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I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
Published Online April 2013 in MECS (http://www.mecs-press.org/)
DOI: 10.5815/ijigsp.2013.05.07
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
A Comparative Analysis of Image Scaling
Algorithms
Chetan Suresh
Department of Electrical and Electronics Engineering, BITS Pilani
Pilani - 333031, Rajasthan, India
E-mail: shivchetan@gmail.com
Sanjay Singh, Ravi Saini, Anil K Saini
Scientist, IC Design Group,
CSIR – Central Electronics Engineering Research Institute (CSIR-CEERI)
Pilani – 333031, Rajasthan, India
Abstract— Image scaling, fundamental task of
numerous image processing and computer vision
applications, is the process of resizing an image by pixel
interpolation. Image scaling leads to a number of
undesirable image artifacts such as aliasing, blurring and
moiré. However, with an increase in the number of
pixels considered for interpolation, the image quality
improves. This poses a quality-time trade off in which
high quality output must often be compromised in the
interest of computation complexity. This paper presents
a comprehensive study and comparison of different
image scaling algorithms. The performance of the
scaling algorithms has been reviewed on the basis of
number of computations involved and image quality.
The search table modification to the bicubic image
scaling algorithm greatly reduces the computational load
by avoiding massive cubic and floating point operations
without significantly losing image quality.
Index Terms— Image Scaling, Nearest-neighbour,
Bilinear, Bicubic, Lanczos, Modified Bicubic
I. INTRODUCTION
Image scaling is a geometric transformation used to
resize digital images and finds widespread use in
computer graphics, medical image processing, military
surveillance, and quality control [1]. It plays a key role
in many applications [2] including pyramid construction
[3]-[4], super-sampling, multi-grid solutions [5], and
geometric normalization [6].
In surveillance-based applications, images have to be
monitored at a high frame rate. Since, the images need
not be of the same size, image scaling is necessary for
comparison and manipulation of images. However,
image scaling is a computationally intensive process due
to the convolution operation, which is necessary to
band-limit the discrete input and thereby diminishes
undesirable aliasing artifacts [2].
Various image scaling algorithms are available in
literature and employ different interpolation techniques
to the same input image. Some of the common
interpolation algorithms are the nearest neighbour,
bilinear [7], and bicubic [8]-[9]. Lanczos algorithm
utilizes the 3-lobed Lanczos window function to
implement interpolation [10].
There are many other higher order interpolators which
take more surrounding pixels into consideration, and
thus also require more computations. These algorithms
include spline [11] and sinc interpolation [12], and retain
the most of image details after an interpolation. They are
extremely useful when the image requires multiple
rotations/distortions in separate steps. However, for
single-step enlargements or rotations, these higher-order
algorithms provide diminishing visual improvement and
processing time increases significantly.
Novel interpolation algorithms have also been
proposed such as auto-regression based method [13],
fuzzy area-based scaling [14], interpolation using
classification and stitching [15], isophote-based
interpolation [16], and even interpolation scheme
combined with Artificial Neural Networks [17].
Although these algorithms perform well, they require a
lengthy processing time due to their complexity. This is
intolerable for real-time image scaling in video
surveillance system. Hence, these algorithms have not
been considered for the comparative analysis in this
paper.
In this paper, firstly, image interpolation algorithms are
classified and reviewed; then evaluation and comparison
of five image interpolation algorithms are discussed in
depth based on the reason that evaluation of image
interpolation is essential in the aspect of designing a real-
time video surveillance system. Analysis results of the
five interpolation algorithms are summarized and
presented.
II. IMAGE SCALING
Image scaling is obtained by performing interpolation
over one or two directions to approximate a pixel’s
colour and intensity based on the values at neighbouring
56 A Comparative Analysis of Image Scaling Algorithms
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
pixels. More the adjacent pixels used for interpolation,
better the quality of interpolated output image.
Digital image interpolation is the process of
generating a continuous intensity surface from discrete
image data samples. Generally, almost every geometric
transformation like translating, rotating, scaling, and
warping requires interpolation to be performed on an
image [18]. Such transformations are essential to any
commercial digital image processing software. The
perceived quality of the interpolated images is affected
by several issues such as sharpness of edges, freedom
from artifacts and reconstruction of high frequency
details [18].
Interpolation algorithms attempt to generate
continuous data from a set of discrete data samples
through an interpolation function. These interpolation
methods aim to minimize the visual defects arising from
the inevitable resampling error and improve the quality
of re-sampled images [19]. Interpolation function is
performed by convolution operation which involves a
large number of addition and multiplication operations.
Hence, a trade-off is required between computation
complexity and quality of the scaled image.
Based on the content awareness of the algorithm,
image scaling algorithms can be classified as Adaptive
image scaling and Non-adaptive image scaling.
Adaptive image scaling algorithms modify their
interpolation technique based on the image content
being a smooth texture [20] or a sharp edge [21]-[22].
As the interpolation method changes in real-time, these
algorithms are complex and computationally intensive.
They find widespread use in image editing software as
they ensure a high quality scaled image. As the focus is
on analysing image scaling algorithms for real-time
applications, these algorithms are beyond the scope of
the paper.
Non-adaptive image scaling algorithms like nearest
neighbour, bilinear, bicubic and Lanczos algorithms
have a fixed interpolation method irrespective of the
image content.
III. COMPARATIVE ANALYSIS OF IMAGE SCALING
ALGORITHMS
This section discusses the Non-adaptive Image scaling
algorithms like nearest neighbour, bilinear, bicubic,
modified bicubic, and Lanczos. Let P(x,y) represent the
pixel in input image of MxN dimensions and U(i,j)
represents the pixel in scaled/resized output image of
size M’xN’. Let T be the transformation used for scaling.
The each pixel of output image is computed by applying
the transformation T on input image pixels as shown in
Fig. 1.
Figure 1. Image scaling procedure
A. NEAREST NEIGHBOUR IMAGE SCALING
The simplest image interpolation method is to select
the value of the nearest input image pixel and assigning
the same value to scaled image pixel. The nearest
neighbour algorithm (Fig. 2) selects the value of the
nearest known pixel and does not consider the values of
other neighbouring pixels, yielding a piecewise constant
function [23].
For nearest neighbour algorithm the level of
complexity is low leading to a fast computation time.
But the scaled image quality is low and high aliasing
effect is observed.
Figure 2. Nearest neighbour image scaling algorithm
B. BILINEAR IMAGE SCALING
Another simple interpolation method is linear
interpolation, a slight improvement over the nearest
neighbour interpolation algorithm. In linear interpolation,
the interpolated value is computed based on the
weighted average of two data points. The weights are
inversely proportional to the distance of the end points
from the interpolated data point.
Bilinear interpolation algorithm [7] performs linear
interpolation in one direction followed by linear
interpolation of the interpolated values in the other
direction. The algorithm uses 4 diagonal pixels
surrounding the corresponding source image pixel for
interpolation (Fig. 3). It computes a weighted average
depending on the nearness and brightness of the 4
diagonal pixels and assigns that value to the pixel in the
output image.
A Comparative Analysis of Image Scaling Algorithms 57
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
Figure 3. Bilinear image scaling algorithm
Bilinear offers considerable improvement in image
quality with a slightly increased complexity. The
aliasing effect is reduced though blurring is observed.
C. BICUBIC IMAGE SCALING
Bicubic interpolation algorithm [8]-[9] performs cubic
interpolation in one direction followed by cubic
interpolation of the interpolated values in the other
direction (Fig. 4).
Figure 4. Bicubic image scaling algorithm
The bicubic interpolation approximates a sinc
interpolation by using cubic polynomial waveforms
instead of linear waveforms when computing an output
pixel value. The algorithm uses 16 nearest pixels
surrounding the closest corresponding pixel in the
source image for interpolation.
Bicubic offers high scaled image quality at the cost of
considerably high complexity. Edge halo effect is
observed though aliasing and blurring are reduced.
D. LANCZOS IMAGE SCALING
The Lanczos interpolation algorithm [10] uses a
windowed form of sinc filter (an ideal low-pass filter) to
perform interpolation on a 2-D grid. Sinc function of a
variable can be mathematically obtained by dividing the
sine function of the variable by itself [9]. Sinc function
theoretically never goes to zero. Hence, a practical filter
can be implemented by multiplying the sinc function
with a window operator such as Hamming [24]-[25] and
Hann [26] to obtain a filter with a finite size.
The Lanczos filter can be obtained by multiplying the
sinc function with the Lanczos window which is
truncated to zero outside of the main lobe [27]. The size
of the Lanczos window is defined by the order of the
convolution kernel.
Figure 5. Lanczos image scaling algorithm
The number of neighbouring pixels considered varies
as the order of the kernel. If the order is chosen to be 2,
16 pixels are considered while if the order is 3, 36
neighbouring pixels are utilized for interpolation. For
58 A Comparative Analysis of Image Scaling Algorithms
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
sufficient image quality, the order is chosen to be 3 in
the implementation (Fig. 5).
The Lanczos algorithm gives an output scaled image
of the same quality as bicubic but at the cost of higher
number of computations as 36 pixels is used for
interpolating the value of each output pixel compared to
16 for bicubic. The Lanczos algorithm is comparatively
more efficient for multiple scaling operations.
E. MODIFIED BICUBIC IMAGE SCALING
According to the bicubic convolution kernel equation,
massive calculations of four spots bicubic interpolation
algorithm include large cubic and floating point
multiplication operation. The bicubic interpolation
algorithm discussed above can be slightly modified as
shown below (Fig. 6). The co-efficients a0, a1, a2, a3,
b0, b1, b2, and b3 are now a function of dx and dy (the
difference between the interpolated co-ordinate and
nearest integer source co-ordinate lower than it) instead
of the interpolating pixels. This allows us to compute
and store the values of the co-efficients for pre-
determined values of dx and dy. This avoids the large
number of cubic and floating point operations involved
in bicubic interpolation.
dy/6;*dy*dy + dy/6- = b3
dy/2;*dy*dy- dy/2*dy +dy = b2
dy/2;*dy*dy + dy/2*dy - dy/2 - 1 = b1
dy/6;*dy*dy - /2dy *dy + /3dy - = b0
dx/6;*dx*dx + dx/6- = a3
dx/2;*dx*dx- dx/2*dx + dx = a2
dx/2;*dx*dx + dx/2*dx - dx/2 - 1 = a1
dx/6;*dx*dx - /2 dx* dx + /3 dx- = a0
Where,
C[3]*b3+C[2] *b2+C[1]*b1+C[0]*b0 = Cc
d3*a3+ d2*a2+ d1*a1+d0*a0 =C[jj]
Although the algorithm result has been influenced
slightly, computation load is largely simplified. It
mainly overcomes the disadvantage that hardware
implementation of the algorithm is difficult due to many
floating point computations.
The search table modification to the bicubic
interpolation algorithm is discussed in [28]. The distance,
which the image regards as the unit length l, between
two neighbouring pixels in the source image is divided
equally into 16 sub-intervals. They are [0,1/16),
[1/16,2/16), [2/16,3/16), [3/16,4/16), [4/16,5/16),
[5/16,6/16), [6/16,7/16), [7/16,8/16), [8/16,9/16),
[9/16,10/16), [10/16,11/16), [11/16,12/16),
[12/16,13/16), [13/16,14/16), [14/16,15/16) and
[15/16,1). The co-efficients for all 16 values of dx and
dy can be computed beforehand and stored in memory.
This reduces the computationally intensive process of
determining the co-efficients in real-time. The value of
dx and dy is compared to lie within one of the 16 sub-
intervals and the values of coefficients a0, a1, a2, a2, b1,
b2, b3, and b4 are chosen accordingly from pre-
computed values.
Figure 6. Modified bicubic image scaling algorithm
IV. RESULT ANALYSIS
All five algorithms are implemented in C/C++
language. OpenCV libraries are used for image read and
write/display only. Dev-C++ (4.9.9.2) software installed
on a standard Window XP machine is used for
compilation and execution of C/C++ programs.
Comparison of computational complexity of all five
image scaling algorithms is shown in Table 1. Input test
image of size 627x462 and corresponding scaled output
images of size 150x150 produced by five
implementations are shown in Fig. 7. Fig. 8 shows the
input test image of size 609x594 and corresponding
scaled output images of size 150x150 produced by five
implementations.
Non-adaptive algorithms always face a trade-off
between the three image scaling artifacts – edge halo,
blurring and aliasing. Nearest neighbour interpolation
produces a high aliasing effect resulting in jagged edges.
Bilinear interpolation reduces the aliasing effect but
causes a moderate blurring of the edges. Bicubic
interpolation produces a moderate aliasing, blurring and
an edge halo effect. Lanczos interpolation delivers an
image quality very similar to that of bicubic. Modified
bicubic produces an output of slightly lesser quality as
compared to bicubic as the co-efficients are
approximated to reduce computational complexity.
Computationally, nearest neighbour interpolation is
the least intensive as it considers only one pixel for
A Comparative Analysis of Image Scaling Algorithms 59
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
interpolation. Bilinear uses 4 diagonal pixels for
interpolation and therefore, requires more computation
than the nearest neighbour method. Bicubic and Lanczos
interpolation are computationally very intensive as they
require 16 and 36 pixels respectively for interpolating an
output pixel value. Lanczos interpolation also utilizes
the sine function repeatedly which itself requires a large
number of addition and multiplication operations
according to Taylor series approximation. Modified
bicubic interpolation reduces the number of
computations significantly as the co-efficients are
computed using search table.
Table 1 : Computational Complexity Comparison
Algorithm
Addition/
Subtractions
Multiplications/Divisions
Sin
Nearest Neighbour
0
2
0
Bilinear
9
12
0
Bicubic
57
69
0
Lanczos
47
118
24
Modified Bicubic
17
24
0
Figure 7. Input test image and corresponding output image for each algorithm
60 A Comparative Analysis of Image Scaling Algorithms
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
Figure 8. Input test image and corresponding output image for each algorithm
V. CONCLUSION
Image scaling has become a fundamental processing
task and plays an important role in video surveillance
applications. Although there are a myriad of
interpolation algorithms are available in literature, not
all of them are suitable for implementing real-time
image scaling. In this paper, we discussed the main non-
adaptive image interpolation algorithms suitable for real-
time applications. A comparative analysis of five image
interpolation algorithms is presented based on the results
of their software implementation. Of the five image
interpolation algorithms evaluated, the modified bicubic
algorithm offers the best trade-off between image
quality and computational complexity for real-time
image scaling in surveillance applications.
ACKNOWLEDGMENT
The authors express their deep sense of gratitude to
Dr. Chandra Shekhar, Director CSIR-CEERI for
encouraging research and development activities.
Authors would like to thanks Dr. AS Mandal and Raj
Singh, Group Leader, IC Design Group, CSIR-CEERI,
for their constructive suggestions throughout the year.
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Chetan Suresh is pursuing his
undergraduate study in BITS-Pilani,
Rajasthan, India. He is a final year
student of Electrical and Electronics
Engineering. Currently, he is
working as a student intern in
Cambridge Silicon Radio,
Bangalore. His research interests are FPGA Prototyping
and Computer Architecture.
62 A Comparative Analysis of Image Scaling Algorithms
Copyright © 2013 MECS I.J. Image, Graphics and Signal Processing, 2013, 5, 55-62
Sanjay Singh is working
as Scientist in CSIR-Central
Electronics Engineering Research
Institute, Pilani, Rajasthan, India. He
is Member of IEEE - USA, IACSIT
- Singapore, and IAENG - Hong
Kong. Currently, he is involved in
various projects sponsored by Indian Government on
Computer Vision and Smart Cameras. His research
interests are VLSI architectures for image & video
processing algorithms, FPGA Prototyping, and
Computer Vision. Prior to joining this research
lab, he received his Master in Technology, Master in
Electronics, and Bachelor in Science in 2007, 2005, and
2003 respectively from Kurukshetra University,
Kurukshetra, Haryana, India. He earned Gold Medal
(First Position in University) during his Master in
Technology and Master in Electronics. He topped
college during his Bachelor in Science. He received
more than 20 Merit Certificates and Scholarships during
his academic career.
Ravi Saini is working as Scientist in
CSIR-Central Electronics
Engineering Research Institute,
Pilani, Rajasthan, India. He is
Member of IEEE – USA. His
research interests include VLSI
Architectures, ASIC and ASIP
Design, HDLs, and FPGA
Prototyping. He received his Master in Technology in
2002 from Punjab University, India and Master in
Electronics in 2000 from DAVV, Indore, India.
Anil Kumar Saini is working
as Scientist in CSIR-Central
Electronics Engineering Research
Institute, Pilani, Rajasthan, India.
He is Member of IEEE – USA and
IACSIT – Singapore. His research
interests include Analog and
Mixed Signal Design, Embedded
System Design, and CMOS RF IC design. Prior to
joining this research lab, he worked in Cadence, India.
He received his Master in Technology and Master in
Science in 2003 and 2000 respectively from IIT Roorkee,
India.
