did not find any precise dataset of it. The result shows
the unicity of pupillary distance. This research also shows the com-
putational time, false alarming rate, noise reduction which is de-
scribed the performance of the purposed framework.
Keywords
Pixellary pupil distance, Pupillary Distance, Bio-metrics, Eyes,
Distance Equation, Pupil Detection, Pupil Measurement, Edge De-
tection
1. INTRODUCTION
Pupillary distance is unique. This research has explored the unique
measurement of Pupillary Distance. There are many problems
which are not defined by the mathematical equation. Researchers
are trying to identify mathematical equations which are not defined
yet. The unique measurement of Pupillary Distance is one of them.
The most popular distance equations of two-point cannot solve the
problem. As a result, The research proposed two conceptual frame-
works [1] which have been presented distance equation of Pupillary
Distance. The research proposed the equation from the perspec-
tive of computer vision. The research use pixel instead of point to
describe the second framework which called Pixellary Pupil Dis-
tance [1] where pixellary introduces as a new word. The experi-
ment of the Pixellary Pupil Distance proved that pixel equation can
measure the unique Pupillary Distance for all human being.
Pixellary Pupil Distance is using pixel to measure unique distance
because a pixel is the smallest unit of an image. It used RGB value.
The red, green and blue use 8 bits each, which have integer values
from 0 to 255 [2]. As A biometric information is an asset for ev-
ery human [3] and The Euclidean Equation deals with two points
which did not define any unique distance as a biometric informa-
tion for pupillary distance [4]. Cartesian, Manhattan, vector pro-
jection equations are the most important equations to measure the
distance between two points which did not give a unique distance
of Pupils. After getting the failure result of the basic equation, This
research investigated the proposed conceptual models and equa-
tions. This research has experimented a new biometric information
as pupillary distance. This research is showing the experimentation
of Pixellary Pupil Distance which calculated by the smallest unit of
an image. This research also shows the Task description, dataset de-
scription, Comparison of Computation Time, Detection Rate, False
Alarm Rate and Noise Reduction as Result.
The rest of the paper is organized as follows. The following section
discusses literature review. Section 3 contains task description of
the experiment. Section 4 discusses dataset. Section 5 discusses the
result. Section 6 discusses Analysis and Discussion of the result.
Section 7 discusses the Limitation and Future Work. Finally, This
research concludes in section 8.
2. LITERATURE REVIEW
The pupil is one of the smallest units of eyes. The pupil is located
at the center of Irish. It was presented that there are two types of
pupil according to its color [5]. They have studied several eye track-
ing systems such as E-learning, Irish recognition, Eye Control for
Accessible and assistive, Car Assistant System and Field of View
Estimation and they did not describe any experimental result.
Pupil localization is very important to detect pupil. It was widely in-
vestigated to identify pupil coordinate, center and centroid point us-
ing several algorithms. Pupil centroid and its coordinate have been
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International Journal of Computer Applications (0975 - 8887)
Volume 180 - No.9, January 2018
Abridge of Pupils
Pupil Localization
Pupil Detecting
Pupil Estimation and Measurement
Abridge of Pixel
Fig. 1: A Block Diagram for Current Challenges of Pupils
used to localized pupil using Ada boosting eye classifier [6]. The
Algorithm showed 47% accuracy for eye region detection in face
region where the precision rate of detection in face region is 92%.
The accuracy of Ensembles Regression Tree [7] measured 85.75%
with 5% error rate and 99.7% accuracy recorded at 25% error
rate after reinvestigation. On the other hand, Adaptive GBDT [8]
recorded 99.89% accuracy at 25% error rate after reinvestigation
where It localized pupil coordinate at 91.54% at 5% error rate.The
Starburst model [9] has localized pupil center at the average frame
rate of 196.76(ms) where It recorded 91.92% accuracy.
Pupil detection is required to measure the accurate pupil distance
using pixel value. The curvature algorithm [10] detect pupil center.
The accuracy rate is 40% which is detected pupil boundary in an
error of less 0.1 degrees. The detection of pupil sized is identified
at 91% accuracy where 90% is the correct differentiation between
narcoleptic and control subjects using The Modified Adaptive Res-
onance Theorem using NNs [11]. The Canny Algorithm [12] [13]
able to detect pupil contour and edge at 10% error rate. Pupil con-
tour is detected by Morphology algorithm [14] where the error rate
is 10% on left pupil and 6% of right pupil. The Support Vector Ma-
chine(SVM) [15] is able to detect the coordinate of the area in eyes
with approximately 1.73% error rate. On the other hand, Correla-
tion matching and SVM are time consuming [15]. Although it had
the highest accuracy.
The measurement and estimation are highly needed for accurate
calculation of Pupil distance. It is the way to discover the pupil
center and diameter and area. Pupil size and blink rate used to dis-
cover pupil boundary point by Dual Ellipse Fitting Method [16]
in 2014. Novel self-tuning threshold method used for segmenting
the pupil from background images where Blink detection accuracy
is 99.7%. The Eyelink system [7] estimated the gaze position and
area is using the tracking of the eye data. The second order regres-
sor of PA varied ranging from 0.02% to 95.4%in the left eye where
it is 1.0% to 87.1% in the right eye. Transform [6], The Circle Area
Equation [17] and Ellipse Equation [17] used to measure the diam-
eter, center of the pupil in 2016. It was grated to use the Transform
in measuring Pupil diameter and center point due to the accuracy
level of Circle Area equation.
There are three major types of image which are Grayscale, Binary
and RGB [18]. Pixel is the smallest unit of an image. Every pixel
coincides with any one value. The value of the pixel between 0 and
255 in an 8-bit Grayscale image where zero is taken to be black, and
255 is taken to be white. The value of the pixel between 0 and 1 in a
binary image where zero is taken to be black, and one is taken to be
white. The value of the pixel between 0 and 255 in an RGB image.
RGB color space constructs all the colors from the combination
of the Red, Green and Blue colors. The red, green and blue use 8
bits each, which have integer values from 0 to 255 [2]. The value
of a pixel at any point corresponding to the intensity of the light
photons striking at that point. Each pixel store a value proportional
to the light intensity at that particular location. This research have
used RGB color space to calculate the Pupillary Distance.
3. TASK DESCRIPTION
The measurement of Pupillary Distance experiment is the core
task of this research. The experimental justification was the tough-
est challenge of this research. Although This research has exper-
imented the system using MATLAB. This research has divided
the experiment part into 7 sub-sections for describing convenience.
Before This research is going to analyze the result of the exper-
iment, it describes the experiment under section headline. The 7
sub-sections are:
(3.1) Face Detection
(3.2) Face Straighten
(3.3) Eye Detection
(3.4) Pupil Detection
(3.5) Pixel Extraction
(3.6) Pixel Distance Calculation
(3.7) Pupillary Distance Calculation
Besides that, This research describes dataset on Dataset Section.
This research tested the proposed research and come up with pupil-
lary distance which discusses at Result section. Then, Analysis
and Discussion contains Comparison of Computation Time, De-
tection Rate, False Alarm Rate and Noise Reduction.
3.1 Face Detection
Face detection is the first step of purposed experiment. When pro-
posed research get an image, it read the image. After reading the
image, the proposed research will detect the face from the image.
The Algorithm of face detection has been well established. SVM,
Template Matching, Eigenvector, distributing based using Gaussian
distribution and multilayer perceptron are the common and well
performance algorithms [19]. The proposed research has divided
the image into two halves for better detection. Proposed research
used the existing algorithm of face detection with the help of Mat-
lab. Cascade Object Detector is used to detect the face which is
experimented on Viola-Jones algorithm [20].
3.2 Face Straighten
The SURF Operator is the local feature detector and descriptor. It
has given invariance of scaling and rotation, strong robustness, and
prominent separating capacity between different features [21]. Pro-
posed research experiment face straightens for removing the initial
noise. The Image which takes as input, those may not be center cap-
tured. Proposed research do face straighten for getting the accurate
result.
3.3 Eye Detection
Eye detection is one of the major preprocessing stages before Irish
and pupil detection said by Amer Al-Rahayfeh and Maid Faezipour
[22]. Sobel filter can be used to extract edge feature. The proposed
research found several Algorithm which used to detect eye using
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International Journal of Computer Applications (0975 - 8887)
Volume 180 - No.9, January 2018
template matching [21]. Although, Support vector machine used to
classify the images of an eye or non-eye patterns. As eyes are not
symmetrical like as faces, one classifier of each eye used to train
said by Yu Shiqi [20]. Cascade Object Detector is used to detect
the eyes which are experimented according to Yu Shiqi algorithm.
3.4 Pupil Detection
Pupil detection is most important part of the paper. Several frame-
works have been discussed pupil detection [19]. Those algorithms
accuracy is not effective. As Proposed research need to pupil cen-
ter and contour, its used Circle Equation Algorithm to detect the
pupil. It has given low accuracy to detect pupil diameter [17]. The
proposed research found that object polarity is dark. So, it modified
the algorithm according to the sensitivity of darkness. Proposed re-
search observed that pupil size is 6 pixel to 8 pixels. The proposed
research found that the algorithm is better than exiting algorithm
which is tested using Matlab.
3.5 Pixel Extraction
Pixel Extraction is one of the cores for features for distance calcula-
tion. The proposed research has found the pupil center co-ordinate
and pupil size from pupil detection step. After getting the center
coordinates of pupils, this research did average the value of x-axis
for removing pixel noise. Because x-axis coordinate is not same.
As a result, this research found same pupils size most of the cases
which are reduced size and noise. Proposed research extracted the
pupil contour using modified Circle Equation Algorithm. Proposed
research also extracted the intermediate pixel of pupils which has
set the value to zero.
3.6 Pixel Distance Calculation
The proposed research analyzes the only pixel of pupils and its in-
termediate. First, Proposed research calculates the no of rows. This
research finds the first row of the left pupil of first non zero column
and subtracts with the right pupil of first non zero column. This re-
search also calculates a number of the pixel from the left pupil of
first non zero column to right pupil of first non zero column in the
same matrix. which this research called the pixel distance for a spe-
cific pixel of two pupils. This research carried the same calculation
for all rows and column of left pupil to right pupil. when this re-
search get any two zero column at the intermediate of a calculation,
this research stop calculation for that row. because it’s the finishing
pixel of left pupil. This research also stores pixel co-ordinate of the
right pupil for calculation.
In this step, this research has solved below equation [1]:
Pj
i=Lj
i
−Rj
i+Distanceof Lj
itoRj
i
3.7 Pupillary Distance Calculation
This research calculates work with the calculating result of Pixel
Distance. This research sum the subtracted value of all specific
pixel with its distance value. Then this research reorganizes the
value as per subtracted value. Finally, this research sum all value
which this research called pupillary distance.
In this step, this research experimented below equation [1]:
P upilDistance =
j
X
i
P
4. DATASET
This research used several databases. That dataset is not perfect for
pupil detection. Some datasets used for face recognition. Specific
datasets are used for Irish recognition. Since pupil is the smallest
unit of an eye that’s why those datasets are not given any significant
result. For this reason, this research constructed a database with 20
peoples of multiple images. This research did not change the light
effect. This research inspired the audience to make shocking eyes.
So that this research can clearly capture the image of full Irish. As a
result, the purposed framework detected the pupil from that image
easily.
5. RESULT
This research has measured 20 subjects pupillary distance, each of
5 images. This research provides the information in the tabular for-
mat. This research shows the PD as pupillary distance, CT as com-
putational time, FAR as False Alarming Rate and NRR as Noise
Reduction Rate. The highest PD is 32432 and lowest is PD 18933
which is the average of 5 images without false recognition. The
computational time shows an average time of 5 images where it
defers from 1500ms to 2100ms. As this research experiments 5 im-
ages of each subject which is 100% for a subject. False Alarming
Rate is 20% when an image has been miscalculated of that sub-
ject, 40% means two images of that subject and so on. On the other
hand, this research let 100% noise reduction if no false alarming
has not occurred.
In Table 1, this research called ‘subject‘ to one individual image,
PD as pupillary distance, CT as Computational Time, FAR as False
Alarming Rate and NRR as Noise Reduction Rate.
6. ANALYSIS AND DISCUSSION
The experimental result of the purposed framework has shown in
tabular format in the immediate upper section where this research
has shown the pupillary distance, computational time, False alarm-
ing rate and Noise Reduction. This research has shown the average
pupillary distance of each individual. The lowest pupillary distance
is 18933 and highest is 32432. The average computational time of
all subjects is 1813ms where the lowest computational time is 1560
and highest is 2100ms. The False Alarming Rate occurred in 30%
subjects. But the impact rate is 8% among all images. The noise
reduction rate has been increased to 70% which is impact 92% im-
ages of the dataset which is shown in Fig-2.
Fig. 2: The graph shows False Alarming Rate Vs Noise Reduction Rate
The lowest pupillary distance is 18933 at 9th subject where com-
putational time is 1680ms which is lower than the average compu-
tational time of the dataset. The noise reduction rate is 100% where
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International Journal of Computer Applications (0975 - 8887)
Volume 180 - No.9, January 2018
Table 1. : Result of 20 subjects each of 5 images
Sub. No PD CT/Image FAR NRR
1 26983 1700 0% 100%
2 20021 1600 20% 80%
3 23002 1750 0% 100%
4 25983 1850 0% 100%
5 24029 1750 0% 100%
6 23094 1800 0% 100%
7 27128 2010 20% 80%
8 30943 2050 0% 100%
9 18933 1680 0% 100%
10 32432 1930 20% 80%
11 29123 1750 0% 100%
12 22923 1980 0% 100%
13 27452 1780 40% 60%
14 21523 1920 0% 100%
15 20329 1840 0% 100%
16 19021 2100 40% 60%
17 27392 1560 0% 100%
18 23458 1660 0% 100%
19 25123 1750 0% 100%
20 23843 1800 20% 80%
the false alarming rate is 0%. On the other hand, The highest pupil-
lary distance is 32432 at 10th subject where computational time is
1930ms which is greater than the average computational time of the
dataset. The false alarming rate is 20% where the noise reduction
rate is 80%.
Fig. 3: The graph shows subject vs computational time
If this research looks the subject vs computational time graph, this
research observed that computational time is in between 1560ms to
2100ms, once a number of images are remaining same. The com-
putational time is proportional to the pupillary distance where the
False Alarming Rate or Noise Reduction Rate does not depend on
pupillary distance. The pupillary distance is different of every in-
dividual at the same light intensity where it will be different for an
individual if the light intensity change.
7. LIMITATION AND FUTURE WORK
This research has experimented pixellary pupil distance to calcu-
late the pupillary distance which is given a unique result. This re-
search has a scope to experiment with the biggest data set. On the
other hand, this research did not provide any comparison with the
millimeter scale. It is also a scope for further research improve-
ment.This research did not distinguish between gender or age us-
ing the research output. This research did not consider with focal
length, the light intensity which is biggest opportunity to research
on pixellary pupil distance. Although, the proposed research will
suggest you a new path to research on pupillary distance.
8. CONCLUSION
Pupillary distance is bio-metric information which is not proved by
any researcher yet. But this research has shown a path to make it as
biometric information. The challenge of pupil detection solved by
the purposed framework and dataset. This research has also exper-
imented pupillary distance according to the purposed framework
which is the biggest milestone for computer vision. This research
has shown that Modified Circle Algorithm can detect pupil bet-
ter than all other algorithms to proposed framework. This research
modified the object polarity, pupil size, and sensitivity to detect it
more accurately. This research did not consider light intensity, fo-
cal length, age, gender. Finally, this research calculates the pupil-
lary distance using pixel which has shown a straight path to the
researcher to discover more about pupillary distance and there is
the biggest scope to study about pupillary distance.
9. REFERENCES
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