ArticlePDF Available

Abstract and Figures

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.
Content may be subject to copyright.
105
ELECTRONICS AND ELECTRICAL ENGINEERING
ISSN 1392 – 1215 2011. No. 4(110)
ELEKTRONIKA IR ELEKTROTECHNIKA
SIGNAL TECHNOLOGY
T 121
SIGNALŲ TECHNOLOGIJA
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: vytautas.vysniauskas@tf.su.lt
Introduction
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
domain.
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


2
,,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
used


12
,,
00
NM
MSE O j k P j k
jk
NM


, (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


12
2,,
00
NM
RMSE O j k P j k
jk
NM


. (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
106
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
methods.
Table 1. Edge Rate and Magnification RMSE Correlation
Method
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
1
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
method.
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
Fi
g
.3.Section of Ma
g
nification Ratio and RMSE
Fig. 2. Magnification Ratio and RMSE
Fig. 1. Edge Rate Index and Magnification RMSE Index
Relation
Fig. 4. Original Image
107
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
value.
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.
Conclusions
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
Fi
g
. 10. MSE Distribution in Intermediate RMSE Ima
g
e
Fi
g
. 11. M
S
E Di
s
tri
bu
ti
o
n in Hi
g
h RM
S
E Ima
ge
Fig. 8. Images with Low, Intermediate and High RMSE
108
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.
References
1. Gonzalez R. C. Woods R.E. Digital Image Processing, 2nd.
ed. – Prentice–hall, 2002. – 793 p.
2. Acharya T., Ajoy K. R., Sammon M. J. Image Processing
Principles and Applications. – A John Wiley & Sons, 2005. –
428 p.
3. Pratt W. K. Digital Image Processing. – A John Wiley &
Sons, 2007. – 785 p.
4. Burger W., Burge M. J. Principles of Digital Image
Processing. – Springer, 2009. – 428 p.
5. Netravali A. N., Haskell B. G. Digital Pictures:
Representation, Compression and Standards, 2nd ed. – New
York: Plenum Press, 1995. – 706 p.
6. Unser M., Aldroubi A., Eden M. Fast B–spline Transforms
for Continuous Image Representation and Interpolation //
IEEE Trans. Pattern Anal. 1991. – Vol. 13. – No. 3. – P. 277–
285.
7. Vyšniauskas V. Triangle Based Image Magnification. –
Electronics and Electrical Engineering. – Kaunas:
Technologija, 2006. – No. 6(70). – P. 45–48.
8. Freeman W. T., Jones T. R., Paszor E. C. Example–Based
Supper–Resolution // MERL, Mitsubishi Electric Research
Labs. – 201 Broadway Cambridge, 2001. – MA 02139.
9. Candocia F. M., Principe J. C. Superresolution of Images
Base on Local Correlations // IEEE Transactions on Neural
Networks, 1999. – Vol. 10. – No. 2. – P. 372–380.
10. Winkler S. Digital Video Quality Vision Models and
Metrics. – John Wiley & Sons Ltd, 2005. – 175 p.
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.).
Article
Full-text available
Image magnification has a wide range of application, including the uploading of images to a web page, display of images in mobile phones, PDAs or screens. Due to the limited memory in these devices, the need to use simple image magnification algorithms arises. Mathematical morphology based on algebraic framework endows it with strong properties and allows multiple extensions for image magnification. In specific, extensions to fuzzy sets using morphological operators namely, dilation and erosion are performed while preserving the properties of these operators. This paper utilizes this approach that helps in magnifying the images, called, Interval-valued Fuzzy Lattice Morphology-based Image Transformation (IFLM-IT). The IFLM-IT method obtains as input an original colour RGB image using Cartesian Co-ordinate system. Next, Fuzzy Lattice Morphology-based Image Transformation is applied to reduce original colour RGB image to smaller size aiming at attaining better quality image. In this work, we associate Interval-valued Fuzzy Sets to magnify transformed image to original size. Based on this set, the magnified image is compared with the original colour image. We show certain experimental results and study how the Interval-valued Fuzzy Lattice Morphology-based Image Transformation has influence on the results obtained by the algorithm. Comprehensive evaluations on a large dataset well demonstrate the better performance of IFLM-IT method over other state-of-the-arts for image magnification.
Article
Full-text available
Efficient algorithms for the continuous representation of a discrete signal in terms of B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m are described. Expressions for the z-transforms of the sampled B-spline functions are determined and a convolution property of these kernels is established. It is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering. Fast computational algorithms based on the recursive implementations of these filters are proposed. A B-spline interpolator can also be characterized in terms of its transfer function and its global impulse response (cardinal spline of order n). The case of the cubic spline is treated in greater detail. The present approach is compared with previous methods that are reexamined from a critical point of view. It is concluded that B-spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner
Article
Full-text available
An adaptive two-step paradigm for the superresolution of optical images is developed in this paper. The procedure locally projects image samples onto a family of kernels that are learned from image data. First, an unsupervised feature extraction is performed on local neighborhood information from a training image. These features are then used to cluster the neighborhoods into disjoint sets for which an optimal mapping relating homologous neighborhoods across scales can be learned in a supervised manner. A super-resolved image is obtained through the convolution of a low-resolution test image with the established family of kernels. Results demonstrate the effectiveness of the approach.
Article
The book covers theoretical aspects and practical algorithms of image digitisation and compression and includes in-depth discussion of the state of the art in relation to digitisation of bi-level images, colour pictures, video conferencing and television, including JBIG, JPEG, H. 261, CCIR601, CCIR723, MPEG1, MPEG2 and HDTV. -after Publisher
Article
A gray tone image possesses ambiguity within pixels because of the possible multi-valued levels of brightness in the image. This indeterminacy is due to the inherent vagueness or imprecision embedded in an image, which can be adequately modeled using fuzzy sets. The fundamentals of fuzzy set theory has been reviewed in this chapter. Fuzzy enhancement techniques, such as fuzzy contrast enhancement, has been presented in detail. Fuzzy spatial filters have found applications for noise removal - this has been discussed here. Fuzzy histogram modeling has been presented. A number of mage segmentation techniques by fuzzy methods have been described here. The chapter concludes with an introductory note on neuro-fuzzy techniques for image analysis.
Book
Visual quality assessment is an interdisciplinary topic that links image/video processing, psychology and physiology. Many engineers are familiar with the image/video processing; transmission networks side of things but not with the perceptual aspects pertaining to quality. Digital Video Quality first introduces the concepts of human vision and visual quality. Based on these, specific video quality metrics are developed and their design is presented. These metrics are then evaluated and used in a number of applications, including image/video compression, transmission and watermarking. Introduces the concepts of human vision and vision quality. Presents the design and development of specific video quality metrics. Evaluates video quality metrics in the context of image/video compression, transmission and watermarking. Presents tools developed for the analysis of video quality.