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Different image magnification methods are related very close with each other except the simplest Box method that does not use any interpolation. All tested methods show about the same RMSE results for the same picture. Lanczos methods show the best results and simplest Box method shows the worst results. Statistically, difference between interpolation methods, is less than one percent. But, for example, Lanczos works well where intensity gradient is higher, but brings more errors when intensity changes softly. Pixels with errors surround the edges, but can cover wide areas near edges. Image noise can increase RMSE value dramatically, concurrently noise can be invisible on image and produce a little intensity ripple but have a lot of pixels and produce high RMSE value.
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ISSN 1392 – 1215 2011. No. 4(110)
T 121
Image Magnification Method Comparison
V. Vysniauskas, G. Daunys, K. Vysniauskaite
Department of Electronics, Faculty of Technology, Siauliai University,
Vilniaus str. 141, Siauliai, 763535, Lithuania, +370 677 63066, e-mail:
Image magnification is a process of obtaining an
image at resolution higher than taken from image sensor.
Image magnification synonyms are interpolation,
enlargement, zooming, etc. To create higher resolution
image, previous image must be complemented with new
pixels and their intensity must be calculated.
Commonly, image magnification is accomplished
through convolution of the image samples with a single
kernel – typically the nearest neighbour [1–4] bilinear,
bicubic [3–5] or cubic B-spline kernel [3, 4, 6]
interpolation, triangle based [3, 4, 7] and training-based
algorithms [3, 4, 8, 9] that use artificial neural networks.
The main observable problem in image magnification
is phenomenon called “magnification blur”. Most visible
“magnification blur” is on edges (contours). So it is likely
that magnified image with great amount of edges will look
ugly and image with fewer edges look better.
Unfortunately real image contains a lot of noise.
Sources of noise are very different. Thermal noise of image
sensor is more visible on dark areas of picture; quantization
noise comes on edges and areas with great intensity
gradient. The other noise, we call it compression noise,
arise during image compression when row image from
sensor area is converted to most useful TIF, JPG, PNG or
other format. And yet another source of noise is image
shrinking. We get a calculation error because shrinking
coefficient mostly is fractional number on integer discrete
Actually we don’t know what was done with the
image previously. Except occasion when we get row image
as BMP from well known source. All other image formats
have a lot of processing noise. Well known salt and pepper
noise with single white and black pixels is almost invisible
in image, but brings a great distortion during magnification.
It is great that this kind of noise can be filtered out.
Unfortunately the noise always grow-up and nothing
decrease it. So commonly image is noisy.
Image quality analysis
To estimate quality of image magnification algorithm
several methods of error or noise calculation are used. The
same technique is used to test compression algorithms.
To test magnification quality a very simple algorithm
with three simple steps is used: image for testing is scaled-
down in some number, after that it is magnified in the same
number, so we have the original and magnified image and it
is possible to compare them by some comparison method.
The simplest way to compare images is to measure the
difference between a pair of similar images pixel by pixel.
The most common difference measure is the mean-
square error (MSE). The mean-square error measure is
popular because it correlates reasonable with subjective
visual quality tests and it is mathematically tractable. [10]
To measure difference for only one pixel square error (SE)
is used
,,SE O j k P j k , (1)
where O(j,k) – pixel from original image; P(j,k) – the same
pixel from processed image.
To estimate entire image mean-square error (MSE) is
MSE O j k P j k
, (2)
where O(j,k) – pixel from original image, P(j,k) – the same
pixel from processed image, N and M – number of rows and
columns in the image.
Root mean-square error (RMSE) is also useful and
brings less value
RMSE O j k P j k
. (3)
All these equations to compare processing results will
be used here.
Image Magnification Analysis
To get common results a lot of digital images from
different sources and with different sizes were chosen. All
images were converted to gray-scale to simplify processing.
Because whole numbers were used for magnification,
images were cropped to avoid fractions during scaling-
down. Is the magnification error related with number of
pixels corresponding to edges?
Edge ratio for each image was calculated. Edge ratio
was calculated as sum of edge pixels on Canny filtered
image divided by number of image pixels. Also RMSE for
the same set of images with five magnification methods
presented in Matlab were calculated. For all methods results
and pixel numbers was sorted and indexed. Calculation
results are shown in Fig. 1.
There is evidence, as shown in Fig. 1, that there is no
clear relation between Edge Rate Index and image RMSE
index. From the same data correlation shown in Table 1
was calculated.
Table 1 shows that there is weak relation between
Edge Rate and RMSE of different magnification methods,
but there is strong relation between different magnification
Table 1. Edge Rate and Magnification RMSE Correlation
1 2 3 4 5 5
Edge Rate 1
Box 0,531 1
Triangle 0,553 0,993 1
Cubic 0,548 0,983 0,996 1
Lanczos2 0,546 0,982 0,996 1,000 1
Lanczos3 0,540 0,974 0,991 0,999 0,999
Actually when there are two images with different
RMSE, for one method, the image with lower RMSE yields
the lower RMSE result with any other magnification
Also the same result is with other magnification ratio;
hence magnification error depends on image content and
magnification ratio and a little bit less on magnification
method as shown in Fig. 2. Data was sorted with the
simplest magnification method Box.
Chart Fig. 2 is very dense therefore a small section of
data was picked up and shown in Fig. 3. This figure shows
how near are some RMSE with different magnifications
methods. Less RMSE is better, so other methods are better
except triangle that for some images is worse.
Where do magnification errors arise? Fig. 4 is original
image and Fig. 5 is 2 times scaled-down and then 2 times
magnified image.
Both images are almost the same – differences are
invisible, but exist. Errors are in some places and have
Fig. 5. Scaled Down and Magnified by 2 Image
.3.Section of Ma
nification Ratio and RMSE
Fig. 2. Magnification Ratio and RMSE
Fig. 1. Edge Rate Index and Magnification RMSE Index
Fig. 4. Original Image
some values. Low value errors are invisible. Therefore to
show all pixels with errors, their values are set to maximal
intensity, and image is inverted to save ink. Hence dark
pixels show pixels with any error Fig. 6.
As shown in Fig. 6 and Fig. 7 there is a weak relation
between error pixel map and edge of image. Area with
errors is about on the same place as edge but areas with
errors are bigger.
Error pixel map Fig. 6 is gray level image where
darker pixel shows higher error. Where density of edge is
greater the error density is greater too and pixel on error
map is darker.
Fig. 6. Error Pixel Map
Fig. 7. Edge of Image
The other question is error distribution by error value.
Accordingly from previous image set three images that
draw lowest, intermediate and highest RMSE values were
picked-up. “Ice-cream desert” – left image in Fig. 8 has
large flat areas with the same intensity accordingly the
RMSE value is low; the middle image – “Great Canyon”
has more areas with different intensity and more lines so it
draws higher RMSE than the first; the third or right image –
“Birch Tree Forest” has a large number of small areas with
different intensity – grass on the ground and trunk and
branches on sky background that draws a very high RMSE
Original image was scaled-down by factor two, then
magnified with five last-mentioned magnification methods
by factor two, later difference between original and
magnified image pixel by pixel was calculated and modulus
of data was calculated. Now it is possible to show pixels
number distribution by error value.
The other question is RMS distribution by error value.
Previously error distribution by pixel number was shown,
but that do not show how error value influence MSE. Hence
next three figures show MSE values for each error value
and their contribution to all MSE value of image.
In images with higher MSE present higher values
errors and that brings greater error rate to MSE, as shown in
Fig. 9–Fig. 11.
After analysis and image result observation, greater
error values originate in areas with high intensity gradient.
For example, third image “Birch Tree Forest” contains a lot
of dark and light areas, while “Ice-cream Desert” has big
areas with small intensity gradient. As small tree branches
noise can bring dramatic grow of RMSE.
Image magnification error distribution depends on
various factors. Idea that magnification error can depend on
Edge Rate of image is not confirmed, but a weak relation
exists. Different magnification methods are related very
close. All tested methods show about the same RMSE
Fig. 9. MSE Distribution in Low RMSE Image
. 10. MSE Distribution in Intermediate RMSE Ima
. 11. M
E Di
n in Hi
h RM
E Ima
Fig. 8. Images with Low, Intermediate and High RMSE
results for the same picture. Lanczos3 method shows the
best results and Box method shows the worst results.
Pixels with errors surround the edges, but can cover
wide areas, so magnification errors are located surround the
edges. Image noise can increase RMSE value dramatically,
concurrently noise can be invisible on image and produce a
little intensity ripple but a lot of pixels produce high RMSE.
Human eye do not recognize a small intensity change
and little error values below 8 or 16 are invisible; it depends
on local image intensity, but calculations draw the RMSE
increase. As shown in Fig. 9–Fig. 11 RMSE peak for Cubic
and Lanczos method is below 20 of RMSE value, so that
errors are about invisible. Visible error number, that RMSE
are above 16, decreases very quickly.
Sometimes images with the same visual quality can
bring very different RMSE results. Mathematical methods
to estimate image quality are stricter than visual quality
estimation, but are useful for automatic calculation.
Images with high number of high gradient areas give
the higher RMSE value, so that image looks worse.
Also image compression increase error number in
magnified image, because most of compression methods
are lossy and produce artefacts as ripples near the edge.
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Received 2011 02 06
V. Vysniauskas, G. Daunys, K. Vysniauskaite. Image Magnification Method Comparison // Electronics and Electrical
Engineering. – Kaunas: Technologija, 2011. – No. 4(110). – P. 105–108.
Different image magnification methods are related very close with each other except the simplest Box method that does not use any
interpolation. All tested methods show about the same RMSE results for the same picture. Lanczos methods show the best results and
simplest Box method shows the worst results. Statistically, difference between interpolation methods, is less than one percent. But, for
example, Lanczos works well where intensity gradient is higher, but brings more errors when intensity changes softly. Pixels with errors
surround the edges, but can cover wide areas near edges. Image noise can increase RMSE value dramatically, concurrently noise can be
invisible on image and produce a little intensity ripple but have a lot of pixels and produce high RMSE value. Ill. 11, bibl. 10, tabl. 1 (in
English; abstracts in English and Lithuanian).
V. Vyšniauskas, G. Daunys, K. Vyšniauskaitė. Vaizdo didinimo metodų palyginimas // Elektronika ir elektrotechnika. – Kaunas:
Technologija, 2011. – Nr. 4(110). – P. 105–108.
Įvairūs vaizdo didinimo metodai yra labai glaudžiai susiję vienas su kitu, išskyrus paprasčiausią daugybos metodą, kai nenaudojama
jokia interpoliacija. Visais išbandytais metodais gaunami maždaug tokie pat to paties vaizdo vidutinio kvadratinio nuokrypio rezultatai.
Lanczos metodais gaunami geriausi rezultatai, o paprasčiausiu daugybos metodu blogiausi. Statistiškai, skirtumas tarp interpoliacijos
metodų yra mažesnis nei vienas procentas. Bet, pavyzdžiui, Lanczos metodas veikia gerai, kai intensyvumo gradientas yra didesnis,
tačiau būna daugiau klaidų, kai intensyvumas keičiasi švelniai. Taškai su klaidomis gaubia kontūrus, bet gali apimti plačias sritis aplink
juos. Vaizdo triukšmas gali labai padidinti vidutinio kvadratinio nuokrypio vertę, triukšmas gali būti nematomas paveikslėlyje ir atrodyti
kaip nedidelės intensyvumo pulsacijos, bet daug taškų sukuria didelę vidutinio kvadratinio nuokrypio vertę. Il. 11, bibl. 10, lent. 1
(anglų kalba; santraukos anglų ir lietuvių k.).
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