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An Analysis of Performance for Commonly Used Interpolation Method
Conference Paper · April 2016
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2. RESEARCH ARTICLEXXXXXXXXXXXXXXXXX
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Copyright © 2015 American Scientific PublishersAdvanced Science Letters
All rights reservedVol. XXXXXXXXX
Printed in the United States of America
An Analysis of Performance for Commonly Used
Interpolation Method
M. B Hisham1,2
, ShahrulNizamYaakob2
, Raof R.A.A2
, A.B.A. Nazren1,2
, N.M.Wafi1,2
1
Embedded, Network And Computer (ENAC),
2
School of Computer and Communication Engineering, University Malaysia Perlis,
01000Kangar, Perlis, Malaysia,
Interpolation is an imaging method that use to expand or reduced the number of pixels in a digital image. Basically, there are
many way to perform an interpolation technique but in this research, only some method of interpolation techniques will be
focus in order to acquire a high quality image after the image is enlarged. In this paper, nearest neighbor interpolation,
bilinear interpolation and bicubic interpolation is analyzed based on the image interpolation algorithms principle. The aim is
to study the performance of these methods in term of quality image. Furthermore, the paper also provided some explanation
for the methods as the concept that applied to calculate pixel value and how the image is magnified. At the end of the
research, the performance of all interpolation algorithms is examined by making comparison based on the value of Peak
Signal to Noise Ratio (PSNR) and visual inspection.
Keywords: Interpolation, Nearest Neighbor, Bilinear, Bicubic
1. INTRODUCTION
Super resolution is a process to achieve the best image
quality through the single low-resolution image or
multiple low-resolution (LR) images of the same scene [1,
2]. The reason why the Super-resolution (SR) imaging is
emerged is to overcome or compensate the limitation or
shortcomings of the image acquisition device/system
and/or possibly ill-posed acquisition conditions to
produce a higher-resolution image based on a set of
images that were acquired from the same scene [3].Hence,
it is necessary to generate an image with higher quality
through super resolution image reconstruction.
In super resolution, enlargement of an image is a basic
in creating a good quality of image. In several methods in
super resolution, image enlargement is often used
especially when zooming a small part of an image.
Enlarging an image is generally common for the smaller
images which turn into a larger size of image. It provided
a detail view when a small portion of an image is zoomed.
*
Email Address: hishambadrul9009@gmail.com
Images are magnified to enhance image resolution,
increase image quality, and improve identification. This
technique is aiming to eliminating image distortion, such
as blurring and rough edges, upon image enlargement and
at the same time, the image quality is maintained. The
basic principle of enlargement image is by increasing the
number of pixels so that low resolution image is
converting to high resolution image. When enlarge a
small image, the pixels with empty space is create. By
using the methods in super resolution, the empty spaced
pixels are filled with appropriate value.
Presently, the interpolation method is most
frequently used image enlargement method. In the result,
the performance of image enlargement for different
interpolation algorithms was compared by using the value
of Peak Signal to Noise Ratio (PSNR). These PSNR
values can be used to prove which method that gives a
good images quality. It also gives the guidance for the
user to choose a suitable algorithm to achieve optimum
results according to different application.

3. Adv. Sci. Lett. X, XXX–XXX, 2015RESEARCH ARTICLE
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2.INTERPOLATION
Interpolation is the process of increasing the size of
images by creating new pixel value and filling the proper
value by some algorithms [4, 9]. The mean value of near
most pixels is used to add pixel values to this newly
generated pixel [5]. In order to estimate the value of
unknown point, interpolations use two or more known
data [6]. The basic in image interpolation is to have
reference image as the base to construct a new scaled
image. the constructed image will be larger depending on
the scaling. When enlarging an image, it absolutely
creating some empty spaces in the original base image as
shown in figure 1. Interpolation algorithms used to find
appropriate spot to place the empty spaces inside the
original image and top up each empty spaces with proper
value.
Fig.1. Image with scaling of 2
A. Nearest Neighbor Interpolation
There are many way to perform the interpolation.
One of them is Nearest Neighbor interpolation. Nearest
Neighbor algorithm is the simplest interpolation
algorithm [7]. Each unknown pixel is assigned with an
intensity value that is same as its neighboring pixels [8].
Moreover, this method is fastest implementation of image
scaling technique [9].
Therefore, Nearest Neighbor method is very useful
when the speed is the main concern especially for
zooming for a small part of the image. Having a reference
image is the principle in image scaling and by using this
image as a base; a new scaled image can be constructed.
When enlarge an image, it actually creating an empty
space on the original base image. For Nearest Neighbor
method, the empty spaces are replaced by the nearest
pixel.
Fig.2. Nearest Neighbor algorithms
Let say, the size of original image, A: RxC and size
of scaled image, B is R'xC'. The row scale factor, 𝑆𝑟 and
column scale factor, 𝑆𝑐is.
𝑆𝑟 =
𝑅 − 1
𝑅′
, 𝑆𝑐 =
𝐶 − 1
𝐶′
(1)
For each(𝑟′
, 𝑐′) in B, the corresponding fractional
pixel location, (𝑟𝑓, 𝑐𝑓)in A is:
𝑟𝑓, 𝑐𝑓 = 𝑆𝑟 ∙ 𝑟′
, 𝑆𝑐 ∙ 𝑐′
(2)
The closest integer pixel location 𝑟, 𝑐 , in A:
𝑟, 𝑐 = 𝑟𝑓, 𝑐𝑓 (3)
Where value of (𝑟, 𝑐)is the result of fractional pixel
location,(𝑟𝑓, 𝑐𝑓)which has been rounded whereby it is
used to gain 𝐵(𝑟′, 𝑐′).
𝐵 𝑟′
, 𝑐′
= 𝐴 𝑟, 𝑐 (4)
B. Bilinear Interpolation
Bilinear interpolation is extension of linear
interpolation. The main idea is to implement linear
interpolation in two directions [10, 13].Bilinear
interpolation algorithm is an interpolation technique that
reduces the visual distortion by the fractional zoom
calculation.
The concept of this method used is just like midpoint.
It uses four Nearest Neighbor of pixels whose value is to
be determined. From the below figure, it can be seen how
an intermediate pixel at point (𝑟𝑓, 𝑐𝑓) is created by
interpolating nearest four pixels which is 𝑟, 𝑐 , 𝑟 +
1,𝑐, 𝑟,𝑐+1 and 𝑟+1,𝑐+1.
Fig.3. Diagram for Bilinear Interpolation
An original image has been chosen before it
converting into a matrix form and another matrix with a
new size is created which contain zero elements. This
matrix is padded with the matrix of image so that the
resulted matrix will contains zero elements in every
alternate row and column. Then, the final pixel value of
𝐵 𝑟′
, 𝑐′ is calculating as below:
The value of 𝑆𝑟 and 𝑆𝑐 is the row and column scale
factor of original image of A and newly scaled image, B.

4. RESEARCH ARTICLEXXXXXXXXXXXXXXXXX
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𝑆𝑟 =
𝑅 − 1
𝑅′
, 𝑆𝑐 =
𝐶 − 1
𝐶′
(5)
For each pixel (𝑟′
, 𝑐′)in output image, B, compute
the fractional location (𝑟𝑓, 𝑐𝑓)in original image, A
.
𝑟𝑓, 𝑐𝑓 = 𝑆𝑟 ∙ 𝑟′
, 𝑆𝑐 ∙ 𝑐′
(6)
𝑟, 𝑐 = 𝑟𝑓 , 𝑐𝑓 (7)
where 𝑟, 𝑐 is round down value of 𝑟𝑓, 𝑐𝑓 . By using
𝑟, 𝑐 , the integer part of 𝑟𝑓, 𝑐𝑓 to find the 4 neighboring
location in A.
∆ 𝑟,∆ 𝑐 = 𝑟𝑓 − 𝑟, 𝑟𝑓 − 𝑐 (8)
Then, compute 𝐵(𝑟′
, 𝑐′)from a weighted sum of A at
each the location. The weight computed from ∆ 𝑟and ∆ 𝑐.
𝐵 𝑟′
, 𝑐′
= (𝐴 𝑟, 𝑐 ∙ 1 − ∆ 𝑟 ∙ 1 − ∆ 𝑐
+ 𝐴 𝑟 + 1, 𝑐 ∙ ∆ 𝑟 ∙ 1 − ∆ 𝑐
+ 𝐴 𝑟, 𝑐 + 1 ∙ 1 − ∆ 𝑟 ∙ ∆ 𝑐
+ 𝐴 𝑟 + 1, 𝑐 + 1 ∙ ∆ 𝑟 ∙ ∆ 𝑐 ) (9)
C. Bicubic Interpolation
In mathematics, Bicubic interpolation is an extension
of cubic interpolation data point. In image enhancement,
Bicubic interpolation is often chosen compare with
Nearest Neighbor and bilinear interpolation when speed is
not taken into account. If earlier, previous method only
use nearest four pixels but in this method, the nearest 16
pixels are used to create an intermediate pixel, 𝐵(𝑟′
, 𝑐′)
[11]. See figure 4 for more detail.
Fig.4. Diagram for Bicubic Interpolation
In above figure, an intermediate pixel 𝐵(𝑟′
, 𝑐′) is
created by interpolating nearest 4x4 pixels
from 𝐴(𝑟, 𝑐)to 𝐴(𝑟 + 2, 𝑐 + 2). The row scale factor, Sr and
column scale factor, Sc for original image of A and new
scaled image B is computed.
𝑆𝑟 =
𝑅
𝑅′
, 𝑆𝑐 =
𝐶
𝐶′
(10)
Then, to find the value of𝐵(𝑟′
, 𝑐′), the equation below
is used to interpolate nearest 16 pixels.
𝐵 𝑟′, 𝑐′ = 𝑎𝑖𝑗 𝐴𝑖𝑗
3
𝑗=0
(11)
3
𝑖=0
Where 𝐴𝑖𝑗 are values of 16 nearest pixels of
𝐵(𝑟′
, 𝑐′).The coefficients of 𝑎𝑖𝑗can be found by using La-
grange equation.
𝑎𝑖𝑗 = 𝑎𝑖 × 𝑏𝑗 (12)
𝑎𝑖 =
𝑟′ − 𝑆𝑟 × 𝑥 + 𝑘
𝑆𝑟 × 𝑥 + 𝑖 − 𝑆𝑟 × 𝑥 + 𝑘
(13)
3
𝑘=0, 𝑘≠𝑖
𝑏𝑖 =
𝑐′ − 𝑆𝑐 × 𝑦 + 𝑘
𝑆𝑐 × 𝑦 + 𝑖 − 𝑆𝑐 × 𝑦 + 𝑘
(13)
3
𝑘=0, 𝑘≠𝑗
Where 𝑎𝑖 is the 𝑖 𝑡𝑕
row of A and 𝑏𝑗 is the 𝑗 𝑡𝑕
column of
A. The value of k is considered not equal to 𝑖. Meanwhile,
x and y is the value of each rowsand columns that divided
by scale factor, 𝑆𝑟 and 𝑆𝑐.
3.EXPERIMENTAL RESULT
In order to test and compare the performance of all
three interpolation method, several different images are
captured. Those images are captured by twice for every
single of testing image where first sample is taken in 120
centimeter from camera (which is called sample 1) and
the second sample is taken in 60 centimeters from the
camera (called sample 2). Rationally, the image of sample
1 is considered as small image for original image of
sample 2 for every different testing image.
By using the algorithms, the images sample 1 are
enlarging by two scale factor. The resultant images which
acquired from that implementation will be compared to its
original image which is sample 2 of every testing image.
Therefore, Peak Signal to Noise Ratio (PSNR) is
applied on the resultant images in order to evaluate the
performance of interpolation methods. By using its
calculation, PSNR values prove which one has really
higher quality than others. PSNR is most easily defined
via the mean squared error (MSE). Consider I is noise-
free monochrome image and K is its noisy approximation,
MSE is defined as [12]:
𝑀𝑆𝐸 =
1
𝑚𝑛
[𝐼 𝑖, 𝑗 − 𝐾(𝑖, 𝑗)]2
𝑛−1
𝑗=0
𝑚−1
𝑖=0
(15)
The PSNR (in dB) is defined as:
𝑃𝑆𝑁𝑅 = 10 ∙ 𝑙𝑜𝑔10
𝑀𝐴𝑋1
2
𝑀𝑆𝐸
= 20 ∙ 𝑙𝑜𝑔10
𝑀𝐴𝑋1
𝑀𝑆𝐸
(16)
Table 1 has shown the value of PSNR between
magnified image of sample 1 and sample 2 for those
interpolation methods after the test for all of testing image
has been done. This PSNR value computes the peak to
signal ratio, in decibel, between two images. This ratio is
often used as a quality measurement between the original
and a magnified image. Therefore, the higher value in

5. Adv. Sci. Lett. X, XXX–XXX, 2015RESEARCH ARTICLE
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PSNR means the quality of image is higher.
Table.1. PSNR Value For Three Interpolation
Method
Testing Image Nearest Bilinear Bicubic
Image 1 20.6239 20.7859 20.9603
Image 2 22.8448 22.8676 22.9120
Image 3 23.6664 24.0662 24.4238
Image 4 24.3410 24.5270 25.5025
From the table above, it shown that the Nearest
Neighbor interpolation give lowest quality compare to
others. This method assigns a pixel value with an error
equal at most to half a pixel. Consequently, its produces a
blocky appearance and increase the visibility of jagged
that resulting a poor quality image. Meanwhile, Bilinear
interpolation gives better result than previous method.
From the observation, this method produces much
smoother looking image than Nearest Neighbor. However,
the image can still be somewhat jagged and also resulting
in blurring or loss of image resolution due to the
alteration of grey level in the process. The method that
provided highest quality interpolated image is Bicubic
interpolation. This method produces smoother edge than
bilinear and nearest neighbor. It's also very effective and
generate a better image that are very close to the original
image.
4. CONCLUSIONS
Nearest neighbor interpolation is simplest algorithms
to be implemented and make the pixels bigger. Low of
computation load makes this method easy to be
performed. In this method, the value of a pixel in the new
image is the value of the nearest pixel of the original
image. However, these algorithms create a jagged and
blocky appearance on the resultant image.
In interpolation, bilinear interpolation is more
difficult than nearest neighbor interpolation and it has
larger calculation. Therefore, bilinear interpolation
generates an image of smoother appearance than nearest
neighbor interpolation but alteration of grey level in the
process causing blurring or loss of image resolution.
Bicubic interpolation absolutely can give a better
image quality than previous methods. This method is the
best method among them when the execution time is not
taken into account. Therefore, the algorithm is always
chosen in many images processing image software as
Photoshop, After Effects and Avid etc. Nevertheless, it
need larger amount of calculation and its computation
complexity is higher than bilinear algorithms.
ACKNOWLEDGMENTS
This work was supported financially by the Ministry
of Education under Fundamental Research Grant Scheme
(FRGS9003-00464).
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Received: 22 September 2010. Accepted: 18 October 2010
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